% This file was generated by Isabelle's Sledgehammer. 2021-05-14 08:17:30.285

% Explicit typings (87)
fof(gsy_c_FWState_Olock__action_OLock,axiom,(
    gg_lock_action(lock_Lock) )).

fof(gsy_c_FWState_Olock__action_OReleaseAcquire,axiom,(
    gg_lock_action(lock_ReleaseAcquire) )).

fof(gsy_c_FWState_Olock__action_OUnlock,axiom,(
    gg_lock_action(lock_Unlock) )).

fof(gsy_c_FWState_Olock__action_OUnlockFail,axiom,(
    gg_lock_action(lock_UnlockFail) )).

fof(gsy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,axiom,(
    ! [B_1,B_2,B_3] : gg_Pro3873016545244360254nteger(comp_f7201406323132290986nteger(B_1,B_2,B_3)) )).

fof(gsy_c_Fun_Ocomp_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,axiom,(
    ! [B_1,B_2,B_3] : gg_Pro3873016545244360254nteger(comp_f8192611244414835094nteger(B_1,B_2,B_3)) )).

fof(gsy_c_Groups_Oplus__class_Oplus_001t__String__Oliteral,axiom,(
    ! [B_1,B_2] : gg_literal(plus_plus_literal(B_1,B_2)) )).

fof(gsy_c_Groups_Ozero__class_Ozero_001t__String__Oliteral,axiom,(
    gg_literal(zero_zero_literal) )).

fof(gsy_c_HOL_Oundefined_001t__FWState__Oconditional____action_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_J,axiom,(
    gg_con5341393946966126678action(undefi6058560421690208209action(conditional_action(finfun(d,list(lock_action))))) )).

fof(gsy_c_HOL_Oundefined_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,axiom,(
    gg_con1658195355420310406nteger(undefi2108171508992306123nteger(conditional_action(product_prod(code_integer,code_integer)))) )).

fof(gsy_c_HOL_Oundefined_001t__FWState__Olock____action,axiom,(
    gg_lock_action(undefi7758937781083205211action(lock_action)) )).

fof(gsy_c_HOL_Oundefined_001t__HOL__Obool,axiom,(
    gg_bool(undefined_bool(bool)) )).

fof(gsy_c_HOL_Oundefined_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    gg_Pro3873016545244360254nteger(undefi1033673839054323203nteger(product_prod(code_integer,code_integer))) )).

fof(gsy_c_HOL_Oundefined_001t__String__Oliteral,axiom,(
    gg_literal(undefined_literal(literal)) )).

fof(gsy_c_HOL_Oundefined_001t__fun_It__HOL__Obool_Mt__fun_It__HOL__Obool_Mt__HOL__Obool_J_J,axiom,(
    gg_fun3685953732742162768l_bool(undefi3038429660610680597l_bool(fun(bool,fun(bool,bool)))) )).

fof(gsy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,axiom,(
    ! [B_1] : gg_Pro3873016545244360254nteger(produc1036614310332009927e_term(B_1)) )).

fof(gsy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,axiom,(
    ! [B_1] : gg_Pro3873016545244360254nteger(produc6871402876963107537e_term(B_1)) )).

fof(gsy_c_String_OLiteral,axiom,(
    ! [B_1,B_2,B_3,B_4,B_5,B_6,B_7,B_8] : gg_literal(literal2(B_1,B_2,B_3,B_4,B_5,B_6,B_7,B_8)) )).

fof(gsy_c_Transfer_ORel_001t__HOL__Obool_001t__HOL__Obool,axiom,(
    ! [B_1] : gg_fun3685953732742162768l_bool(rel_bool_bool(B_1)) )).

fof(gsy_c_aa_001t__Code____Numeral__Ointeger_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Code_integer_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Cod6977894654539884864nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Code____Numeral__Onatural_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Code_natural_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con5738070099517397040r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con8041701148131775130l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con2963671653528250637l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_J_001t__FWState__Oconditional____action_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_J,axiom,(
    ! [B_1,B_2] : gg_con5341393946966126678action(aa_con2705967329354826990action(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con7928759629550899106f_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con3870485526895031954t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con7178005104978336878f_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,axiom,(
    ! [B_1,B_2] : gg_con1658195355420310406nteger(aa_con6461004814926059446nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con1857799385180533354r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con2405514096714695195t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,axiom,(
    ! [B_1,B_2] : gg_con1658195355420310406nteger(aa_con4378243020094724544nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con7619967807693704308r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con622330552509534035l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FWState__Oconditional____action_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_con2486123596027147847t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fin5805139829343551406n_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_bool_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Int__Oint_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_int_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_lis2459260365661518090c_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Nat__Onat_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_nat_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_nat8379393489429068301nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro5843519176478241656r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Pro4693618923521437820nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro8754844875067278050l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Pro5363176462251620070nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro8583703122606646890f_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro4501881432599481050t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Pro479190544307753694nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro4904543688695909180f_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro2232559814647311250t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Pro1630239690174064534nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro8832322792688638508l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro6098352494050694700t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Pro4916877589482262832nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro7150874649148492216r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Pro8576478981779400380nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro7591400126937138665t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro3640759179027349698r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_Pro1639709801714681030nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro916321633901839137l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_Pro5031108791230793749t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set7459647962600473637l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set5766309472476915338f_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set7889613490507791238f_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set3135850010578026034t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set1680211184867041100t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set3464050655127758210r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set6451871791712458035t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set1981577615330639756r_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set4207312397001245291l_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_set462754579954174303t_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__Typerep__Otyperep_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_typerep_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fun8257100190732734890m_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_fun7803427576885940654nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fun1066343515980309147m_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fun8146989869410979616m_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,axiom,(
    ! [B_1,B_2] : gg_Pro3873016545244360254nteger(aa_fun4316239577885714468nteger(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fun545845183243510123m_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fun5805272694093550202f_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fun1922592006021787503m_bool(B_1,B_2)) )).

fof(gsy_c_aa_001t__fun_It__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_Mt__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_J_001t__HOL__Obool,axiom,(
    ! [B_1,B_2] : gg_bool(aa_fun2503262930792141262c_bool(B_1,B_2)) )).

fof(gsy_c_fFalse,axiom,(
    gg_bool(fFalse) )).

fof(gsy_c_fTrue,axiom,(
    gg_bool(fTrue) )).

fof(gsy_c_fconj,axiom,(
    gg_fun3685953732742162768l_bool(fconj) )).

fof(gsy_c_fdisj,axiom,(
    gg_fun3685953732742162768l_bool(fdisj) )).

fof(gsy_c_fequal_001t__HOL__Obool,axiom,(
    gg_fun3685953732742162768l_bool(fequal_bool) )).

% Relevant facts (1115)
fof(fact_0_thr__a__def,axiom,(
    thr_a_d_a_b_c_e_f = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,produc3535155421234910955list_f),produc8710481132536983823list_f) )).

% thr_a_def
fof(fact_1_fst__conv,axiom,(
    ! [X1,X2] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X1),X2)) = X1 )).

% fst_conv
fof(fact_2_fst__conv,axiom,(
    ! [X1,X2] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X1),X2)) = X1 )).

% fst_conv
fof(fact_3_fst__conv,axiom,(
    ! [X1,X2] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X1),X2)) = X1 )).

% fst_conv
fof(fact_4_fst__conv,axiom,(
    ! [X1,X2] : aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X1),X2)) = X1 )).

% fst_conv
fof(fact_5_fst__conv,axiom,(
    ! [X1,X2] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X1),X2)) = X1 )).

% fst_conv
fof(fact_6_obs__a__def,axiom,(
    obs_a_d_a_b_c_e_f = comp_P8441265476687562528list_f(comp_P9196084097856615518list_f(comp_P4727187950229163873list_f(comp_P4844579239011320789list_f(produc7200483066056472223list_f,produc6347154330667827118list_f),produc5461435702946143345list_f),produc7287154213363835177list_f),produc8710481132536983823list_f) )).

% obs_a_def
fof(fact_7_cond__a__def,axiom,(
    cond_a_d_a_b_c_e_f = comp_P1274227037634964381list_f(comp_P5019820574536571553list_f(produc4949502379994040371list_f,produc7287154213363835177list_f),produc8710481132536983823list_f) )).

% cond_a_def
fof(fact_8_interrupt__a__def,axiom,(
    interr5756268207484649009_c_e_f = comp_P1151571275026987962list_f(comp_P3718283140659731780list_f(comp_P1342733116751693639list_f(comp_P7034530251472854715list_f(produc3338296310991575901list_f,produc6347154330667827118list_f),produc5461435702946143345list_f),produc7287154213363835177list_f),produc8710481132536983823list_f) )).

% interrupt_a_def
fof(fact_9_wset__a__def,axiom,(
    wset_a_d_a_b_c_e_f = comp_P2261067389098190747list_f(comp_P5472528119234947763list_f(comp_P3272176189973965824list_f(produc3180365725429668208list_f,produc5461435702946143345list_f),produc7287154213363835177list_f),produc8710481132536983823list_f) )).

% wset_a_def
fof(fact_10_old_Oprod_Oinject,axiom,(
    ! [A,B,A2,B2] :
      ( ( gg_Pro3873016545244360254nteger(B)
        & gg_Pro3873016545244360254nteger(B2) )
     => ( aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A2),B2)
      <=> ( A = A2
          & B = B2 ) ) ) )).

% old.prod.inject
fof(fact_11_old_Oprod_Oinject,axiom,(
    ! [A,B,A2,B2] :
      ( aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A2),B2)
    <=> ( A = A2
        & B = B2 ) ) )).

% old.prod.inject
fof(fact_12_old_Oprod_Oinject,axiom,(
    ! [A,B,A2,B2] :
      ( ( gg_Pro3873016545244360254nteger(B)
        & gg_Pro3873016545244360254nteger(B2) )
     => ( aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A2),B2)
      <=> ( A = A2
          & B = B2 ) ) ) )).

% old.prod.inject
fof(fact_13_old_Oprod_Oinject,axiom,(
    ! [A,B,A2,B2] :
      ( aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A2),B2)
    <=> ( A = A2
        & B = B2 ) ) )).

% old.prod.inject
fof(fact_14_old_Oprod_Oinject,axiom,(
    ! [A,B,A2,B2] :
      ( aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A2),B2)
    <=> ( A = A2
        & B = B2 ) ) )).

% old.prod.inject
fof(fact_15_prod_Oinject,axiom,(
    ! [X1,X2,Y1,Y2] :
      ( ( gg_Pro3873016545244360254nteger(X2)
        & gg_Pro3873016545244360254nteger(Y2) )
     => ( aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X1),X2) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Y1),Y2)
      <=> ( X1 = Y1
          & X2 = Y2 ) ) ) )).

% prod.inject
fof(fact_16_prod_Oinject,axiom,(
    ! [X1,X2,Y1,Y2] :
      ( aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X1),X2) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Y1),Y2)
    <=> ( X1 = Y1
        & X2 = Y2 ) ) )).

% prod.inject
fof(fact_17_prod_Oinject,axiom,(
    ! [X1,X2,Y1,Y2] :
      ( ( gg_Pro3873016545244360254nteger(X2)
        & gg_Pro3873016545244360254nteger(Y2) )
     => ( aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X1),X2) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Y1),Y2)
      <=> ( X1 = Y1
          & X2 = Y2 ) ) ) )).

% prod.inject
fof(fact_18_prod_Oinject,axiom,(
    ! [X1,X2,Y1,Y2] :
      ( aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X1),X2) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Y1),Y2)
    <=> ( X1 = Y1
        & X2 = Y2 ) ) )).

% prod.inject
fof(fact_19_prod_Oinject,axiom,(
    ! [X1,X2,Y1,Y2] :
      ( aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X1),X2) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Y1),Y2)
    <=> ( X1 = Y1
        & X2 = Y2 ) ) )).

% prod.inject
fof(fact_20_prod__cases3,axiom,(
    ! [Y] :
      ~ ! [A3,B3,C] : Y != aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,B3),C)) )).

% prod_cases3
fof(fact_21_prod__cases3,axiom,(
    ! [Y] :
      ~ ! [A3,B3,C] : Y != aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,B3),C)) )).

% prod_cases3
fof(fact_22_prod__cases3,axiom,(
    ! [Y] :
      ~ ! [A3,B3,C] : Y != aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,B3),C)) )).

% prod_cases3
fof(fact_23_prod__cases3,axiom,(
    ! [Y] :
      ~ ! [A3,B3,C] : Y != aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B3),C)) )).

% prod_cases3
fof(fact_24_prod__cases3,axiom,(
    ! [Y] :
      ~ ! [A3,B3,C] : Y != aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B3),C)) )).

% prod_cases3
fof(fact_25_old_Oprod_Oexhaust,axiom,(
    ! [Y] :
      ~ ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => Y != aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3) ) )).

% old.prod.exhaust
fof(fact_26_old_Oprod_Oexhaust,axiom,(
    ! [Y] :
      ~ ! [A3,B3] : Y != aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3) )).

% old.prod.exhaust
fof(fact_27_old_Oprod_Oexhaust,axiom,(
    ! [Y] :
      ~ ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => Y != aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3) ) )).

% old.prod.exhaust
fof(fact_28_old_Oprod_Oexhaust,axiom,(
    ! [Y] :
      ~ ! [A3,B3] : Y != aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3) )).

% old.prod.exhaust
fof(fact_29_old_Oprod_Oexhaust,axiom,(
    ! [Y] :
      ~ ! [A3,B3] : Y != aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3) )).

% old.prod.exhaust
fof(fact_30_lock__action_Osize_I5_J,axiom,(
    size_s8978095283902022239action(lock_Lock) = zero_zero_nat )).

% lock_action.size(5)
fof(fact_31_prod__induct3,axiom,(
    ! [P,X] :
      ( ! [A3,B3,C] : pp(aa_Pro7150874649148492216r_bool(P,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,B3),C))))
     => pp(aa_Pro7150874649148492216r_bool(P,X)) ) )).

% prod_induct3
fof(fact_32_prod__induct3,axiom,(
    ! [P,X] :
      ( ! [A3,B3,C] : pp(aa_Pro916321633901839137l_bool(P,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,B3),C))))
     => pp(aa_Pro916321633901839137l_bool(P,X)) ) )).

% prod_induct3
fof(fact_33_prod__induct3,axiom,(
    ! [P,X] :
      ( ! [A3,B3,C] : pp(aa_Pro3640759179027349698r_bool(P,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,B3),C))))
     => pp(aa_Pro3640759179027349698r_bool(P,X)) ) )).

% prod_induct3
fof(fact_34_prod__induct3,axiom,(
    ! [P,X] :
      ( ! [A3,B3,C] : pp(aa_Pro5031108791230793749t_bool(P,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B3),C))))
     => pp(aa_Pro5031108791230793749t_bool(P,X)) ) )).

% prod_induct3
fof(fact_35_prod__induct3,axiom,(
    ! [P,X] :
      ( ! [A3,B3,C] : pp(aa_Pro7591400126937138665t_bool(P,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B3),C))))
     => pp(aa_Pro7591400126937138665t_bool(P,X)) ) )).

% prod_induct3
fof(fact_36_typerep__lock__action__def,axiom,(
    ! [T] : typere7107042215916526635action(T) = typerep(literal2(fFalse,fTrue,fTrue,fFalse,fFalse,fFalse,fTrue,literal2(fTrue,fTrue,fTrue,fFalse,fTrue,fFalse,fTrue,literal2(fTrue,fTrue,fFalse,fFalse,fTrue,fFalse,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,fTrue,literal2(fTrue,fFalse,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,fTrue,literal2(fTrue,fFalse,fTrue,fFalse,fFalse,fTrue,fTrue,literal2(fFalse,fTrue,fTrue,fTrue,fFalse,fTrue,fFalse,literal2(fFalse,fFalse,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fFalse,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fTrue,fTrue,fTrue,fFalse,fTrue,literal2(fTrue,fFalse,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,fTrue,literal2(fTrue,fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fFalse,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,zero_zero_literal))))))))))))))))))),nil_typerep) )).

% typerep_lock_action_def
fof(fact_37_Pair__inject,axiom,(
    ! [A,B,A2,B2] :
      ( ( gg_Pro3873016545244360254nteger(B)
        & gg_Pro3873016545244360254nteger(B2) )
     => ( aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A2),B2)
       => ~ ( A = A2
           => B != B2 ) ) ) )).

% Pair_inject
fof(fact_38_Pair__inject,axiom,(
    ! [A,B,A2,B2] :
      ( aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A2),B2)
     => ~ ( A = A2
         => B != B2 ) ) )).

% Pair_inject
fof(fact_39_Pair__inject,axiom,(
    ! [A,B,A2,B2] :
      ( ( gg_Pro3873016545244360254nteger(B)
        & gg_Pro3873016545244360254nteger(B2) )
     => ( aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A2),B2)
       => ~ ( A = A2
           => B != B2 ) ) ) )).

% Pair_inject
fof(fact_40_Pair__inject,axiom,(
    ! [A,B,A2,B2] :
      ( aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A2),B2)
     => ~ ( A = A2
         => B != B2 ) ) )).

% Pair_inject
fof(fact_41_Pair__inject,axiom,(
    ! [A,B,A2,B2] :
      ( aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A2),B2)
     => ~ ( A = A2
         => B != B2 ) ) )).

% Pair_inject
fof(fact_42_mem__Collect__eq,axiom,(
    ! [A,P] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),collec3392354462482085612at_nat(P)))
    <=> pp(aa_Pro2232559814647311250t_bool(P,A)) ) )).

% mem_Collect_eq
fof(fact_43_mem__Collect__eq,axiom,(
    ! [A,P] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),collec7088162979684241874at_nat(P)))
    <=> pp(aa_Pro6098352494050694700t_bool(P,A)) ) )).

% mem_Collect_eq
fof(fact_44_lock__action_Osize_I6_J,axiom,(
    size_s8978095283902022239action(lock_Unlock) = zero_zero_nat )).

% lock_action.size(6)
fof(fact_45_lock__action_Osize_I7_J,axiom,(
    size_s8978095283902022239action(lock_UnlockFail) = zero_zero_nat )).

% lock_action.size(7)
fof(fact_46_prod__cases,axiom,(
    ! [P,P2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => pp(aa_Pro7150874649148492216r_bool(P,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3))) )
     => pp(aa_Pro7150874649148492216r_bool(P,P2)) ) )).

% prod_cases
fof(fact_47_prod__cases,axiom,(
    ! [P,P2] :
      ( ! [A3,B3] : pp(aa_Pro916321633901839137l_bool(P,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)))
     => pp(aa_Pro916321633901839137l_bool(P,P2)) ) )).

% prod_cases
fof(fact_48_prod__cases,axiom,(
    ! [P,P2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => pp(aa_Pro3640759179027349698r_bool(P,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3))) )
     => pp(aa_Pro3640759179027349698r_bool(P,P2)) ) )).

% prod_cases
fof(fact_49_prod__cases,axiom,(
    ! [P,P2] :
      ( ! [A3,B3] : pp(aa_Pro5031108791230793749t_bool(P,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)))
     => pp(aa_Pro5031108791230793749t_bool(P,P2)) ) )).

% prod_cases
fof(fact_50_prod__cases,axiom,(
    ! [P,P2] :
      ( ! [A3,B3] : pp(aa_Pro7591400126937138665t_bool(P,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)))
     => pp(aa_Pro7591400126937138665t_bool(P,P2)) ) )).

% prod_cases
fof(fact_51_surj__pair,axiom,(
    ! [P2] :
    ? [X3,Y3] :
      ( gg_Pro3873016545244360254nteger(Y3)
      & P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3) ) )).

% surj_pair
fof(fact_52_surj__pair,axiom,(
    ! [P2] :
    ? [X3,Y3] : P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3) )).

% surj_pair
fof(fact_53_surj__pair,axiom,(
    ! [P2] :
    ? [X3,Y3] :
      ( gg_Pro3873016545244360254nteger(Y3)
      & P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3) ) )).

% surj_pair
fof(fact_54_surj__pair,axiom,(
    ! [P2] :
    ? [X3,Y3] : P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3) )).

% surj_pair
fof(fact_55_surj__pair,axiom,(
    ! [P2] :
    ? [X3,Y3] : P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3) )).

% surj_pair
fof(fact_56_lock__action_Osize_I8_J,axiom,(
    size_s8978095283902022239action(lock_ReleaseAcquire) = zero_zero_nat )).

% lock_action.size(8)
fof(fact_57_ord__eq__le__trans,axiom,(
    ! [A,B,C2] :
      ( A = B
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),C2))
       => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),C2)) ) ) )).

% ord_eq_le_trans
fof(fact_58_comp__eq__dest,axiom,(
    ! [A,B,C2,D,V] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,A),B) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,C2),D)
     => aa_Pro5496877705301569838_a_b_c(A,aa_Pro2582230449628027978list_f(B,V)) = aa_Pro5496877705301569838_a_b_c(C2,aa_Pro2582230449628027978list_f(D,V)) ) )).

% comp_eq_dest
fof(fact_59_comp__eq__dest__lhs,axiom,(
    ! [A,B,C2,V] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,A),B) = C2
     => aa_Pro5496877705301569838_a_b_c(A,aa_Pro2582230449628027978list_f(B,V)) = aa_Pro5002280679056845916_a_b_c(C2,V) ) )).

% comp_eq_dest_lhs
fof(fact_60_ssubst__Pair__rhs,axiom,(
    ! [R,S,R2,S2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,R),S)),R2))
     => ( S2 = S
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,R),S2)),R2)) ) ) )).

% ssubst_Pair_rhs
fof(fact_61_ssubst__Pair__rhs,axiom,(
    ! [R,S,R2,S2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,R),S)),R2))
     => ( S2 = S
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,R),S2)),R2)) ) ) )).

% ssubst_Pair_rhs
fof(fact_62_ssubst__Pair__rhs,axiom,(
    ! [R,S,R2,S2] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,R),S)),R2))
     => ( S2 = S
       => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,R),S2)),R2)) ) ) )).

% ssubst_Pair_rhs
fof(fact_63_ssubst__Pair__rhs,axiom,(
    ! [R,S,R2,S2] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,R),S)),R2))
     => ( S2 = S
       => pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,R),S2)),R2)) ) ) )).

% ssubst_Pair_rhs
fof(fact_64_ssubst__Pair__rhs,axiom,(
    ! [R,S,R2,S2] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,R),S)),R2))
     => ( S2 = S
       => pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,R),S2)),R2)) ) ) )).

% ssubst_Pair_rhs
fof(fact_65_ssubst__Pair__rhs,axiom,(
    ! [R,S,R2,S2] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,R),S)),R2))
     => ( S2 = S
       => pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,R),S2)),R2)) ) ) )).

% ssubst_Pair_rhs
fof(fact_66_ssubst__Pair__rhs,axiom,(
    ! [R,S,R2,S2] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,R),S)),R2))
     => ( S2 = S
       => pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,R),S2)),R2)) ) ) )).

% ssubst_Pair_rhs
fof(fact_67_old_Oprod_Ocase,axiom,(
    ! [F,X1,X2] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,X1),X2)) = aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,X1),X2) )).

% old.prod.case
fof(fact_68_lock__action_Osize_I1_J,axiom,(
    lock_s5444299122428672615action(lock_Lock) = zero_zero_nat )).

% lock_action.size(1)
fof(fact_69_swap__simp,axiom,(
    ! [X,Y] : aa_Pro5898173003354238552nteger(produc1086329213251557139e_term,produc1348435034978110643e_term(X,Y)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Y),X) )).

% swap_simp
fof(fact_70_swap__simp,axiom,(
    ! [X,Y] : aa_Pro4815109388110020atural(produc1330708496420339496e_term,produc8292168106141693128e_term(X,Y)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Y),X) )).

% swap_simp
fof(fact_71_swap__simp,axiom,(
    ! [X,Y] : produc1307869722612112413e_term(produc8269329332333466045e_term(X,Y)) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Y),X) )).

% swap_simp
fof(fact_72_swap__simp,axiom,(
    ! [X,Y] : produc5312348804003511852e_term(produc5954221522141377484e_term(X,Y)) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Y),X) )).

% swap_simp
fof(fact_73_swap__simp,axiom,(
    ! [X,Y] : aa_Pro6578783190714238164nt_int(produc593905189003790336e_term,produc712526726438796704e_term(X,Y)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Y),X) )).

% swap_simp
fof(fact_74_swap__simp,axiom,(
    ! [X,Y] : aa_Pro8370694987415157336e_term(produc4020879745696496883nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = produc1348435034978110643e_term(Y,X) )).

% swap_simp
fof(fact_75_swap__simp,axiom,(
    ! [X,Y] : aa_Pro8744562413343955908e_term(produc4828621720215076938atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)) = produc8292168106141693128e_term(Y,X) )).

% swap_simp
fof(fact_76_swap__simp,axiom,(
    ! [X,Y] : aa_Pro4807357506740610520e_term(produc423065341330332521nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = produc8269329332333466045e_term(Y,X) )).

% swap_simp
fof(fact_77_swap__simp,axiom,(
    ! [X,Y] : aa_Pro3237035770383364308e_term(produc919001381036393046nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = produc5954221522141377484e_term(Y,X) )).

% swap_simp
fof(fact_78_swap__simp,axiom,(
    ! [X,Y] : aa_Pro7337360478596779988e_term(produc4733693951299379074nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = produc712526726438796704e_term(Y,X) )).

% swap_simp
fof(fact_79_curryI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro7150874649148492216r_bool(F,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)))
     => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(produc4474112600322492150r_bool(F),A),B)) ) )).

% curryI
fof(fact_80_curryI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro916321633901839137l_bool(F,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)))
     => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(produc6713470815768014175l_bool(F),A),B)) ) )).

% curryI
fof(fact_81_curryI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro3640759179027349698r_bool(F,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)))
     => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(produc8830213710918866432r_bool(F),A),B)) ) )).

% curryI
fof(fact_82_curryI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5031108791230793749t_bool(F,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)))
     => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(produc7693670431277826643t_bool(F),A),B)) ) )).

% curryI
fof(fact_83_curryI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro7591400126937138665t_bool(F,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)))
     => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(produc6897183239252912167t_bool(F),A),B)) ) )).

% curryI
fof(fact_84_lock__action_Osize_I2_J,axiom,(
    lock_s5444299122428672615action(lock_Unlock) = zero_zero_nat )).

% lock_action.size(2)
fof(fact_85_rtranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,By),Bz))))
     => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,Ax),Ay),Az))
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))))
             => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ab),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ac),Ba))))
               => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,A3),Aa),B3))
                 => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,Bx),By),Bz)) ) ) ) )).

% rtranclp_induct3
fof(fact_86_rtranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ay),Az))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,By),Bz))))
     => ( pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,Ax),Ay),Az))
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ay),Az))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Aa),B3))))
             => ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Aa),B3))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ab),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ac),Ba))))
               => ( pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,A3),Aa),B3))
                 => pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,Bx),By),Bz)) ) ) ) )).

% rtranclp_induct3
fof(fact_87_rtranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,By),Bz))))
     => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,Ax),Ay),Az))
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))))
             => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ab),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ac),Ba))))
               => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,A3),Aa),B3))
                 => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,Bx),By),Bz)) ) ) ) )).

% rtranclp_induct3
fof(fact_88_rtranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,By),Bz))))
     => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,Ax),Ay),Az))
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))))
             => ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ab),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ac),Ba))))
               => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,A3),Aa),B3))
                 => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,Bx),By),Bz)) ) ) ) )).

% rtranclp_induct3
fof(fact_89_rtranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,By),Bz))))
     => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,Ax),Ay),Az))
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))))
             => ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ab),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ac),Ba))))
               => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,A3),Aa),B3))
                 => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,Bx),By),Bz)) ) ) ) )).

% rtranclp_induct3
fof(fact_90_lock__action_Osize_I3_J,axiom,(
    lock_s5444299122428672615action(lock_UnlockFail) = zero_zero_nat )).

% lock_action.size(3)
fof(fact_91_tranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi8529500889210449652nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,By),Bz))))
     => ( ! [A3,Aa,B3] :
            ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))))
           => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,A3),Aa),B3)) )
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi8529500889210449652nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))))
             => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ab),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ac),Ba))))
               => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,A3),Aa),B3))
                 => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(P,Bx),By),Bz)) ) ) ) )).

% tranclp_induct3
fof(fact_92_tranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi8051899945757726539atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ay),Az))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,By),Bz))))
     => ( ! [A3,Aa,B3] :
            ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ay),Az))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Aa),B3))))
           => pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,A3),Aa),B3)) )
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi8051899945757726539atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ay),Az))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Aa),B3))))
             => ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Aa),B3))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ab),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ac),Ba))))
               => ( pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,A3),Aa),B3))
                 => pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(P,Bx),By),Bz)) ) ) ) )).

% tranclp_induct3
fof(fact_93_tranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi9016935491298155882nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,By),Bz))))
     => ( ! [A3,Aa,B3] :
            ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))))
           => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,A3),Aa),B3)) )
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi9016935491298155882nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay),Az))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))))
             => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ab),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ac),Ba))))
               => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,A3),Aa),B3))
                 => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(P,Bx),By),Bz)) ) ) ) )).

% tranclp_induct3
fof(fact_94_tranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi7747454463607967063nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,By),Bz))))
     => ( ! [A3,Aa,B3] :
            ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))))
           => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,A3),Aa),B3)) )
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi7747454463607967063nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))))
             => ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ab),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ac),Ba))))
               => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,A3),Aa),B3))
                 => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(P,Bx),By),Bz)) ) ) ) )).

% tranclp_induct3
fof(fact_95_tranclp__induct3,axiom,(
    ! [R,Ax,Ay,Az,Bx,By,Bz,P] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi4304854299479087747nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,By),Bz))))
     => ( ! [A3,Aa,B3] :
            ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))))
           => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,A3),Aa),B3)) )
       => ( ! [A3,Aa,B3,Ab,Ac,Ba] :
              ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi4304854299479087747nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay),Az))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))))
             => ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ab),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ac),Ba))))
               => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,A3),Aa),B3))
                 => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,Ab),Ac),Ba)) ) ) )
         => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(P,Bx),By),Bz)) ) ) ) )).

% tranclp_induct3
fof(fact_96_apsnd__conv,axiom,(
    ! [F,X,Y] : aa_Pro605336214283753216nteger(produc7284161782193780781e_term(F),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),aa_Pro4693618923521437820nteger(F,Y)) )).

% apsnd_conv
fof(fact_97_apsnd__conv,axiom,(
    ! [F,X,Y] : aa_Pro7626634194206414894atural(produc2400445711499960492e_term(F),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),aa_Pro4262726347734369532atural(F,Y)) )).

% apsnd_conv
fof(fact_98_apsnd__conv,axiom,(
    ! [F,X,Y] : aa_Pro8016721334973800684nteger(produc4820624280922754359e_term(F),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),aa_Pro4693618923521437820nteger(F,Y)) )).

% apsnd_conv
fof(fact_99_apsnd__conv,axiom,(
    ! [F,X,Y] : aa_Pro7619707155024403014nt_int(produc276867580179041192e_term(F),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),aa_Pro6970504127699319548nt_int(F,Y)) )).

% apsnd_conv
fof(fact_100_apsnd__conv,axiom,(
    ! [F,X,Y] : aa_Pro7656415901706311326nt_int(produc5581269045473686908e_term(F),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),aa_Pro6970504127699319548nt_int(F,Y)) )).

% apsnd_conv
fof(fact_101_lock__action_Osize_I4_J,axiom,(
    lock_s5444299122428672615action(lock_ReleaseAcquire) = zero_zero_nat )).

% lock_action.size(4)
fof(fact_102_comp__apply,axiom,(
    ! [F,G,X] : aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),X) = aa_Pro5496877705301569838_a_b_c(F,aa_Pro2582230449628027978list_f(G,X)) )).

% comp_apply
fof(fact_103_fst__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = A
     => X = A ) )).

% fst_eqD
fof(fact_104_fst__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)) = A
     => X = A ) )).

% fst_eqD
fof(fact_105_fst__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = A
     => X = A ) )).

% fst_eqD
fof(fact_106_fst__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = A
     => X = A ) )).

% fst_eqD
fof(fact_107_fst__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = A
     => X = A ) )).

% fst_eqD
fof(fact_108_fst__apsnd,axiom,(
    ! [F,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro605336214283753216nteger(produc7284161782193780781e_term(F),X)) = aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X) )).

% fst_apsnd
fof(fact_109_fst__apsnd,axiom,(
    ! [F,X] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro7626634194206414894atural(produc2400445711499960492e_term(F),X)) = aa_Pro5217105177887748324e_term(produc1168782837711296254atural,X) )).

% fst_apsnd
fof(fact_110_fst__apsnd,axiom,(
    ! [F,X] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro8016721334973800684nteger(produc4820624280922754359e_term(F),X)) = aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,X) )).

% fst_apsnd
fof(fact_111_fst__apsnd,axiom,(
    ! [F,X] : aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,aa_Pro7619707155024403014nt_int(produc276867580179041192e_term(F),X)) = aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,X) )).

% fst_apsnd
fof(fact_112_fst__apsnd,axiom,(
    ! [F,X] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro7656415901706311326nt_int(produc5581269045473686908e_term(F),X)) = aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X) )).

% fst_apsnd
fof(fact_113_diag__imp__eq__le,axiom,(
    ! [A4,R2] :
      ( ! [X3] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
         => pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(R2,X3),X3)) )
     => ! [X4,Y4] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X4),A4))
         => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Y4),A4))
           => ( X4 = Y4
             => pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(R2,X4),Y4)) ) ) ) ) )).

% diag_imp_eq_le
fof(fact_114_diag__imp__eq__le,axiom,(
    ! [A4,R2] :
      ( ! [X3] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
         => pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(R2,X3),X3)) )
     => ! [X4,Y4] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X4),A4))
         => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Y4),A4))
           => ( X4 = Y4
             => pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(R2,X4),Y4)) ) ) ) ) )).

% diag_imp_eq_le
fof(fact_115_converse__tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi8529500889210449652nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)))
     => ( ! [A3,B3] :
            ( gg_Pro3873016545244360254nteger(B3)
           => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)))
             => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3)) ) )
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)))
               => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi8529500889210449652nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Aa),Ba))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Ax),Ay)) ) ) ) )).

% converse_tranclp_induct2
fof(fact_116_converse__tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi8051899945757726539atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)))
     => ( ! [A3,B3] :
            ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)))
           => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)))
             => ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi8051899945757726539atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)))
               => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Aa),Ba))
                 => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Ax),Ay)) ) ) ) )).

% converse_tranclp_induct2
fof(fact_117_converse__tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi9016935491298155882nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)))
     => ( ! [A3,B3] :
            ( gg_Pro3873016545244360254nteger(B3)
           => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)))
             => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3)) ) )
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)))
               => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi9016935491298155882nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Aa),Ba))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Ax),Ay)) ) ) ) )).

% converse_tranclp_induct2
fof(fact_118_converse__tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi7747454463607967063nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)))
     => ( ! [A3,B3] :
            ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)))
           => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)))
             => ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi7747454463607967063nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Aa),Ba))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Ax),Ay)) ) ) ) )).

% converse_tranclp_induct2
fof(fact_119_converse__tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi4304854299479087747nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)))
     => ( ! [A3,B3] :
            ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)))
           => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)))
             => ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi4304854299479087747nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Aa),Ba))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Ax),Ay)) ) ) ) )).

% converse_tranclp_induct2
fof(fact_120_curryD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(produc4474112600322492150r_bool(F),A),B))
     => pp(aa_Pro7150874649148492216r_bool(F,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B))) ) )).

% curryD
fof(fact_121_curryD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(produc6713470815768014175l_bool(F),A),B))
     => pp(aa_Pro916321633901839137l_bool(F,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B))) ) )).

% curryD
fof(fact_122_curryD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(produc8830213710918866432r_bool(F),A),B))
     => pp(aa_Pro3640759179027349698r_bool(F,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B))) ) )).

% curryD
fof(fact_123_curryD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(produc7693670431277826643t_bool(F),A),B))
     => pp(aa_Pro5031108791230793749t_bool(F,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B))) ) )).

% curryD
fof(fact_124_curryD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(produc6897183239252912167t_bool(F),A),B))
     => pp(aa_Pro7591400126937138665t_bool(F,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B))) ) )).

% curryD
fof(fact_125_comp__def,axiom,(
    ! [F,G,X4] : aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),X4) = aa_Pro5496877705301569838_a_b_c(F,aa_Pro2582230449628027978list_f(G,X4)) )).

% comp_def
fof(fact_126_order__less__irrefl,axiom,(
    ! [X] : ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),X)) )).

% order_less_irrefl
fof(fact_127_curryE,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(produc4474112600322492150r_bool(F),A),B))
     => pp(aa_Pro7150874649148492216r_bool(F,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B))) ) )).

% curryE
fof(fact_128_curryE,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(produc6713470815768014175l_bool(F),A),B))
     => pp(aa_Pro916321633901839137l_bool(F,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B))) ) )).

% curryE
fof(fact_129_curryE,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(produc8830213710918866432r_bool(F),A),B))
     => pp(aa_Pro3640759179027349698r_bool(F,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B))) ) )).

% curryE
fof(fact_130_curryE,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(produc7693670431277826643t_bool(F),A),B))
     => pp(aa_Pro5031108791230793749t_bool(F,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B))) ) )).

% curryE
fof(fact_131_curryE,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(produc6897183239252912167t_bool(F),A),B))
     => pp(aa_Pro7591400126937138665t_bool(F,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B))) ) )).

% curryE
fof(fact_132_snd__conv,axiom,(
    ! [X1,X2] :
      ( gg_Pro3873016545244360254nteger(X2)
     => aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X1),X2)) = X2 ) )).

% snd_conv
fof(fact_133_snd__conv,axiom,(
    ! [X1,X2] : aa_Pro7386464516095682491atural(produc3992340709582277180atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X1),X2)) = X2 )).

% snd_conv
fof(fact_134_snd__conv,axiom,(
    ! [X1,X2] :
      ( gg_Pro3873016545244360254nteger(X2)
     => aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X1),X2)) = X2 ) )).

% snd_conv
fof(fact_135_snd__conv,axiom,(
    ! [X1,X2] : aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X1),X2)) = X2 )).

% snd_conv
fof(fact_136_snd__conv,axiom,(
    ! [X1,X2] : aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X1),X2)) = X2 )).

% snd_conv
fof(fact_137_snd__conv,axiom,(
    ! [X1,X2] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X1),X2)) = X2 )).

% snd_conv
fof(fact_138_snd__conv,axiom,(
    ! [X1,X2] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(X1),X2)) = X2 )).

% snd_conv
fof(fact_139_lock__action_Odistinct_I1_J,axiom,(
    lock_Lock != lock_Unlock )).

% lock_action.distinct(1)
fof(fact_140_antisym,axiom,(
    ! [A,B] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),B))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
       => A = B ) ) )).

% antisym
fof(fact_141_internal__case__prod__def,axiom,(
    produc6882689234361595027atural = produc8282080750456430313atural )).

% internal_case_prod_def
fof(fact_142_Collect__mem__eq,axiom,(
    ! [A5] : collec3392354462482085612at_nat(aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),A5)) = A5 )).

% Collect_mem_eq
fof(fact_143_Collect__mem__eq,axiom,(
    ! [A5] : collec7088162979684241874at_nat(aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),A5)) = A5 )).

% Collect_mem_eq
fof(fact_144_lock__action_Osimps_I10_J,axiom,(
    lock_ReleaseAcquire != lock_Unlock )).

% lock_action.simps(10)
fof(fact_145_tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi8529500889210449652nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)))
     => ( ! [A3,B3] :
            ( gg_Pro3873016545244360254nteger(B3)
           => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)))
             => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3)) ) )
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi8529500889210449652nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)))
               => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Bx),By)) ) ) ) )).

% tranclp_induct2
fof(fact_146_tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi8051899945757726539atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)))
     => ( ! [A3,B3] :
            ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)))
           => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi8051899945757726539atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)))
             => ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)))
               => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3))
                 => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Bx),By)) ) ) ) )).

% tranclp_induct2
fof(fact_147_tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi9016935491298155882nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)))
     => ( ! [A3,B3] :
            ( gg_Pro3873016545244360254nteger(B3)
           => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)))
             => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3)) ) )
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi9016935491298155882nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)))
               => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Bx),By)) ) ) ) )).

% tranclp_induct2
fof(fact_148_tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi7747454463607967063nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)))
     => ( ! [A3,B3] :
            ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)))
           => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi7747454463607967063nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)))
             => ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Bx),By)) ) ) ) )).

% tranclp_induct2
fof(fact_149_tranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi4304854299479087747nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)))
     => ( ! [A3,B3] :
            ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)))
           => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi4304854299479087747nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)))
             => ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Bx),By)) ) ) ) )).

% tranclp_induct2
fof(fact_150_rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)))
               => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Bx),By)) ) ) ) )).

% rtranclp_induct2
fof(fact_151_rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)))
     => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)))
             => ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)))
               => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3))
                 => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Bx),By)) ) ) ) )).

% rtranclp_induct2
fof(fact_152_rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)))
               => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Bx),By)) ) ) ) )).

% rtranclp_induct2
fof(fact_153_rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)))
             => ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Bx),By)) ) ) ) )).

% rtranclp_induct2
fof(fact_154_rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)))
             => ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Bx),By)) ) ) ) )).

% rtranclp_induct2
fof(fact_155_converse__rtranclpE2,axiom,(
    ! [R,Xa,Xb,Za,Zb] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Xa),Xb)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Za),Zb)))
     => ( aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Xa),Xb) != aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Za),Zb)
       => ~ ! [A3,B3] :
              ( gg_Pro3873016545244360254nteger(B3)
             => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Xa),Xb)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)))
               => ~ pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Za),Zb))) ) ) ) ) )).

% converse_rtranclpE2
fof(fact_156_converse__rtranclpE2,axiom,(
    ! [R,Xa,Xb,Za,Zb] :
      ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Xa),Xb)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Za),Zb)))
     => ( aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Xa),Xb) != aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Za),Zb)
       => ~ ! [A3,B3] :
              ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Xa),Xb)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)))
             => ~ pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Za),Zb))) ) ) ) )).

% converse_rtranclpE2
fof(fact_157_converse__rtranclpE2,axiom,(
    ! [R,Xa,Xb,Za,Zb] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Xa),Xb)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Za),Zb)))
     => ( aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Xa),Xb) != aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Za),Zb)
       => ~ ! [A3,B3] :
              ( gg_Pro3873016545244360254nteger(B3)
             => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Xa),Xb)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)))
               => ~ pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Za),Zb))) ) ) ) ) )).

% converse_rtranclpE2
fof(fact_158_converse__rtranclpE2,axiom,(
    ! [R,Xa,Xb,Za,Zb] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Xa),Xb)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Za),Zb)))
     => ( aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Xa),Xb) != aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Za),Zb)
       => ~ ! [A3,B3] :
              ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Xa),Xb)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)))
             => ~ pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Za),Zb))) ) ) ) )).

% converse_rtranclpE2
fof(fact_159_converse__rtranclpE2,axiom,(
    ! [R,Xa,Xb,Za,Zb] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Xa),Xb)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Za),Zb)))
     => ( aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Xa),Xb) != aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Za),Zb)
       => ~ ! [A3,B3] :
              ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Xa),Xb)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)))
             => ~ pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Za),Zb))) ) ) ) )).

% converse_rtranclpE2
fof(fact_160_case__prod__conv,axiom,(
    ! [F,A,B] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,A),B)) = aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,A),B) )).

% case_prod_conv
fof(fact_161_lock__action_Odistinct_I11_J,axiom,(
    lock_UnlockFail != lock_ReleaseAcquire )).

% lock_action.distinct(11)
fof(fact_162_lock__action_Odistinct_I12_J,axiom,(
    lock_ReleaseAcquire != lock_UnlockFail )).

% lock_action.distinct(12)
fof(fact_163_image__eqI,axiom,(
    ! [B,F,X,A4] :
      ( B = aa_Pro262675715343573244at_nat(F,X)
     => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_5168914502847457605at_nat(F,A4))) ) ) )).

% image_eqI
fof(fact_164_image__eqI,axiom,(
    ! [B,F,X,A4] :
      ( B = aa_Pro314188276017538018at_nat(F,X)
     => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_1119892238107900587at_nat(F,A4))) ) ) )).

% image_eqI
fof(fact_165_image__eqI,axiom,(
    ! [B,F,X,A4] :
      ( B = aa_Pro5901169740204579478at_nat(F,X)
     => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_6706873702294942047at_nat(F,A4))) ) ) )).

% image_eqI
fof(fact_166_image__eqI,axiom,(
    ! [B,F,X,A4] :
      ( B = aa_Pro7157000481330941564at_nat(F,X)
     => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_6321802852832981957at_nat(F,A4))) ) ) )).

% image_eqI
fof(fact_167_converse__rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(R,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)))
               => ( pp(aa_Pro7150874649148492216r_bool(aa_Pro2322970417635306224r_bool(transi6710926795423753046nteger(R),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Aa),Ba))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtranclp_induct2
fof(fact_168_converse__rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)))
     => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(R,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)))
             => ( pp(aa_Pro916321633901839137l_bool(aa_Pro1056503316412650306l_bool(transi1363109050521148333atural(R),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)))
               => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Aa),Ba))
                 => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtranclp_induct2
fof(fact_169_converse__rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(R,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)))
               => ( pp(aa_Pro3640759179027349698r_bool(aa_Pro8124660830630096900r_bool(transi2328144596061577676nteger(R),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Aa),Ba))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtranclp_induct2
fof(fact_170_converse__rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(R,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)))
             => ( pp(aa_Pro5031108791230793749t_bool(aa_Pro1780005615354958634t_bool(transi3679935816330914233nt_int(R),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Aa),Ba))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtranclp_induct2
fof(fact_171_converse__rtranclp__induct2,axiom,(
    ! [R,Ax,Ay,Bx,By,P] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(R,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)))
             => ( pp(aa_Pro7591400126937138665t_bool(aa_Pro4967935860478815442t_bool(transi5065094279540041445nt_int(R),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Aa),Ba))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtranclp_induct2
fof(fact_172_lock__action_Odistinct_I2_J,axiom,(
    lock_Unlock != lock_Lock )).

% lock_action.distinct(2)
fof(fact_173_lock__action_Odistinct_I3_J,axiom,(
    lock_Lock != lock_UnlockFail )).

% lock_action.distinct(3)
fof(fact_174_lock__action_Odistinct_I4_J,axiom,(
    lock_UnlockFail != lock_Lock )).

% lock_action.distinct(4)
fof(fact_175_lock__action_Odistinct_I5_J,axiom,(
    lock_Lock != lock_ReleaseAcquire )).

% lock_action.distinct(5)
fof(fact_176_prod_Ocollapse,axiom,(
    ! [Prod] : aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Prod)),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Prod)) = Prod )).

% prod.collapse
fof(fact_177_prod_Ocollapse,axiom,(
    ! [Prod] : aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Prod)),aa_Pro7386464516095682491atural(produc3992340709582277180atural,Prod)) = Prod )).

% prod.collapse
fof(fact_178_prod_Ocollapse,axiom,(
    ! [Prod] : aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Prod)),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Prod)) = Prod )).

% prod.collapse
fof(fact_179_prod_Ocollapse,axiom,(
    ! [Prod] : aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Prod)),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Prod)) = Prod )).

% prod.collapse
fof(fact_180_prod_Ocollapse,axiom,(
    ! [Prod] : aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Prod)),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Prod)) = Prod )).

% prod.collapse
fof(fact_181_prod_Ocollapse,axiom,(
    ! [Prod] : aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod)) = Prod )).

% prod.collapse
fof(fact_182_prod_Ocollapse,axiom,(
    ! [Prod] : aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(aa_Pro1491988591844232024action(produc3089225533250117581list_f,Prod)),aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Prod)) = Prod )).

% prod.collapse
fof(fact_183_lock__action_Odistinct_I6_J,axiom,(
    lock_ReleaseAcquire != lock_Lock )).

% lock_action.distinct(6)
fof(fact_184_bspec,axiom,(
    ! [A4,P,X] :
      ( ! [X3] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
         => pp(aa_Pro2232559814647311250t_bool(P,X3)) )
     => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
       => pp(aa_Pro2232559814647311250t_bool(P,X)) ) ) )).

% bspec
fof(fact_185_bspec,axiom,(
    ! [A4,P,X] :
      ( ! [X3] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
         => pp(aa_Pro6098352494050694700t_bool(P,X3)) )
     => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
       => pp(aa_Pro6098352494050694700t_bool(P,X)) ) ) )).

% bspec
fof(fact_186_lock__action_Odistinct_I7_J,axiom,(
    lock_Unlock != lock_UnlockFail )).

% lock_action.distinct(7)
fof(fact_187_lock__action_Odistinct_I8_J,axiom,(
    lock_UnlockFail != lock_Unlock )).

% lock_action.distinct(8)
fof(fact_188_lock__action_Odistinct_I9_J,axiom,(
    lock_Unlock != lock_ReleaseAcquire )).

% lock_action.distinct(9)
fof(fact_189_eq__fst__iff,axiom,(
    ! [A,P2] :
      ( A = aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,P2)
    <=> ? [B4] :
          ( gg_Pro3873016545244360254nteger(B4)
          & P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B4) ) ) )).

% eq_fst_iff
fof(fact_190_eq__fst__iff,axiom,(
    ! [A,P2] :
      ( A = aa_Pro5217105177887748324e_term(produc1168782837711296254atural,P2)
    <=> ? [B4] : P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B4) ) )).

% eq_fst_iff
fof(fact_191_eq__fst__iff,axiom,(
    ! [A,P2] :
      ( A = aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,P2)
    <=> ? [B4] :
          ( gg_Pro3873016545244360254nteger(B4)
          & P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B4) ) ) )).

% eq_fst_iff
fof(fact_192_eq__fst__iff,axiom,(
    ! [A,P2] :
      ( A = aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,P2)
    <=> ? [B4] : P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B4) ) )).

% eq_fst_iff
fof(fact_193_eq__fst__iff,axiom,(
    ! [A,P2] :
      ( A = aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,P2)
    <=> ? [B4] : P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B4) ) )).

% eq_fst_iff
fof(fact_194_imageE,axiom,(
    ! [B,F,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_5168914502847457605at_nat(F,A4)))
     => ~ ! [X3] :
            ( B = aa_Pro262675715343573244at_nat(F,X3)
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4)) ) ) )).

% imageE
fof(fact_195_imageE,axiom,(
    ! [B,F,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_6706873702294942047at_nat(F,A4)))
     => ~ ! [X3] :
            ( B = aa_Pro5901169740204579478at_nat(F,X3)
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4)) ) ) )).

% imageE
fof(fact_196_imageE,axiom,(
    ! [B,F,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_1119892238107900587at_nat(F,A4)))
     => ~ ! [X3] :
            ( B = aa_Pro314188276017538018at_nat(F,X3)
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4)) ) ) )).

% imageE
fof(fact_197_imageE,axiom,(
    ! [B,F,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_6321802852832981957at_nat(F,A4)))
     => ~ ! [X3] :
            ( B = aa_Pro7157000481330941564at_nat(F,X3)
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4)) ) ) )).

% imageE
fof(fact_198_fstI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Y),Z)
     => aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X) = Y ) )).

% fstI
fof(fact_199_fstI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Y),Z)
     => aa_Pro5217105177887748324e_term(produc1168782837711296254atural,X) = Y ) )).

% fstI
fof(fact_200_fstI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Y),Z)
     => aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,X) = Y ) )).

% fstI
fof(fact_201_fstI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Y),Z)
     => aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,X) = Y ) )).

% fstI
fof(fact_202_fstI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Y),Z)
     => aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X) = Y ) )).

% fstI
fof(fact_203_subsetI,axiom,(
    ! [A4,B5] :
      ( ! [X3] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),B5)) )
     => pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(A4),B5)) ) )).

% subsetI
fof(fact_204_subsetI,axiom,(
    ! [A4,B5] :
      ( ! [X3] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),B5)) )
     => pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(A4),B5)) ) )).

% subsetI
fof(fact_205_lock__action_Oexhaust,axiom,(
    ! [Y] :
      ( gg_lock_action(Y)
     => ( Y != lock_Lock
       => ( Y != lock_Unlock
         => ( Y != lock_UnlockFail
           => Y = lock_ReleaseAcquire ) ) ) ) )).

% lock_action.exhaust
fof(fact_206_case__prod__beta,axiom,(
    ! [F,P2] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),P2) = aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,produc1773691148792264405atural(P2)),produc8662200840462671639atural(P2)) )).

% case_prod_beta
fof(fact_207_prod_Ocase__eq__if,axiom,(
    ! [F,Prod] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),Prod) = aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,produc1773691148792264405atural(Prod)),produc8662200840462671639atural(Prod)) )).

% prod.case_eq_if
fof(fact_208_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member3048279782668807382at_nat(produc2653010282673554021at_nat(produc487386426758144856at_nat(A,B),produc487386426758144856at_nat(A2,B2)),lex_pr8029265285556086080at_nat(R,S))
    <=> ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),A2)),R))
        | ( A = A2
          & pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,B),B2)),S)) ) ) ) )).

% in_lex_prod
fof(fact_209_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member1995966531042493578at_nat(produc7904928797850150681at_nat(produc6350711070570205562at_nat(A,B),produc6350711070570205562at_nat(A2,B2)),lex_pr4669217892513370978at_nat(R,S))
    <=> ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),A2)),R))
        | ( A = A2
          & pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),B2)),S)) ) ) ) )).

% in_lex_prod
fof(fact_210_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member8062223511168850704at_nat(produc4662710985925991255at_nat(aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B),aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A2),B2)),lex_pr8801849515957261039at_nat(R,S))
    <=> ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),A2)),R))
        | ( A = A2
          & pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,B),B2)),S)) ) ) ) )).

% in_lex_prod
fof(fact_211_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A2),B2)),lex_pr1077031100652534907nteger(R,S))
    <=> ( member3700727801235295592e_term(aa_fun7771121184386139346e_term(aa_fun4065348690927510012e_term(produc4524505180950781815e_term,A),A2),R)
        | ( A = A2
          & member335077259223437328nteger(produc4911887526399440471nteger(B,B2),S) ) ) ) )).

% in_lex_prod
fof(fact_212_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A2),B2)),lex_pr1259140058498121682atural(R,S))
    <=> ( member6696522579696035046e_term(aa_fun4911770908974218129e_term(aa_fun2697409318952501244e_term(produc2490241672432993909e_term,A),A2),R)
        | ( A = A2
          & member3756964795865971088atural(aa_Pro1971126414814181170atural(aa_Pro1220262147015971502atural(produc4480994950612372183atural,B),B2),S) ) ) ) )).

% in_lex_prod
fof(fact_213_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A2),B2)),lex_pr6076955716468153073nteger(R,S))
    <=> ( member4029292764886269052e_term(aa_fun5226388938339153500e_term(aa_fun8207328719306366460e_term(produc3162429585645302667e_term,A),A2),R)
        | ( A = A2
          & member335077259223437328nteger(produc4911887526399440471nteger(B,B2),S) ) ) ) )).

% in_lex_prod
fof(fact_214_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A2),B2)),lex_pr8367635270142648798nt_int(R,S))
    <=> ( member4091929172832610526e_term(aa_fun2949903775304958861e_term(aa_fun6902241088844395516e_term(produc3936376198816598125e_term,A),A2),R)
        | ( A = A2
          & member8566619992076573584nt_int(produc3646306378393792727nt_int(B,B2),S) ) ) ) )).

% in_lex_prod
fof(fact_215_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A2),B2)),lex_pr8375880113396875018nt_int(R,S))
    <=> ( member7160087484201369222e_term(aa_fun5006721999989859937e_term(aa_fun4495630950452421628e_term(produc6842831835191658517e_term,A),A2),R)
        | ( A = A2
          & member8566619992076573584nt_int(produc3646306378393792727nt_int(B,B2),S) ) ) ) )).

% in_lex_prod
fof(fact_216_in__lex__prod,axiom,(
    ! [A,B,A2,B2,R,S] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A2),B2))),lex_prod_nat_nat(R,S)))
    <=> ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),A2)),R))
        | ( A = A2
          & pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),B2)),S)) ) ) ) )).

% in_lex_prod
fof(fact_217_prod_Oswap__def,axiom,(
    ! [P2] : produc850777735424141840atural(P2) = produc1272419604612767874atural(aa_Pro3673693039631929973atural(produc6591912806276919810atural,P2),aa_Pro5806155842103967332atural(produc497848011034438852atural,P2)) )).

% prod.swap_def
fof(fact_218_prod_Oswap__def,axiom,(
    ! [P2] : aa_Pro5898173003354238552nteger(produc1086329213251557139e_term,P2) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,produc4396344233071841541e_term(P2)),produc1036614310332009927e_term(P2)) )).

% prod.swap_def
fof(fact_219_prod_Oswap__def,axiom,(
    ! [P2] : aa_Pro6578783190714238164nt_int(produc593905189003790336e_term,P2) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,produc5809966282694449650e_term(P2)),produc7591554002014400180e_term(P2)) )).

% prod.swap_def
fof(fact_220_prod_Oswap__def,axiom,(
    ! [P2] : aa_Pro8370694987415157336e_term(produc4020879745696496883nteger,P2) = produc1348435034978110643e_term(aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,P2),aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,P2)) )).

% prod.swap_def
fof(fact_221_prod_Oswap__def,axiom,(
    ! [P2] : aa_Pro7337360478596779988e_term(produc4733693951299379074nt_int,P2) = produc712526726438796704e_term(aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,P2),aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,P2)) )).

% prod.swap_def
fof(fact_222_prod_Oswap__def,axiom,(
    ! [P2] : aa_Pro4815109388110020atural(produc1330708496420339496e_term,P2) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,produc494427485787539738e_term(P2)),produc6894241650771334620e_term(P2)) )).

% prod.swap_def
fof(fact_223_prod_Oswap__def,axiom,(
    ! [P2] : produc1307869722612112413e_term(P2) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,produc471588711979312655e_term(P2)),produc6871402876963107537e_term(P2)) )).

% prod.swap_def
fof(fact_224_prod_Oswap__def,axiom,(
    ! [P2] : produc5312348804003511852e_term(P2) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,produc2792815338335494174e_term(P2)),produc1824988175421621472e_term(P2)) )).

% prod.swap_def
fof(fact_225_prod_Oswap__def,axiom,(
    ! [P2] : aa_Pro8744562413343955908e_term(produc4828621720215076938atural,P2) = produc8292168106141693128e_term(aa_Pro7386464516095682491atural(produc3992340709582277180atural,P2),aa_Pro5217105177887748324e_term(produc1168782837711296254atural,P2)) )).

% prod.swap_def
fof(fact_226_prod_Oswap__def,axiom,(
    ! [P2] : aa_Pro4807357506740610520e_term(produc423065341330332521nteger,P2) = produc8269329332333466045e_term(aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,P2),aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,P2)) )).

% prod.swap_def
fof(fact_227_sndI,axiom,(
    ! [X,Y,Z] :
      ( gg_Pro3873016545244360254nteger(Z)
     => ( X = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Y),Z)
       => aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X) = Z ) ) )).

% sndI
fof(fact_228_sndI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Y),Z)
     => aa_Pro7386464516095682491atural(produc3992340709582277180atural,X) = Z ) )).

% sndI
fof(fact_229_sndI,axiom,(
    ! [X,Y,Z] :
      ( gg_Pro3873016545244360254nteger(Z)
     => ( X = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Y),Z)
       => aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,X) = Z ) ) )).

% sndI
fof(fact_230_sndI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Y),Z)
     => aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,X) = Z ) )).

% sndI
fof(fact_231_sndI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Y),Z)
     => aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,X) = Z ) )).

% sndI
fof(fact_232_sndI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro7165575656943818355atural(produc6639722614265839536atural(Y),Z)
     => aa_Pro3673693039631929973atural(produc6591912806276919810atural,X) = Z ) )).

% sndI
fof(fact_233_sndI,axiom,(
    ! [X,Y,Z] :
      ( X = aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(Y),Z)
     => aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,X) = Z ) )).

% sndI
fof(fact_234_snd__swap,axiom,(
    ! [X] : produc4396344233071841541e_term(aa_Pro8370694987415157336e_term(produc4020879745696496883nteger,X)) = aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X) )).

% snd_swap
fof(fact_235_snd__swap,axiom,(
    ! [X] : produc494427485787539738e_term(aa_Pro8744562413343955908e_term(produc4828621720215076938atural,X)) = aa_Pro5217105177887748324e_term(produc1168782837711296254atural,X) )).

% snd_swap
fof(fact_236_snd__swap,axiom,(
    ! [X] : produc471588711979312655e_term(aa_Pro4807357506740610520e_term(produc423065341330332521nteger,X)) = aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,X) )).

% snd_swap
fof(fact_237_snd__swap,axiom,(
    ! [X] : produc2792815338335494174e_term(aa_Pro3237035770383364308e_term(produc919001381036393046nt_int,X)) = aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,X) )).

% snd_swap
fof(fact_238_snd__swap,axiom,(
    ! [X] : produc5809966282694449650e_term(aa_Pro7337360478596779988e_term(produc4733693951299379074nt_int,X)) = aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X) )).

% snd_swap
fof(fact_239_snd__swap,axiom,(
    ! [X] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,produc4706846762625845986atural(X)) = produc4353917038236142998atural(X) )).

% snd_swap
fof(fact_240_snd__swap,axiom,(
    ! [X] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,produc2793610610439131777action(X)) = produc904728346056738509action(X) )).

% snd_swap
fof(fact_241_eq__snd__iff,axiom,(
    ! [B,P2] :
      ( gg_Pro3873016545244360254nteger(B)
     => ( B = aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,P2)
      <=> ? [A6] : P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A6),B) ) ) )).

% eq_snd_iff
fof(fact_242_eq__snd__iff,axiom,(
    ! [B,P2] :
      ( B = aa_Pro7386464516095682491atural(produc3992340709582277180atural,P2)
    <=> ? [A6] : P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A6),B) ) )).

% eq_snd_iff
fof(fact_243_eq__snd__iff,axiom,(
    ! [B,P2] :
      ( gg_Pro3873016545244360254nteger(B)
     => ( B = aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,P2)
      <=> ? [A6] : P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A6),B) ) ) )).

% eq_snd_iff
fof(fact_244_eq__snd__iff,axiom,(
    ! [B,P2] :
      ( B = aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,P2)
    <=> ? [A6] : P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A6),B) ) )).

% eq_snd_iff
fof(fact_245_eq__snd__iff,axiom,(
    ! [B,P2] :
      ( B = aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,P2)
    <=> ? [A6] : P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A6),B) ) )).

% eq_snd_iff
fof(fact_246_eq__snd__iff,axiom,(
    ! [B,P2] :
      ( B = aa_Pro3673693039631929973atural(produc6591912806276919810atural,P2)
    <=> ? [A6] : P2 = aa_Pro7165575656943818355atural(produc6639722614265839536atural(A6),B) ) )).

% eq_snd_iff
fof(fact_247_eq__snd__iff,axiom,(
    ! [B,P2] :
      ( B = aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,P2)
    <=> ? [A6] : P2 = aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(A6),B) ) )).

% eq_snd_iff
fof(fact_248_list_Odistinct_I1_J,axiom,(
    ! [X21,X22] : nil_typerep != aa_lis9041531584263668358yperep(cons_typerep(X21),X22) )).

% list.distinct(1)
fof(fact_249_fst__swap,axiom,(
    ! [X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro5898173003354238552nteger(produc1086329213251557139e_term,X)) = produc4396344233071841541e_term(X) )).

% fst_swap
fof(fact_250_fst__swap,axiom,(
    ! [X] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro4815109388110020atural(produc1330708496420339496e_term,X)) = produc494427485787539738e_term(X) )).

% fst_swap
fof(fact_251_fst__swap,axiom,(
    ! [X] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,produc1307869722612112413e_term(X)) = produc471588711979312655e_term(X) )).

% fst_swap
fof(fact_252_fst__swap,axiom,(
    ! [X] : aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,produc5312348804003511852e_term(X)) = produc2792815338335494174e_term(X) )).

% fst_swap
fof(fact_253_fst__swap,axiom,(
    ! [X] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro6578783190714238164nt_int(produc593905189003790336e_term,X)) = produc5809966282694449650e_term(X) )).

% fst_swap
fof(fact_254_fst__swap,axiom,(
    ! [X] : produc4353917038236142998atural(produc850777735424141840atural(X)) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,X) )).

% fst_swap
fof(fact_255_fst__swap,axiom,(
    ! [X] : produc904728346056738509action(produc4978107797632510849list_f(X)) = aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,X) )).

% fst_swap
fof(fact_256_prod__eq__iff,axiom,(
    ! [S,T2] :
      ( S = T2
    <=> ( aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,S) = aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,T2)
        & aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,S) = aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,T2) ) ) )).

% prod_eq_iff
fof(fact_257_prod__eq__iff,axiom,(
    ! [S,T2] :
      ( S = T2
    <=> ( aa_Pro5217105177887748324e_term(produc1168782837711296254atural,S) = aa_Pro5217105177887748324e_term(produc1168782837711296254atural,T2)
        & aa_Pro7386464516095682491atural(produc3992340709582277180atural,S) = aa_Pro7386464516095682491atural(produc3992340709582277180atural,T2) ) ) )).

% prod_eq_iff
fof(fact_258_prod__eq__iff,axiom,(
    ! [S,T2] :
      ( S = T2
    <=> ( aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,S) = aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,T2)
        & aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,S) = aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,T2) ) ) )).

% prod_eq_iff
fof(fact_259_prod__eq__iff,axiom,(
    ! [S,T2] :
      ( S = T2
    <=> ( aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,S) = aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,T2)
        & aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,S) = aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,T2) ) ) )).

% prod_eq_iff
fof(fact_260_prod__eq__iff,axiom,(
    ! [S,T2] :
      ( S = T2
    <=> ( aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,S) = aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,T2)
        & aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,S) = aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,T2) ) ) )).

% prod_eq_iff
fof(fact_261_prod__eq__iff,axiom,(
    ! [S,T2] :
      ( S = T2
    <=> ( aa_Pro5806155842103967332atural(produc497848011034438852atural,S) = aa_Pro5806155842103967332atural(produc497848011034438852atural,T2)
        & aa_Pro3673693039631929973atural(produc6591912806276919810atural,S) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,T2) ) ) )).

% prod_eq_iff
fof(fact_262_prod__eq__iff,axiom,(
    ! [S,T2] :
      ( S = T2
    <=> ( aa_Pro1491988591844232024action(produc3089225533250117581list_f,S) = aa_Pro1491988591844232024action(produc3089225533250117581list_f,T2)
        & aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,S) = aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,T2) ) ) )).

% prod_eq_iff
fof(fact_263_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y),X)),image_5168914502847457605at_nat(product_swap_nat_nat,A4)))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y)),A4)) ) )).

% pair_in_swap_image
fof(fact_264_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Y),X)),image_6321802852832981957at_nat(produc7225117575323628663at_nat,A4)))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X),Y)),A4)) ) )).

% pair_in_swap_image
fof(fact_265_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( member3123075103536333008e_term(produc1348435034978110643e_term(Y,X),image_3828502615931292449e_term(produc4020879745696496883nteger,A4))
    <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)),A4)) ) )).

% pair_in_swap_image
fof(fact_266_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( member181435700844474941e_term(produc712526726438796704e_term(Y,X),image_8901118184550381725e_term(produc4733693951299379074nt_int,A4))
    <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)),A4)) ) )).

% pair_in_swap_image
fof(fact_267_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Y),X)),image_1355980631870373665nteger(produc1086329213251557139e_term,A4)))
    <=> member3123075103536333008e_term(produc1348435034978110643e_term(X,Y),A4) ) )).

% pair_in_swap_image
fof(fact_268_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Y),X)),image_8142540896667839901nt_int(produc593905189003790336e_term,A4)))
    <=> member181435700844474941e_term(produc712526726438796704e_term(X,Y),A4) ) )).

% pair_in_swap_image
fof(fact_269_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( member6576571850643990885e_term(produc8292168106141693128e_term(Y,X),image_4365711024791534733e_term(produc4828621720215076938atural,A4))
    <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)),A4)) ) )).

% pair_in_swap_image
fof(fact_270_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( member3214315348813689050e_term(produc8269329332333466045e_term(Y,X),image_428506118188189345e_term(produc423065341330332521nteger,A4))
    <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)),A4)) ) )).

% pair_in_swap_image
fof(fact_271_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( member5531304980329882217e_term(produc5954221522141377484e_term(Y,X),image_657775545667824029e_term(produc919001381036393046nt_int,A4))
    <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)),A4)) ) )).

% pair_in_swap_image
fof(fact_272_pair__in__swap__image,axiom,(
    ! [Y,X,A4] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Y),X)),image_4849335757690464653atural(produc1330708496420339496e_term,A4)))
    <=> member6576571850643990885e_term(produc8292168106141693128e_term(X,Y),A4) ) )).

% pair_in_swap_image
fof(fact_273_snd__eqD,axiom,(
    ! [X,Y,A] :
      ( ( gg_Pro3873016545244360254nteger(Y)
        & gg_Pro3873016545244360254nteger(A) )
     => ( aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = A
       => Y = A ) ) )).

% snd_eqD
fof(fact_274_snd__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro7386464516095682491atural(produc3992340709582277180atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)) = A
     => Y = A ) )).

% snd_eqD
fof(fact_275_snd__eqD,axiom,(
    ! [X,Y,A] :
      ( ( gg_Pro3873016545244360254nteger(Y)
        & gg_Pro3873016545244360254nteger(A) )
     => ( aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = A
       => Y = A ) ) )).

% snd_eqD
fof(fact_276_snd__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = A
     => Y = A ) )).

% snd_eqD
fof(fact_277_snd__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = A
     => Y = A ) )).

% snd_eqD
fof(fact_278_snd__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X),Y)) = A
     => Y = A ) )).

% snd_eqD
fof(fact_279_snd__eqD,axiom,(
    ! [X,Y,A] :
      ( aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(X),Y)) = A
     => Y = A ) )).

% snd_eqD
fof(fact_280_fst__comp__apsnd,axiom,(
    ! [F] : comp_P3990188960041576470nteger(produc3971164842776949671nteger,produc7284161782193780781e_term(F)) = produc3971164842776949671nteger )).

% fst_comp_apsnd
fof(fact_281_fst__comp__apsnd,axiom,(
    ! [F] : comp_P8739097636480170179atural(produc1168782837711296254atural,produc2400445711499960492e_term(F)) = produc1168782837711296254atural )).

% fst_comp_apsnd
fof(fact_282_fst__comp__apsnd,axiom,(
    ! [F] : comp_P8645197615446898700nteger(produc5986598495681327645nteger,produc4820624280922754359e_term(F)) = produc5986598495681327645nteger )).

% fst_comp_apsnd
fof(fact_283_fst__comp__apsnd,axiom,(
    ! [F] : comp_P8214188666173692375nt_int(produc6655012789309278474nt_int,produc276867580179041192e_term(F)) = produc6655012789309278474nt_int )).

% fst_comp_apsnd
fof(fact_284_fst__comp__apsnd,axiom,(
    ! [F] : comp_P5310741988796926467nt_int(produc2507970727455213110nt_int,produc5581269045473686908e_term(F)) = produc2507970727455213110nt_int )).

% fst_comp_apsnd
fof(fact_285_rec__prod__split,axiom,(
    produc2276705271987446478atural = produc8282080750456430313atural )).

% rec_prod_split
fof(fact_286_snd__apsnd,axiom,(
    ! [F,X] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro4026365172444991930atural(produc4464772112783624294atural(F),X)) = aa_Pro4262726347734369532atural(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X)) )).

% snd_apsnd
fof(fact_287_snd__apsnd,axiom,(
    ! [F,X] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro7428252341792638716list_f(produc3341670575178904229action(F),X)) = aa_Pro777963009888889592list_f(F,aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,X)) )).

% snd_apsnd
fof(fact_288_case__prod__curry,axiom,(
    ! [F] : aa_fun4394021921911188166atural(produc8282080750456430313atural,produc3440786442043642122atural(F)) = F )).

% case_prod_curry
fof(fact_289_curry__case__prod,axiom,(
    ! [F] : produc3440786442043642122atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F)) = F )).

% curry_case_prod
fof(fact_290_exI__realizer,axiom,(
    ! [P,Y,X] :
      ( pp(aa_fun8257100190732734890m_bool(aa_Pro1039824329702270498m_bool(P,Y),X))
     => pp(aa_fun8257100190732734890m_bool(aa_Pro1039824329702270498m_bool(P,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y))),aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)))) ) )).

% exI_realizer
fof(fact_291_exI__realizer,axiom,(
    ! [P,Y,X] :
      ( pp(aa_fun545845183243510123m_bool(aa_Pro3890205135341880141m_bool(P,Y),X))
     => pp(aa_fun545845183243510123m_bool(aa_Pro3890205135341880141m_bool(P,aa_Pro7386464516095682491atural(produc3992340709582277180atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y))),aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)))) ) )).

% exI_realizer
fof(fact_292_exI__realizer,axiom,(
    ! [P,Y,X] :
      ( pp(aa_fun8146989869410979616m_bool(aa_Pro6439351403099769752m_bool(P,Y),X))
     => pp(aa_fun8146989869410979616m_bool(aa_Pro6439351403099769752m_bool(P,aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y))),aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)))) ) )).

% exI_realizer
fof(fact_293_exI__realizer,axiom,(
    ! [P,Y,X] :
      ( pp(aa_fun1922592006021787503m_bool(aa_Pro7796564485022453065m_bool(P,Y),X))
     => pp(aa_fun1922592006021787503m_bool(aa_Pro7796564485022453065m_bool(P,aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y))),aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)))) ) )).

% exI_realizer
fof(fact_294_exI__realizer,axiom,(
    ! [P,Y,X] :
      ( pp(aa_fun1066343515980309147m_bool(aa_Pro5354883135473551477m_bool(P,Y),X))
     => pp(aa_fun1066343515980309147m_bool(aa_Pro5354883135473551477m_bool(P,aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y))),aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)))) ) )).

% exI_realizer
fof(fact_295_exI__realizer,axiom,(
    ! [P,Y,X] :
      ( pp(aa_Code_natural_bool(aa_Pro6792619557268184595l_bool(P,Y),X))
     => pp(aa_Code_natural_bool(aa_Pro6792619557268184595l_bool(P,aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X),Y))),aa_Pro5806155842103967332atural(produc497848011034438852atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X),Y)))) ) )).

% exI_realizer
fof(fact_296_exI__realizer,axiom,(
    ! [P,Y,X] :
      ( pp(aa_fin5805139829343551406n_bool(aa_Pro7928877276181251434n_bool(P,Y),X))
     => pp(aa_fin5805139829343551406n_bool(aa_Pro7928877276181251434n_bool(P,aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(X),Y))),aa_Pro1491988591844232024action(produc3089225533250117581list_f,aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(X),Y)))) ) )).

% exI_realizer
fof(fact_297_snd__comp__apsnd,axiom,(
    ! [F] : comp_P4457869461070014998list_f(produc2867122274176885975_a_b_c,produc265111499003474649action(F)) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),produc8710481132536983823list_f) )).

% snd_comp_apsnd
fof(fact_298_snd__comp__apsnd,axiom,(
    ! [F] : comp_P7610810914149544718atural(produc6591912806276919810atural,produc4464772112783624294atural(F)) = comp_P3067963646784605345atural(F,produc6591912806276919810atural) )).

% snd_comp_apsnd
fof(fact_299_snd__comp__apsnd,axiom,(
    ! [F] : comp_P4267156721827287172list_f(produc8710481132536983823list_f,produc3341670575178904229action(F)) = comp_P2673361230361438154list_f(F,produc8710481132536983823list_f) )).

% snd_comp_apsnd
fof(fact_300_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,(
    ! [P,X,Y,A] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,X),Y))
     => ( A = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)
       => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,A)),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,A))) ) ) )).

% BNF_Greatest_Fixpoint.subst_Pair
fof(fact_301_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,(
    ! [P,X,Y,A] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,X),Y))
     => ( A = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)
       => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,A)),aa_Pro7386464516095682491atural(produc3992340709582277180atural,A))) ) ) )).

% BNF_Greatest_Fixpoint.subst_Pair
fof(fact_302_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,(
    ! [P,X,Y,A] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,X),Y))
     => ( A = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)
       => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,A)),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,A))) ) ) )).

% BNF_Greatest_Fixpoint.subst_Pair
fof(fact_303_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,(
    ! [P,X,Y,A] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,X),Y))
     => ( A = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)
       => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,A)),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,A))) ) ) )).

% BNF_Greatest_Fixpoint.subst_Pair
fof(fact_304_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,(
    ! [P,X,Y,A] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,X),Y))
     => ( A = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)
       => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,A)),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,A))) ) ) )).

% BNF_Greatest_Fixpoint.subst_Pair
fof(fact_305_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,(
    ! [P,X,Y,A] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_Cod7054345612336956751l_bool(P,X),Y))
     => ( A = aa_Pro7165575656943818355atural(produc6639722614265839536atural(X),Y)
       => pp(aa_Pro8754844875067278050l_bool(aa_Cod7054345612336956751l_bool(P,aa_Pro5806155842103967332atural(produc497848011034438852atural,A)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,A))) ) ) )).

% BNF_Greatest_Fixpoint.subst_Pair
fof(fact_306_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,(
    ! [P,X,Y,A] :
      ( pp(aa_Pro4904543688695909180f_bool(aa_fin426239777789757162f_bool(P,X),Y))
     => ( A = aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(X),Y)
       => pp(aa_Pro4904543688695909180f_bool(aa_fin426239777789757162f_bool(P,aa_Pro1491988591844232024action(produc3089225533250117581list_f,A)),aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,A))) ) ) )).

% BNF_Greatest_Fixpoint.subst_Pair
fof(fact_307_conjI__realizer,axiom,(
    ! [P,P2,Q,Q2] :
      ( pp(aa_fun8257100190732734890m_bool(P,P2))
     => ( pp(aa_Pro5843519176478241656r_bool(Q,Q2))
       => ( pp(aa_fun8257100190732734890m_bool(P,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,P2),Q2))))
          & pp(aa_Pro5843519176478241656r_bool(Q,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,P2),Q2)))) ) ) ) )).

% conjI_realizer
fof(fact_308_conjI__realizer,axiom,(
    ! [P,P2,Q,Q2] :
      ( pp(aa_fun545845183243510123m_bool(P,P2))
     => ( pp(aa_Pro8754844875067278050l_bool(Q,Q2))
       => ( pp(aa_fun545845183243510123m_bool(P,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,P2),Q2))))
          & pp(aa_Pro8754844875067278050l_bool(Q,aa_Pro7386464516095682491atural(produc3992340709582277180atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,P2),Q2)))) ) ) ) )).

% conjI_realizer
fof(fact_309_conjI__realizer,axiom,(
    ! [P,P2,Q,Q2] :
      ( pp(aa_fun8146989869410979616m_bool(P,P2))
     => ( pp(aa_Pro5843519176478241656r_bool(Q,Q2))
       => ( pp(aa_fun8146989869410979616m_bool(P,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,P2),Q2))))
          & pp(aa_Pro5843519176478241656r_bool(Q,aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,P2),Q2)))) ) ) ) )).

% conjI_realizer
fof(fact_310_conjI__realizer,axiom,(
    ! [P,P2,Q,Q2] :
      ( pp(aa_fun1922592006021787503m_bool(P,P2))
     => ( pp(aa_Pro4501881432599481050t_bool(Q,Q2))
       => ( pp(aa_fun1922592006021787503m_bool(P,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,P2),Q2))))
          & pp(aa_Pro4501881432599481050t_bool(Q,aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,P2),Q2)))) ) ) ) )).

% conjI_realizer
fof(fact_311_conjI__realizer,axiom,(
    ! [P,P2,Q,Q2] :
      ( pp(aa_fun1066343515980309147m_bool(P,P2))
     => ( pp(aa_Pro4501881432599481050t_bool(Q,Q2))
       => ( pp(aa_fun1066343515980309147m_bool(P,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,P2),Q2))))
          & pp(aa_Pro4501881432599481050t_bool(Q,aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,P2),Q2)))) ) ) ) )).

% conjI_realizer
fof(fact_312_conjI__realizer,axiom,(
    ! [P,P2,Q,Q2] :
      ( pp(aa_Code_natural_bool(P,P2))
     => ( pp(aa_Pro8754844875067278050l_bool(Q,Q2))
       => ( pp(aa_Code_natural_bool(P,aa_Pro5806155842103967332atural(produc497848011034438852atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(P2),Q2))))
          & pp(aa_Pro8754844875067278050l_bool(Q,aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(P2),Q2)))) ) ) ) )).

% conjI_realizer
fof(fact_313_conjI__realizer,axiom,(
    ! [P,P2,Q,Q2] :
      ( pp(aa_fin5805139829343551406n_bool(P,P2))
     => ( pp(aa_Pro4904543688695909180f_bool(Q,Q2))
       => ( pp(aa_fin5805139829343551406n_bool(P,aa_Pro1491988591844232024action(produc3089225533250117581list_f,aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(P2),Q2))))
          & pp(aa_Pro4904543688695909180f_bool(Q,aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(P2),Q2)))) ) ) ) )).

% conjI_realizer
fof(fact_314_comp__apply__eq,axiom,(
    ! [F,G,X,H,K] :
      ( aa_Pro5496877705301569838_a_b_c(F,aa_Pro2582230449628027978list_f(G,X)) = aa_Pro5496877705301569838_a_b_c(H,aa_Pro2582230449628027978list_f(K,X))
     => aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),X) = aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,H),K),X) ) )).

% comp_apply_eq
fof(fact_315_case__prod__unfold,axiom,(
    ! [X4,Xa2] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,X4),Xa2) = aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(X4,produc1773691148792264405atural(Xa2)),produc8662200840462671639atural(Xa2)) )).

% case_prod_unfold
fof(fact_316_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,A4))))
     => pp(aa_nat_bool(aa_nat_fun_nat_bool(A4,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,X)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_317_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,A4))))
     => pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(A4,aa_Pro5901169740204579478at_nat(produc3213797794245857475at_nat,X)),aa_Pro5901169740204579478at_nat(produc6408287024330202629at_nat,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_318_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,X),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,A4))))
     => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(A4,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X)),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_319_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,X),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,A4))))
     => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(A4,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,X)),aa_Pro7386464516095682491atural(produc3992340709582277180atural,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_320_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,X),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,A4))))
     => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(A4,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,X)),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_321_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,X),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,A4))))
     => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(A4,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,X)),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_322_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,X),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,A4))))
     => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(A4,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X)),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_323_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( member2108296798382401941atural(X,collec1991479681304692691atural(produc5868410056131333498l_bool(A4)))
     => pp(aa_Pro8754844875067278050l_bool(aa_Cod7054345612336956751l_bool(A4,aa_Pro5806155842103967332atural(produc497848011034438852atural,X)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_324_Product__Type_OCollect__case__prodD,axiom,(
    ! [X,A4] :
      ( member1992181931100238290list_f(X,collec2941370454899091988list_f(produc4709439930048449441f_bool(A4)))
     => pp(aa_Pro4904543688695909180f_bool(aa_fin426239777789757162f_bool(A4,aa_Pro1491988591844232024action(produc3089225533250117581list_f,X)),aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,X))) ) )).

% Product_Type.Collect_case_prodD
fof(fact_325_exhaustive__int_H_Ocases,axiom,(
    ! [X] :
      ~ ! [F2,D2,I] : X != aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,F2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,D2),I)) )).

% exhaustive_int'.cases
fof(fact_326_full__exhaustive__int_H_Ocases,axiom,(
    ! [X] :
      ~ ! [F2,D2,I] : X != aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,F2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,D2),I)) )).

% full_exhaustive_int'.cases
fof(fact_327_prod_Osplit__sel,axiom,(
    ! [P,F,Prod] :
      ( pp(aa_Pro8832322792688638508l_bool(P,aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),Prod)))
    <=> ( Prod = aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,produc1773691148792264405atural(Prod)),produc8662200840462671639atural(Prod))
       => pp(aa_Pro8832322792688638508l_bool(P,aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,produc1773691148792264405atural(Prod)),produc8662200840462671639atural(Prod)))) ) ) )).

% prod.split_sel
fof(fact_328_empty__iff,axiom,(
    ! [C2] : ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),bot_bo2099793752762293965at_nat)) )).

% empty_iff
fof(fact_329_empty__iff,axiom,(
    ! [C2] : ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),bot_bo5327735625951526323at_nat)) )).

% empty_iff
fof(fact_330_prod_Osplit__sel__asm,axiom,(
    ! [P,F,Prod] :
      ( pp(aa_Pro8832322792688638508l_bool(P,aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),Prod)))
    <=> ~ ( Prod = aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,produc1773691148792264405atural(Prod)),produc8662200840462671639atural(Prod))
          & ~ pp(aa_Pro8832322792688638508l_bool(P,aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,produc1773691148792264405atural(Prod)),produc8662200840462671639atural(Prod)))) ) ) )).

% prod.split_sel_asm
fof(fact_331_insert__iff,axiom,(
    ! [A,B,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),insert8211810215607154385at_nat(B,A4)))
    <=> ( A = B
        | pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),A4)) ) ) )).

% insert_iff
fof(fact_332_insert__iff,axiom,(
    ! [A,B,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),insert5050368324300391991at_nat(B,A4)))
    <=> ( A = B
        | pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),A4)) ) ) )).

% insert_iff
fof(fact_333_UNIV__I,axiom,(
    ! [X] : pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),top_to4669805908274784177at_nat)) )).

% UNIV_I
fof(fact_334_UNIV__I,axiom,(
    ! [X] : pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),top_to8454300755403694231at_nat)) )).

% UNIV_I
fof(fact_335_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc3716618507110716833at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)
             => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro8072183222952159042at_nat(aa_fun3804858034681916022at_nat(C2,X3),Y3))) ) ) ) )).

% mem_case_prodE
fof(fact_336_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc7846996071466247815at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)
             => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro5330295685620130472at_nat(aa_fun3098381869635060060at_nat(C2,X3),Y3))) ) ) ) )).

% mem_case_prodE
fof(fact_337_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc5220494214129680778at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3)
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro5065032141757191596at_nat(aa_fun4407674144259686495at_nat(C2,X3),Y3))) ) ) )).

% mem_case_prodE
fof(fact_338_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc5085394703842144496at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3)
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro1602350909037546002at_nat(aa_fun7997644143818749381at_nat(C2,X3),Y3))) ) ) )).

% mem_case_prodE
fof(fact_339_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc5409226724224080811at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3)
             => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro8072183222952159042at_nat(aa_fun1202306444933629056at_nat(C2,X3),Y3))) ) ) ) )).

% mem_case_prodE
fof(fact_340_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc8326432594814252433at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3)
             => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro5330295685620130472at_nat(aa_fun730111718248227942at_nat(C2,X3),Y3))) ) ) ) )).

% mem_case_prodE
fof(fact_341_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc9029412504376103038at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3)
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro6675321895958450596at_nat(aa_fun4621462025247951699at_nat(C2,X3),Y3))) ) ) )).

% mem_case_prodE
fof(fact_342_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc8326714205345120740at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3)
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro7094643338862014986at_nat(aa_fun4694523806444339897at_nat(C2,X3),Y3))) ) ) )).

% mem_case_prodE
fof(fact_343_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc9025042679509388370at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3)
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro6675321895958450596at_nat(aa_fun2120632890448033575at_nat(C2,X3),Y3))) ) ) )).

% mem_case_prodE
fof(fact_344_mem__case__prodE,axiom,(
    ! [Z,C2,P2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc7603330299348430776at_nat(C2,P2)))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3)
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro7094643338862014986at_nat(aa_fun5513736782981554317at_nat(C2,X3),Y3))) ) ) )).

% mem_case_prodE
fof(fact_345_exhaustive__natural_H_Ocases,axiom,(
    ! [X] :
      ~ ! [F2,D2,I] : X != produc1507819840854600734atural(F2,aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,D2),I)) )).

% exhaustive_natural'.cases
fof(fact_346_prod__eqI,axiom,(
    ! [P2,Q2] :
      ( aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,P2) = aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Q2)
     => ( aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,P2) = aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Q2)
       => P2 = Q2 ) ) )).

% prod_eqI
fof(fact_347_prod__eqI,axiom,(
    ! [P2,Q2] :
      ( aa_Pro5217105177887748324e_term(produc1168782837711296254atural,P2) = aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Q2)
     => ( aa_Pro7386464516095682491atural(produc3992340709582277180atural,P2) = aa_Pro7386464516095682491atural(produc3992340709582277180atural,Q2)
       => P2 = Q2 ) ) )).

% prod_eqI
fof(fact_348_prod__eqI,axiom,(
    ! [P2,Q2] :
      ( aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,P2) = aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Q2)
     => ( aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,P2) = aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Q2)
       => P2 = Q2 ) ) )).

% prod_eqI
fof(fact_349_prod__eqI,axiom,(
    ! [P2,Q2] :
      ( aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,P2) = aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Q2)
     => ( aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,P2) = aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Q2)
       => P2 = Q2 ) ) )).

% prod_eqI
fof(fact_350_prod__eqI,axiom,(
    ! [P2,Q2] :
      ( aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,P2) = aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Q2)
     => ( aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,P2) = aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Q2)
       => P2 = Q2 ) ) )).

% prod_eqI
fof(fact_351_prod__eqI,axiom,(
    ! [P2,Q2] :
      ( aa_Pro5806155842103967332atural(produc497848011034438852atural,P2) = aa_Pro5806155842103967332atural(produc497848011034438852atural,Q2)
     => ( aa_Pro3673693039631929973atural(produc6591912806276919810atural,P2) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,Q2)
       => P2 = Q2 ) ) )).

% prod_eqI
fof(fact_352_prod__eqI,axiom,(
    ! [P2,Q2] :
      ( aa_Pro1491988591844232024action(produc3089225533250117581list_f,P2) = aa_Pro1491988591844232024action(produc3089225533250117581list_f,Q2)
     => ( aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,P2) = aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Q2)
       => P2 = Q2 ) ) )).

% prod_eqI
fof(fact_353_prod_Oexpand,axiom,(
    ! [Prod,Prod2] :
      ( ( aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Prod) = aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Prod2)
        & aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Prod) = aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Prod2) )
     => Prod = Prod2 ) )).

% prod.expand
fof(fact_354_prod_Oexpand,axiom,(
    ! [Prod,Prod2] :
      ( ( aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Prod) = aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Prod2)
        & aa_Pro7386464516095682491atural(produc3992340709582277180atural,Prod) = aa_Pro7386464516095682491atural(produc3992340709582277180atural,Prod2) )
     => Prod = Prod2 ) )).

% prod.expand
fof(fact_355_prod_Oexpand,axiom,(
    ! [Prod,Prod2] :
      ( ( aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Prod) = aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Prod2)
        & aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Prod) = aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Prod2) )
     => Prod = Prod2 ) )).

% prod.expand
fof(fact_356_prod_Oexpand,axiom,(
    ! [Prod,Prod2] :
      ( ( aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Prod) = aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Prod2)
        & aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Prod) = aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Prod2) )
     => Prod = Prod2 ) )).

% prod.expand
fof(fact_357_prod_Oexpand,axiom,(
    ! [Prod,Prod2] :
      ( ( aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Prod) = aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Prod2)
        & aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Prod) = aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Prod2) )
     => Prod = Prod2 ) )).

% prod.expand
fof(fact_358_prod_Oexpand,axiom,(
    ! [Prod,Prod2] :
      ( ( aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod) = aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod2)
        & aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod2) )
     => Prod = Prod2 ) )).

% prod.expand
fof(fact_359_prod_Oexpand,axiom,(
    ! [Prod,Prod2] :
      ( ( aa_Pro1491988591844232024action(produc3089225533250117581list_f,Prod) = aa_Pro1491988591844232024action(produc3089225533250117581list_f,Prod2)
        & aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Prod) = aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Prod2) )
     => Prod = Prod2 ) )).

% prod.expand
fof(fact_360_exhaustive__integer_H_Ocases,axiom,(
    ! [X] :
      ~ ! [F2,D2,I] : X != aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,F2),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,D2),I)) )).

% exhaustive_integer'.cases
fof(fact_361_dropWhile__eq__Nil__conv,axiom,(
    ! [P,Xs] :
      ( dropWhile_typerep(P,Xs) = nil_typerep
    <=> ! [X5] :
          ( member_typerep(X5,set_typerep(Xs))
         => pp(aa_typerep_bool(P,X5)) ) ) )).

% dropWhile_eq_Nil_conv
fof(fact_362_UnCI,axiom,(
    ! [C2,B5,A4] :
      ( ( ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5))
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4)) )
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),sup_su6327502436637775413at_nat(A4,B5))) ) )).

% UnCI
fof(fact_363_UnCI,axiom,(
    ! [C2,B5,A4] :
      ( ( ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4)) )
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),sup_su718114333110466843at_nat(A4,B5))) ) )).

% UnCI
fof(fact_364_Rel__def,axiom,(
    ! [R] :
      ( gg_fun3685953732742162768l_bool(R)
     => rel_bool_bool(R) = R ) )).

% Rel_def
fof(fact_365_surjective__pairing,axiom,(
    ! [T2] : T2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,T2)),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,T2)) )).

% surjective_pairing
fof(fact_366_surjective__pairing,axiom,(
    ! [T2] : T2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,T2)),aa_Pro7386464516095682491atural(produc3992340709582277180atural,T2)) )).

% surjective_pairing
fof(fact_367_surjective__pairing,axiom,(
    ! [T2] : T2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,T2)),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,T2)) )).

% surjective_pairing
fof(fact_368_surjective__pairing,axiom,(
    ! [T2] : T2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,T2)),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,T2)) )).

% surjective_pairing
fof(fact_369_surjective__pairing,axiom,(
    ! [T2] : T2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,T2)),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,T2)) )).

% surjective_pairing
fof(fact_370_surjective__pairing,axiom,(
    ! [T2] : T2 = aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Pro5806155842103967332atural(produc497848011034438852atural,T2)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,T2)) )).

% surjective_pairing
fof(fact_371_surjective__pairing,axiom,(
    ! [T2] : T2 = aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(aa_Pro1491988591844232024action(produc3089225533250117581list_f,T2)),aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,T2)) )).

% surjective_pairing
fof(fact_372_prod_Oexhaust__sel,axiom,(
    ! [Prod] : Prod = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Prod)),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Prod)) )).

% prod.exhaust_sel
fof(fact_373_prod_Oexhaust__sel,axiom,(
    ! [Prod] : Prod = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Prod)),aa_Pro7386464516095682491atural(produc3992340709582277180atural,Prod)) )).

% prod.exhaust_sel
fof(fact_374_prod_Oexhaust__sel,axiom,(
    ! [Prod] : Prod = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Prod)),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Prod)) )).

% prod.exhaust_sel
fof(fact_375_prod_Oexhaust__sel,axiom,(
    ! [Prod] : Prod = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Prod)),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Prod)) )).

% prod.exhaust_sel
fof(fact_376_prod_Oexhaust__sel,axiom,(
    ! [Prod] : Prod = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Prod)),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Prod)) )).

% prod.exhaust_sel
fof(fact_377_prod_Oexhaust__sel,axiom,(
    ! [Prod] : Prod = aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod)) )).

% prod.exhaust_sel
fof(fact_378_prod_Oexhaust__sel,axiom,(
    ! [Prod] : Prod = aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(aa_Pro1491988591844232024action(produc3089225533250117581list_f,Prod)),aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Prod)) )).

% prod.exhaust_sel
fof(fact_379_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro605336214283753216nteger(produc3186735841308740863nteger(F),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun1274623470434842396e_term(F,X)),Y) )).

% apfst_conv
fof(fact_380_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro8872820292021839222nteger(produc3333295048669924213nteger(F),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_fun3693577172319249446e_term(F,X)),Y) )).

% apfst_conv
fof(fact_381_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro7626634194206414894atural(produc8499700979911337623atural(F),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_fun3478251006336822810e_term(F,X)),Y) )).

% apfst_conv
fof(fact_382_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro2148824989012779638nteger(produc3068984984575431029nteger(F),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun1784510506351320614e_term(F,X)),Y) )).

% apfst_conv
fof(fact_383_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro8016721334973800684nteger(produc1779435066467205099nteger(F),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_fun4150438919549131568e_term(F,X)),Y) )).

% apfst_conv
fof(fact_384_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro7619707155024403014nt_int(produc797834107270070439nt_int(F),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_fun6283001615389677586e_term(F,X)),Y) )).

% apfst_conv
fof(fact_385_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro1156610208699797362nt_int(produc2152783933663180243nt_int(F),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun3199491695965942246e_term(F,X)),Y) )).

% apfst_conv
fof(fact_386_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro7712013891223568754nt_int(produc5828266736486832595nt_int(F),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_fun8405180984973938150e_term(F,X)),Y) )).

% apfst_conv
fof(fact_387_apfst__conv,axiom,(
    ! [F,X,Y] : aa_Pro7656415901706311326nt_int(produc652620917742595839nt_int(F),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun78455448157554618e_term(F,X)),Y) )).

% apfst_conv
fof(fact_388_split__cong,axiom,(
    ! [Q2,F,G,P2] :
      ( ! [X3,Y3] :
          ( aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,X3),Y3) = Q2
         => aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,X3),Y3) = aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(G,X3),Y3) )
     => ( P2 = Q2
       => aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),P2) = aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,G),Q2) ) ) )).

% split_cong
fof(fact_389_Un__iff,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),sup_su6327502436637775413at_nat(A4,B5)))
    <=> ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4))
        | pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5)) ) ) )).

% Un_iff
fof(fact_390_Un__iff,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),sup_su718114333110466843at_nat(A4,B5)))
    <=> ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4))
        | pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5)) ) ) )).

% Un_iff
fof(fact_391_full__exhaustive__natural_H_Ocases,axiom,(
    ! [X] :
      ~ ! [F2,D2,I] : X != aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,F2),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,D2),I)) )).

% full_exhaustive_natural'.cases
fof(fact_392_full__exhaustive__integer_H_Ocases,axiom,(
    ! [X] :
      ~ ! [F2,D2,I] : X != aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,F2),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,D2),I)) )).

% full_exhaustive_integer'.cases
fof(fact_393_rev__image__eqI,axiom,(
    ! [X,A4,B,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
     => ( B = aa_Pro262675715343573244at_nat(F,X)
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_5168914502847457605at_nat(F,A4))) ) ) )).

% rev_image_eqI
fof(fact_394_rev__image__eqI,axiom,(
    ! [X,A4,B,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
     => ( B = aa_Pro314188276017538018at_nat(F,X)
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_1119892238107900587at_nat(F,A4))) ) ) )).

% rev_image_eqI
fof(fact_395_rev__image__eqI,axiom,(
    ! [X,A4,B,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
     => ( B = aa_Pro5901169740204579478at_nat(F,X)
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_6706873702294942047at_nat(F,A4))) ) ) )).

% rev_image_eqI
fof(fact_396_rev__image__eqI,axiom,(
    ! [X,A4,B,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
     => ( B = aa_Pro7157000481330941564at_nat(F,X)
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_6321802852832981957at_nat(F,A4))) ) ) )).

% rev_image_eqI
fof(fact_397_zip__assoc,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu734256677615756147nteger(Xs2,zip_Co3543743374963494515nteger(Ys,Zs)) = map_Pr9201890443624836576nteger(produc9168024051880959041nteger(produc2841905496517482549nteger(cOMBC_4961005168062382866nteger(cOMBB_3594209068082048875e_term(cOMBB_8291074081427404491nteger,cOMBB_393519105729595115e_term(cOMBB_5989387779348914613nteger,produc4282985567423050387nteger)),produc1086072967326762835nteger))),zip_Pr2253648799589898899nteger(zip_fu5169926438465571461nteger(Xs2,Ys),Zs)) )).

% zip_assoc
fof(fact_398_zip__assoc,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu4603041458218149578atural(Xs2,zip_Co6031810628546548233atural(Ys,Zs)) = map_Pr1482766749763339340atural(produc7535443376225341485atural(produc5266520496689885729atural(cOMBC_584992996831884992atural(cOMBB_3809075260845034e_term(cOMBB_3125664498253256131atural,cOMBB_8299546231494157162e_term(cOMBB_1689632300987368173atural,produc2566709293081654762atural)),produc3574140220909816553atural))),zip_Pr2520929448577664168atural(zip_fu2539923349611308111atural(Xs2,Ys),Zs)) )).

% zip_assoc
fof(fact_399_zip__assoc,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu197485079333405161nteger(Xs2,zip_Co3543743374963494515nteger(Ys,Zs)) = map_Pr1363073518020136032nteger(produc6956723773201801921nteger(produc709776444021059509nteger(cOMBC_8042027450978176766nteger(cOMBB_2698366874344602869e_term(cOMBB_479309715112053313nteger,cOMBB_8209961359737916533e_term(cOMBB_7697817708099229739nteger,produc7384524951051686153nteger)),produc1086072967326762835nteger))),zip_Pr6229594038713239453nteger(zip_fu6326155852317613967nteger(Xs2,Ys),Zs)) )).

% zip_assoc
fof(fact_400_zip__assoc,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu2408773928738089174nt_int(Xs2,zip_int_int(Ys,Zs)) = map_Pr3737742808059513180nt_int(produc31183362447151933nt_int(produc2486220229921151281nt_int(cOMBC_4697464256936856280nt_int(cOMBB_2080866019554389222e_term(cOMBB_6774721683961317083nt_int,cOMBB_1364847706011589734e_term(cOMBB_1283357136107696901nt_int,produc1560874099174258678nt_int)),product_Pair_int_int))),zip_Pr8357436044021820332nt_int(zip_fu2453293088336910671rm_int(Xs2,Ys),Zs)) )).

% zip_assoc
fof(fact_401_zip__assoc,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu9102111156773635586nt_int(Xs2,zip_int_int(Ys,Zs)) = map_Pr4987214687681148508nt_int(produc8758768018705373245nt_int(produc5151902159463653425nt_int(cOMBC_6627986158283100976nt_int(cOMBB_3131150168756275130e_term(cOMBB_1474206574765321735nt_int,cOMBB_9197500348686874426e_term(cOMBB_2467116309528995889nt_int,produc4852315488734385442nt_int)),product_Pair_int_int))),zip_Pr1837537895503625600nt_int(zip_fu3112013770087605027rm_int(Xs2,Ys),Zs)) )).

% zip_assoc
fof(fact_402_UnE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),sup_su6327502436637775413at_nat(A4,B5)))
     => ( ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4))
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5)) ) ) )).

% UnE
fof(fact_403_UnE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),sup_su718114333110466843at_nat(A4,B5)))
     => ( ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5)) ) ) )).

% UnE
fof(fact_404_zip__left__commute,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu734256677615756147nteger(Xs2,zip_Co3543743374963494515nteger(Ys,Zs)) = map_Pr2316143729491877676nteger(produc6959853386744949957nteger(cOMBB_3408094935000726513nteger(produc584739850835377371nteger,cOMBB_4753170203172410679nteger(cOMBC_8977950768815129852nteger(cOMBB_393519105729595115e_term(cOMBB_5989387779348914613nteger,produc4282985567423050387nteger)),produc1086072967326762835nteger))),zip_Co1205494504491187479nteger(Ys,zip_fu5169926438465571461nteger(Xs2,Zs))) )).

% zip_left_commute
fof(fact_405_zip__left__commute,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu4603041458218149578atural(Xs2,zip_Co6031810628546548233atural(Ys,Zs)) = map_Pr4001626218193654978atural(produc4647150605770207067atural(cOMBB_5040515448565471100atural(produc8174398851230046716atural,cOMBB_7337922482170043054atural(cOMBC_4821272514476200682atural(cOMBB_8299546231494157162e_term(cOMBB_1689632300987368173atural,produc2566709293081654762atural)),produc3574140220909816553atural))),zip_Co7660244294658826966atural(Ys,zip_fu2539923349611308111atural(Xs2,Zs))) )).

% zip_left_commute
fof(fact_406_zip__left__commute,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu197485079333405161nteger(Xs2,zip_Co3543743374963494515nteger(Ys,Zs)) = map_Pr4579580088224315564nteger(produc1513625502823641925nteger(cOMBB_681247301518469873nteger(produc6859320541839489883nteger,cOMBB_8145488450226700727nteger(cOMBC_4772695251711667176nteger(cOMBB_8209961359737916533e_term(cOMBB_7697817708099229739nteger,produc7384524951051686153nteger)),produc1086072967326762835nteger))),zip_Co4196283315349899809nteger(Ys,zip_fu6326155852317613967nteger(Xs2,Zs))) )).

% zip_left_commute
fof(fact_407_zip__left__commute,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu2408773928738089174nt_int(Xs2,zip_int_int(Ys,Zs)) = map_Pr7495471742968680138nt_int(produc4703448491457205603nt_int(cOMBB_2986404968635367552nt_int(produc9125676443435135240nt_int,cOMBB_7745502544921156290nt_int(cOMBC_5576550878828623362nt_int(cOMBB_1364847706011589734e_term(cOMBB_1283357136107696901nt_int,produc1560874099174258678nt_int)),product_Pair_int_int))),zip_in2361505260815139026rm_int(Ys,zip_fu2453293088336910671rm_int(Xs2,Zs))) )).

% zip_left_commute
fof(fact_408_zip__left__commute,axiom,(
    ! [Xs2,Ys,Zs] : zip_fu9102111156773635586nt_int(Xs2,zip_int_int(Ys,Zs)) = map_Pr7776183546865277386nt_int(produc1382607001834865251nt_int(cOMBB_5872364081358007936nt_int(produc2088276820027831816nt_int,cOMBB_7993610997652956098nt_int(cOMBC_1970634365177666650nt_int(cOMBB_9197500348686874426e_term(cOMBB_2467116309528995889nt_int,produc4852315488734385442nt_int)),product_Pair_int_int))),zip_in7290147406150888102rm_int(Ys,zip_fu3112013770087605027rm_int(Xs2,Zs))) )).

% zip_left_commute
fof(fact_409_Rel__abs,axiom,(
    ! [A4,B5,F,G] :
      ( ! [X3,Y3] :
          ( ( gg_bool(X3)
            & gg_bool(Y3) )
         => ( pp(aa_bool_bool(aa_boo8970175072276269406l_bool(rel_bool_bool(A4),X3),Y3))
           => pp(aa_bool_bool(aa_boo8970175072276269406l_bool(rel_bool_bool(B5),aa_bool_bool(F,X3)),aa_bool_bool(G,Y3))) ) )
     => rel_fu209412976606252618l_bool(bNF_re4548936267536770013l_bool(A4,B5),F,G) ) )).

% Rel_abs
fof(fact_410_lex__prod__def,axiom,(
    ! [Ra,Rb] : lex_pr8029265285556086080at_nat(Ra,Rb) = collec3253044014973990424at_nat(produc3254253027406900765t_bool(produc5689685357335670917t_bool(cOMBB_2238165666794131186ol_nat(cOMBB_3104199731091997891at_nat(produc1970299495414637522t_bool),cOMBS_5301232950889283207t_bool(cOMBB_4615779657065937028ol_nat(cOMBB_4088083017688747661at_nat,cOMBB_6955513824563364925ol_nat(cOMBS_6457767331776253883t_bool,cOMBB_4166441949715711812ol_nat(cOMBB_4813502403176724906ol_nat(cOMBB_3950327738894754075at_nat),cOMBB_7721905284830110236ol_nat(cOMBB_4201503070600411334ol_nat(fdisj),cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),Ra))))),cOMBC_5432844299569730948t_bool(cOMBB_1470511346761572292ol_nat(cOMBB_5129520015487172634at_nat,cOMBB_5987020632537166576ol_nat(cOMBC_5836600391518924715t_bool,cOMBB_4166441949715711812ol_nat(cOMBB_4813502403176724906ol_nat(cOMBB_3950327738894754075at_nat),cOMBB_7721905284830110236ol_nat(cOMBB_4201503070600411334ol_nat(fconj),fequal_nat)))),cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),Rb))))))) )).

% lex_prod_def
fof(fact_411_lex__prod__def,axiom,(
    ! [Ra,Rb] : lex_pr4669217892513370978at_nat(Ra,Rb) = collec2200730763347676620at_nat(produc3132996710552569449t_bool(produc2162632091205098121t_bool(cOMBB_939616762350200157at_nat(cOMBB_858161705245420920ol_nat(produc4602806008853628464t_bool),cOMBS_4766649414053171946t_bool(cOMBB_3865874014732187325at_nat(cOMBB_2123595567760207548ol_nat,cOMBB_2037969582880484237at_nat(cOMBS_1476421882506702730t_bool,cOMBB_7892074722853432667at_nat(cOMBB_571549606332118035at_nat(cOMBB_bool_bool_nat),cOMBB_6079270709258741481at_nat(cOMBB_1143792199142760587at_nat(fdisj),cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),Ra))))),cOMBC_5386955363536343038t_bool(cOMBB_5608644763066494149at_nat(cOMBB_3629999415770602094ol_nat,cOMBB_5609757832728192541at_nat(cOMBC_1646952264703196058t_bool,cOMBB_7892074722853432667at_nat(cOMBB_571549606332118035at_nat(cOMBB_bool_bool_nat),cOMBB_6079270709258741481at_nat(cOMBB_1143792199142760587at_nat(fconj),fequal9188845342289841878at_nat)))),cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),Rb))))))) )).

% lex_prod_def
fof(fact_412_lex__prod__def,axiom,(
    ! [Ra,Rb] : lex_pr8801849515957261039at_nat(Ra,Rb) = collec7334067512558549330at_nat(produc282085997471274923t_bool(produc7808502358916064543t_bool(cOMBB_2976772690801511759at_nat(cOMBB_6402209240706646725at_nat(produc6738493412065443883t_bool),cOMBS_8040104487882144362t_bool(cOMBB_6278654488875105531at_nat(cOMBB_1444067409130430619at_nat,cOMBB_3164626593710648671at_nat(cOMBS_5963004598402476862t_bool,cOMBB_7968978829756819823at_nat(cOMBB_7619062392956744359at_nat(cOMBB_3950327738894754075at_nat),cOMBB_6079270709258741481at_nat(cOMBB_1143792199142760587at_nat(fdisj),cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),Ra))))),cOMBC_213517001142981186t_bool(cOMBB_5471853805901070681at_nat(cOMBB_6298731734558261203at_nat,cOMBB_1317090727945068337at_nat(cOMBC_3379778804465295182t_bool,cOMBB_7968978829756819823at_nat(cOMBB_7619062392956744359at_nat(cOMBB_3950327738894754075at_nat),cOMBB_6079270709258741481at_nat(cOMBB_1143792199142760587at_nat(fconj),fequal9188845342289841878at_nat)))),cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),Rb))))))) )).

% lex_prod_def
fof(fact_413_lex__prod__def,axiom,(
    ! [Ra,Rb] : lex_prod_nat_nat(Ra,Rb) = collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,produc5023667602222594023t_bool(cOMBB_2831812752480454468ol_nat(cOMBB_6165210988431530350ol_nat(produc8955392012077580105t_bool),cOMBS_7975979422065336327t_bool(cOMBB_7693806822126743102ol_nat(cOMBB_7554325574139592886ol_nat,cOMBB_4887640759249749643ol_nat(cOMBS_9184950873606742919t_bool,cOMBB_7887238097748047192ol_nat(cOMBB_2778472989460164414ol_nat(cOMBB_bool_bool_nat),cOMBB_7721905284830110236ol_nat(cOMBB_4201503070600411334ol_nat(fdisj),cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),Ra))))),cOMBC_6336148525615794240t_bool(cOMBB_2248581009415873744ol_nat(cOMBB_1789210886255972223ol_nat,cOMBB_8897308571653880148ol_nat(cOMBC_1981652900330269559t_bool,cOMBB_7887238097748047192ol_nat(cOMBB_2778472989460164414ol_nat(cOMBB_bool_bool_nat),cOMBB_7721905284830110236ol_nat(cOMBB_4201503070600411334ol_nat(fconj),fequal_nat)))),cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),Rb))))))) )).

% lex_prod_def
fof(fact_414_takeWhile__append1,axiom,(
    ! [X,Xs,P,Ys2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),aa_lis156294325248309974at_nat(set_Pr5648618587558075414at_nat,Xs)))
     => ( ~ pp(aa_Pro2232559814647311250t_bool(P,X))
       => takeWh6395431351003862016at_nat(P,append985823374593552924at_nat(Xs,Ys2)) = takeWh6395431351003862016at_nat(P,Xs) ) ) )).

% takeWhile_append1
fof(fact_415_takeWhile__append1,axiom,(
    ! [X,Xs,P,Ys2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),aa_lis5603739568514191958at_nat(set_Pr5518436109238095868at_nat,Xs)))
     => ( ~ pp(aa_Pro6098352494050694700t_bool(P,X))
       => takeWh1554011562171007206at_nat(P,append8751754712269456642at_nat(Xs,Ys2)) = takeWh1554011562171007206at_nat(P,Xs) ) ) )).

% takeWhile_append1
fof(fact_416_exE__realizer_H,axiom,(
    ! [P,P2] :
      ( pp(aa_fun8257100190732734890m_bool(aa_Pro1039824329702270498m_bool(P,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,P2)),aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,P2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ~ pp(aa_fun8257100190732734890m_bool(aa_Pro1039824329702270498m_bool(P,Y3),X3)) ) ) )).

% exE_realizer'
fof(fact_417_exE__realizer_H,axiom,(
    ! [P,P2] :
      ( pp(aa_fun545845183243510123m_bool(aa_Pro3890205135341880141m_bool(P,aa_Pro7386464516095682491atural(produc3992340709582277180atural,P2)),aa_Pro5217105177887748324e_term(produc1168782837711296254atural,P2)))
     => ~ ! [X3,Y3] : ~ pp(aa_fun545845183243510123m_bool(aa_Pro3890205135341880141m_bool(P,Y3),X3)) ) )).

% exE_realizer'
fof(fact_418_exE__realizer_H,axiom,(
    ! [P,P2] :
      ( pp(aa_fun8146989869410979616m_bool(aa_Pro6439351403099769752m_bool(P,aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,P2)),aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,P2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ~ pp(aa_fun8146989869410979616m_bool(aa_Pro6439351403099769752m_bool(P,Y3),X3)) ) ) )).

% exE_realizer'
fof(fact_419_exE__realizer_H,axiom,(
    ! [P,P2] :
      ( pp(aa_fun1922592006021787503m_bool(aa_Pro7796564485022453065m_bool(P,aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,P2)),aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,P2)))
     => ~ ! [X3,Y3] : ~ pp(aa_fun1922592006021787503m_bool(aa_Pro7796564485022453065m_bool(P,Y3),X3)) ) )).

% exE_realizer'
fof(fact_420_exE__realizer_H,axiom,(
    ! [P,P2] :
      ( pp(aa_fun1066343515980309147m_bool(aa_Pro5354883135473551477m_bool(P,aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,P2)),aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,P2)))
     => ~ ! [X3,Y3] : ~ pp(aa_fun1066343515980309147m_bool(aa_Pro5354883135473551477m_bool(P,Y3),X3)) ) )).

% exE_realizer'
fof(fact_421_exE__realizer_H,axiom,(
    ! [P,P2] :
      ( pp(aa_Code_natural_bool(aa_Pro6792619557268184595l_bool(P,aa_Pro3673693039631929973atural(produc6591912806276919810atural,P2)),aa_Pro5806155842103967332atural(produc497848011034438852atural,P2)))
     => ~ ! [X3,Y3] : ~ pp(aa_Code_natural_bool(aa_Pro6792619557268184595l_bool(P,Y3),X3)) ) )).

% exE_realizer'
fof(fact_422_exE__realizer_H,axiom,(
    ! [P,P2] :
      ( pp(aa_fin5805139829343551406n_bool(aa_Pro7928877276181251434n_bool(P,aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,P2)),aa_Pro1491988591844232024action(produc3089225533250117581list_f,P2)))
     => ~ ! [X3,Y3] : ~ pp(aa_fin5805139829343551406n_bool(aa_Pro7928877276181251434n_bool(P,Y3),X3)) ) )).

% exE_realizer'
fof(fact_423_Rel__app,axiom,(
    ! [A4,B5,F,G,X,Y] :
      ( rel_fu209412976606252618l_bool(bNF_re4548936267536770013l_bool(A4,B5),F,G)
     => ( pp(aa_bool_bool(aa_boo8970175072276269406l_bool(rel_bool_bool(A4),X),Y))
       => pp(aa_bool_bool(aa_boo8970175072276269406l_bool(rel_bool_bool(B5),aa_bool_bool(F,X)),aa_bool_bool(G,Y))) ) ) )).

% Rel_app
fof(fact_424_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro605336214283753216nteger(produc63072358922508822nteger(F,G),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun1274623470434842396e_term(F,A)),aa_Pro4693618923521437820nteger(G,B)) )).

% map_prod_simp
fof(fact_425_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro1767059176697221775nt_int(produc4728319346741315203nt_int(F,G),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun7763722112327144939e_term(F,A)),aa_Pro87653395603638426nt_int(G,B)) )).

% map_prod_simp
fof(fact_426_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro500179501102819087nteger(produc8646943564923299783nteger(F,G),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun725494399760559339e_term(F,A)),aa_Pro479190544307753694nteger(G,B)) )).

% map_prod_simp
fof(fact_427_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro7656415901706311326nt_int(produc8631014097479913524nt_int(F,G),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun78455448157554618e_term(F,A)),aa_Pro6970504127699319548nt_int(G,B)) )).

% map_prod_simp
fof(fact_428_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro7907784746481409879atural(produc2817918400915399083atural(F,G),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_fun2534482373496464155e_term(F,A)),aa_Pro3593168809004187282atural(G,B)) )).

% map_prod_simp
fof(fact_429_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro8872820292021839222nteger(produc2464009018090205216nteger(F,G),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_fun3693577172319249446e_term(F,A)),aa_Pro4693618923521437820nteger(G,B)) )).

% map_prod_simp
fof(fact_430_map__prod__simp,axiom,(
    ! [F,G,A,B] : produc5875590625826673327nt_int(F,G,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_fun6116396979335496727e_term(F,A)),aa_Pro87653395603638426nt_int(G,B)) )).

% map_prod_simp
fof(fact_431_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro1881300264899033047nteger(produc9188367097266839807nteger(F,G),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun2603856539051944475e_term(F,A)),aa_Pro5363176462251620070nteger(G,B)) )).

% map_prod_simp
fof(fact_432_map__prod__simp,axiom,(
    ! [F,G,A,B] : produc2006055592993132908nt_int(F,G,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun4443069959818331370e_term(F,A)),aa_Pro7164870388581637892nt_int(G,B)) )).

% map_prod_simp
fof(fact_433_map__prod__simp,axiom,(
    ! [F,G,A,B] : aa_Pro2148824989012779638nteger(produc1437091937170647584nteger(F,G),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun1784510506351320614e_term(F,A)),aa_Pro4693618923521437820nteger(G,B)) )).

% map_prod_simp
fof(fact_434_less__than__iff,axiom,(
    ! [X,Y] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y)),less_than))
    <=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X),Y)) ) )).

% less_than_iff
fof(fact_435_equalityCE,axiom,(
    ! [A4,B5,C2] :
      ( A4 = B5
     => ( ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4))
         => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5)) )
       => ~ ( ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4))
           => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5)) ) ) ) )).

% equalityCE
fof(fact_436_equalityCE,axiom,(
    ! [A4,B5,C2] :
      ( A4 = B5
     => ( ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4))
         => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5)) )
       => ~ ( ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4))
           => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5)) ) ) ) )).

% equalityCE
fof(fact_437_apsnd__apfst,axiom,(
    ! [F,G,X] : produc2420998536947800215e_term(F,produc6256696554706808092atural(G,X)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_Cod6552544117257209045e_term(G,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro5363176462251620070nteger(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apsnd_apfst
fof(fact_438_apsnd__apfst,axiom,(
    ! [F,G,X] : produc142070061812922756e_term(F,produc1105131329730397069atural(G,X)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_Cod2745173244843804580e_term(G,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro7164870388581637892nt_int(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apsnd_apfst
fof(fact_439_apsnd__apfst,axiom,(
    ! [F,G,X] : aa_Pro7626634194206414894atural(produc2400445711499960492e_term(F),produc9192780881205123677atural(G,X)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_Cod1528497641474136276e_term(G,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro4262726347734369532atural(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apsnd_apfst
fof(fact_440_apsnd__apfst,axiom,(
    ! [F,G,X] : produc2377606937691733409e_term(F,produc3686774387803128722atural(G,X)) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_Cod2687592440296921567e_term(G,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro5363176462251620070nteger(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apsnd_apfst
fof(fact_441_apsnd__apfst,axiom,(
    ! [F,G,X] : produc546592023539879856e_term(F,produc7641258367388614241atural(G,X)) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_Cod2767372014048222672e_term(G,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro7164870388581637892nt_int(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apsnd_apfst
fof(fact_442_apsnd__apfst,axiom,(
    ! [F,G,X] : aa_Pro605336214283753216nteger(produc7284161782193780781e_term(F),aa_Pro605336214283753216nteger(produc3186735841308740863nteger(G),X)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun1274623470434842396e_term(G,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X))),aa_Pro4693618923521437820nteger(F,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X))) )).

% apsnd_apfst
fof(fact_443_apsnd__apfst,axiom,(
    ! [F,G,X] : produc3643435400298438938e_term(F,produc6768518630390466416nteger(G,X)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun7763722112327144939e_term(G,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X))),aa_Pro87653395603638426nt_int(F,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X))) )).

% apsnd_apfst
fof(fact_444_apsnd__apfst,axiom,(
    ! [F,G,X] : produc1276845895190836367e_term(F,produc556321706008094862nt_int(G,X)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun725494399760559339e_term(G,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X))),aa_Pro479190544307753694nteger(F,aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,X))) )).

% apsnd_apfst
fof(fact_445_apsnd__apfst,axiom,(
    ! [F,G,X] : aa_Pro7656415901706311326nt_int(produc5581269045473686908e_term(F),aa_Pro7656415901706311326nt_int(produc652620917742595839nt_int(G),X)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun78455448157554618e_term(G,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X))),aa_Pro6970504127699319548nt_int(F,aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,X))) )).

% apsnd_apfst
fof(fact_446_apsnd__apfst,axiom,(
    ! [F,G,X] : produc4843463054730981442e_term(F,produc8839301542071919168nteger(G,X)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_fun2534482373496464155e_term(G,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X))),aa_Pro3593168809004187282atural(F,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X))) )).

% apsnd_apfst
fof(fact_447_insertCI,axiom,(
    ! [A,B5,B] :
      ( ( ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),B5))
       => A = B )
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),insert8211810215607154385at_nat(B,B5))) ) )).

% insertCI
fof(fact_448_insertCI,axiom,(
    ! [A,B5,B] :
      ( ( ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),B5))
       => A = B )
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),insert5050368324300391991at_nat(B,B5))) ) )).

% insertCI
fof(fact_449_apfst__apsnd,axiom,(
    ! [F,G,X] : produc7357146669224058630nteger(F,produc8287249056265611856atural(G,X)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_Cod6552544117257209045e_term(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro5363176462251620070nteger(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apfst_apsnd
fof(fact_450_apfst__apsnd,axiom,(
    ! [F,G,X] : produc2234144857242838421nt_int(F,produc5167862320620071534atural(G,X)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_Cod2745173244843804580e_term(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro7164870388581637892nt_int(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apfst_apsnd
fof(fact_451_apfst__apsnd,axiom,(
    ! [F,G,X] : produc9192780881205123677atural(F,aa_Pro4026365172444991930atural(produc4464772112783624294atural(G),X)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_Cod1528497641474136276e_term(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro4262726347734369532atural(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apfst_apsnd
fof(fact_452_apfst__apsnd,axiom,(
    ! [F,G,X] : produc4787224502320379260nteger(F,produc8287249056265611856atural(G,X)) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_Cod2687592440296921567e_term(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro5363176462251620070nteger(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apfst_apsnd
fof(fact_453_apfst__apsnd,axiom,(
    ! [F,G,X] : produc8789751339700060265nt_int(F,produc5167862320620071534atural(G,X)) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_Cod2767372014048222672e_term(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,X))),aa_Pro7164870388581637892nt_int(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X))) )).

% apfst_apsnd
fof(fact_454_apfst__apsnd,axiom,(
    ! [F,G,X] : aa_Pro605336214283753216nteger(produc3186735841308740863nteger(F),aa_Pro605336214283753216nteger(produc7284161782193780781e_term(G),X)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun1274623470434842396e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X))),aa_Pro4693618923521437820nteger(G,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X))) )).

% apfst_apsnd
fof(fact_455_apfst__apsnd,axiom,(
    ! [F,G,X] : produc7771144042766204814nt_int(F,produc6754726782922720843e_term(G,X)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun7763722112327144939e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X))),aa_Pro87653395603638426nt_int(G,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X))) )).

% apfst_apsnd
fof(fact_456_apfst__apsnd,axiom,(
    ! [F,G,X] : produc149713973388521584nteger(F,produc7059637379731103582e_term(G,X)) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_fun725494399760559339e_term(F,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X))),aa_Pro479190544307753694nteger(G,aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,X))) )).

% apfst_apsnd
fof(fact_457_apfst__apsnd,axiom,(
    ! [F,G,X] : aa_Pro7656415901706311326nt_int(produc652620917742595839nt_int(F),aa_Pro7656415901706311326nt_int(produc5581269045473686908e_term(G),X)) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_fun78455448157554618e_term(F,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X))),aa_Pro6970504127699319548nt_int(G,aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,X))) )).

% apfst_apsnd
fof(fact_458_apfst__apsnd,axiom,(
    ! [F,G,X] : produc7738851427554668630atural(F,produc6440452194307058755e_term(G,X)) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_fun2534482373496464155e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X))),aa_Pro3593168809004187282atural(G,aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,X))) )).

% apfst_apsnd
fof(fact_459_snd__apfst,axiom,(
    ! [F,X] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro4026365172444991930atural(produc4623092060929046819atural(F),X)) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,X) )).

% snd_apfst
fof(fact_460_snd__apfst,axiom,(
    ! [F,X] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro7428252341792638716list_f(produc5173547218785033201list_f(F),X)) = aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,X) )).

% snd_apfst
fof(fact_461_fst__apfst,axiom,(
    ! [F,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro605336214283753216nteger(produc3186735841308740863nteger(F),X)) = aa_fun1274623470434842396e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X)) )).

% fst_apfst
fof(fact_462_fst__apfst,axiom,(
    ! [F,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro2148824989012779638nteger(produc3068984984575431029nteger(F),X)) = aa_fun1784510506351320614e_term(F,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,X)) )).

% fst_apfst
fof(fact_463_fst__apfst,axiom,(
    ! [F,X] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro7626634194206414894atural(produc8499700979911337623atural(F),X)) = aa_fun3478251006336822810e_term(F,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,X)) )).

% fst_apfst
fof(fact_464_fst__apfst,axiom,(
    ! [F,X] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro8872820292021839222nteger(produc3333295048669924213nteger(F),X)) = aa_fun3693577172319249446e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X)) )).

% fst_apfst
fof(fact_465_fst__apfst,axiom,(
    ! [F,X] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro8016721334973800684nteger(produc1779435066467205099nteger(F),X)) = aa_fun4150438919549131568e_term(F,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,X)) )).

% fst_apfst
fof(fact_466_fst__apfst,axiom,(
    ! [F,X] : aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,aa_Pro7619707155024403014nt_int(produc797834107270070439nt_int(F),X)) = aa_fun6283001615389677586e_term(F,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,X)) )).

% fst_apfst
fof(fact_467_fst__apfst,axiom,(
    ! [F,X] : aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,aa_Pro7712013891223568754nt_int(produc5828266736486832595nt_int(F),X)) = aa_fun8405180984973938150e_term(F,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X)) )).

% fst_apfst
fof(fact_468_fst__apfst,axiom,(
    ! [F,X] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro1156610208699797362nt_int(produc2152783933663180243nt_int(F),X)) = aa_fun3199491695965942246e_term(F,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,X)) )).

% fst_apfst
fof(fact_469_fst__apfst,axiom,(
    ! [F,X] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro7656415901706311326nt_int(produc652620917742595839nt_int(F),X)) = aa_fun78455448157554618e_term(F,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X)) )).

% fst_apfst
fof(fact_470_rtrancl3p__induct3,axiom,(
    ! [R3,Ax2,Ay2,Az2,X2a,Cx,Cy,Cz,P3] :
      ( pp(aa_Pro7150874649148492216r_bool(rtranc6888836235327271168yperep(cOMBB_1366121701535921875nteger(cOMBB_38662348728028498yperep(produc401098500374025047r_bool),cOMBB_541064536597979447nteger(cOMBB_6520020761449137108yperep(cOMBB_4840141960444740569e_term(produc8194967127080255663r_bool)),produc7629536642697509374r_bool(cOMBB_3116532447780546471e_term(produc7567937587999862614r_bool,R3)))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax2),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay2),Az2)),X2a),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Cx),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Cy),Cz))))
     => ( ! [A3,Aa,B3] : pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(aa_lis8615945955800996119r_bool(aa_Cod6345498316439044307r_bool(aa_Cod13429314964527631r_bool(aa_fun6528391501840603577r_bool(P3,A3),Aa),B3),nil_typerep),A3),Aa),B3))
       => ( ! [A3,Aa,B3,Bs,Ab,Ac,Ba,Bb,Ad,Ae,Bc] :
              ( pp(aa_Pro7150874649148492216r_bool(rtranc6888836235327271168yperep(cOMBB_1366121701535921875nteger(cOMBB_38662348728028498yperep(produc401098500374025047r_bool),cOMBB_541064536597979447nteger(cOMBB_6520020761449137108yperep(cOMBB_4840141960444740569e_term(produc8194967127080255663r_bool)),produc7629536642697509374r_bool(cOMBB_3116532447780546471e_term(produc7567937587999862614r_bool,R3)))),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3)),Bs),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ab),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ac),Ba))))
             => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(aa_lis8615945955800996119r_bool(aa_Cod6345498316439044307r_bool(aa_Cod13429314964527631r_bool(aa_fun6528391501840603577r_bool(P3,A3),Aa),B3),Bs),Ab),Ac),Ba))
               => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(aa_typ7429463677757833639r_bool(aa_Cod715017788918113251r_bool(aa_Cod7358073210240692639r_bool(aa_fun2992804752113726665r_bool(R3,Ab),Ac),Ba),Bb),Ad),Ae),Bc))
                 => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(aa_lis8615945955800996119r_bool(aa_Cod6345498316439044307r_bool(aa_Cod13429314964527631r_bool(aa_fun6528391501840603577r_bool(P3,A3),Aa),B3),append_typerep(Bs,aa_lis9041531584263668358yperep(cons_typerep(Bb),nil_typerep))),Ad),Ae),Bc)) ) ) )
         => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun7590852728353144354r_bool(aa_lis8615945955800996119r_bool(aa_Cod6345498316439044307r_bool(aa_Cod13429314964527631r_bool(aa_fun6528391501840603577r_bool(P3,Ax2),Ay2),Az2),X2a),Cx),Cy),Cz)) ) ) ) )).

% rtrancl3p_induct3
fof(fact_471_rtrancl3p__induct3,axiom,(
    ! [R3,Ax2,Ay2,Az2,X2a,Cx,Cy,Cz,P3] :
      ( pp(aa_Pro916321633901839137l_bool(rtranc3175076457668994903yperep(cOMBB_846735544962047466atural(cOMBB_8624280976385750034yperep(produc8343529308684018112l_bool),cOMBB_9077245891810296610atural(cOMBB_8575074632140792168yperep(cOMBB_3730184279310646956e_term(produc682556209478236825l_bool)),produc8497428277269248530l_bool(cOMBB_622384168059072848e_term(produc9194959526945447403l_bool,R3)))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax2),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ay2),Az2)),X2a),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Cx),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Cy),Cz))))
     => ( ! [A3,Aa,B3] : pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(aa_lis735500130437666114l_bool(aa_Cod6802074752346591475l_bool(aa_Cod7258250240150858788l_bool(aa_fun9048219272017468943l_bool(P3,A3),Aa),B3),nil_typerep),A3),Aa),B3))
       => ( ! [A3,Aa,B3,Bs,Ab,Ac,Ba,Bb,Ad,Ae,Bc] :
              ( pp(aa_Pro916321633901839137l_bool(rtranc3175076457668994903yperep(cOMBB_846735544962047466atural(cOMBB_8624280976385750034yperep(produc8343529308684018112l_bool),cOMBB_9077245891810296610atural(cOMBB_8575074632140792168yperep(cOMBB_3730184279310646956e_term(produc682556209478236825l_bool)),produc8497428277269248530l_bool(cOMBB_622384168059072848e_term(produc9194959526945447403l_bool,R3)))),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Aa),B3)),Bs),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ab),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,Ac),Ba))))
             => ( pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(aa_lis735500130437666114l_bool(aa_Cod6802074752346591475l_bool(aa_Cod7258250240150858788l_bool(aa_fun9048219272017468943l_bool(P3,A3),Aa),B3),Bs),Ab),Ac),Ba))
               => ( pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(aa_typ3428906479396126162l_bool(aa_Cod1419350168365658755l_bool(aa_Cod25706318474166452l_bool(aa_fun6689051435389192863l_bool(R3,Ab),Ac),Ba),Bb),Ad),Ae),Bc))
                 => pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(aa_lis735500130437666114l_bool(aa_Cod6802074752346591475l_bool(aa_Cod7258250240150858788l_bool(aa_fun9048219272017468943l_bool(P3,A3),Aa),B3),append_typerep(Bs,aa_lis9041531584263668358yperep(cons_typerep(Bb),nil_typerep))),Ad),Ae),Bc)) ) ) )
         => pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(aa_fun9177371286630637389l_bool(aa_lis735500130437666114l_bool(aa_Cod6802074752346591475l_bool(aa_Cod7258250240150858788l_bool(aa_fun9048219272017468943l_bool(P3,Ax2),Ay2),Az2),X2a),Cx),Cy),Cz)) ) ) ) )).

% rtrancl3p_induct3
fof(fact_472_rtrancl3p__induct3,axiom,(
    ! [R3,Ax2,Ay2,Az2,X2a,Cx,Cy,Cz,P3] :
      ( pp(aa_Pro3640759179027349698r_bool(rtranc1598346362415149942yperep(cOMBB_6297587082483395785nteger(cOMBB_8173728252348921042yperep(produc1236900166980094561r_bool),cOMBB_7612773275306069037nteger(cOMBB_220180290922983508yperep(cOMBB_2211189884751476963e_term(produc8194967127080255663r_bool)),produc7966764662679685502r_bool(cOMBB_8369330086435582109e_term(produc3729852753559759308r_bool,R3)))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax2),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ay2),Az2)),X2a),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Cx),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Cy),Cz))))
     => ( ! [A3,Aa,B3] : pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(aa_lis6872328170202910349r_bool(aa_Cod1062060236366922569r_bool(aa_Cod6324174988560476549r_bool(aa_fun3491061600886479525r_bool(P3,A3),Aa),B3),nil_typerep),A3),Aa),B3))
       => ( ! [A3,Aa,B3,Bs,Ab,Ac,Ba,Bb,Ad,Ae,Bc] :
              ( pp(aa_Pro3640759179027349698r_bool(rtranc1598346362415149942yperep(cOMBB_6297587082483395785nteger(cOMBB_8173728252348921042yperep(produc1236900166980094561r_bool),cOMBB_7612773275306069037nteger(cOMBB_220180290922983508yperep(cOMBB_2211189884751476963e_term(produc8194967127080255663r_bool)),produc7966764662679685502r_bool(cOMBB_8369330086435582109e_term(produc3729852753559759308r_bool,R3)))),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Aa),B3)),Bs),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ab),aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(produc1086072967326762835nteger,Ac),Ba))))
             => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(aa_lis6872328170202910349r_bool(aa_Cod1062060236366922569r_bool(aa_Cod6324174988560476549r_bool(aa_fun3491061600886479525r_bool(P3,A3),Aa),B3),Bs),Ab),Ac),Ba))
               => ( pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(aa_typ342362482306594589r_bool(aa_Cod5987206055423813209r_bool(aa_Cod7166549366698049813r_bool(aa_fun6579010776543504565r_bool(R3,Ab),Ac),Ba),Bb),Ad),Ae),Bc))
                 => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(aa_lis6872328170202910349r_bool(aa_Cod1062060236366922569r_bool(aa_Cod6324174988560476549r_bool(aa_fun3491061600886479525r_bool(P3,A3),Aa),B3),append_typerep(Bs,aa_lis9041531584263668358yperep(cons_typerep(Bb),nil_typerep))),Ad),Ae),Bc)) ) ) )
         => pp(aa_Code_integer_bool(aa_Cod7250484176784686200r_bool(aa_fun8328143705649857432r_bool(aa_lis6872328170202910349r_bool(aa_Cod1062060236366922569r_bool(aa_Cod6324174988560476549r_bool(aa_fun3491061600886479525r_bool(P3,Ax2),Ay2),Az2),X2a),Cx),Cy),Cz)) ) ) ) )).

% rtrancl3p_induct3
fof(fact_473_rtrancl3p__induct3,axiom,(
    ! [R3,Ax2,Ay2,Az2,X2a,Cx,Cy,Cz,P3] :
      ( pp(aa_Pro5031108791230793749t_bool(rtranc5323057011594291555yperep(cOMBB_5562657749750264566nt_int(cOMBB_7270055073361074962yperep(produc625993674133193396t_bool),cOMBB_4874410044190868510nt_int(cOMBB_702978485530594392yperep(cOMBB_7915570523296049048e_term(produc8560705615207772305t_bool)),produc6326992862953636610t_bool(cOMBB_4062366619956972596e_term(produc3339367878862267359t_bool,R3)))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay2),Az2)),X2a),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Cx),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Cy),Cz))))
     => ( ! [A3,Aa,B3] : pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(aa_lis7578488618070684478t_bool(aa_int4199521047403114475t_bool(aa_int5490438224660835352t_bool(aa_fun6863469173970246151t_bool(P3,A3),Aa),B3),nil_typerep),A3),Aa),B3))
       => ( ! [A3,Aa,B3,Bs,Ab,Ac,Ba,Bb,Ad,Ae,Bc] :
              ( pp(aa_Pro5031108791230793749t_bool(rtranc5323057011594291555yperep(cOMBB_5562657749750264566nt_int(cOMBB_7270055073361074962yperep(produc625993674133193396t_bool),cOMBB_4874410044190868510nt_int(cOMBB_702978485530594392yperep(cOMBB_7915570523296049048e_term(produc8560705615207772305t_bool)),produc6326992862953636610t_bool(cOMBB_4062366619956972596e_term(produc3339367878862267359t_bool,R3)))),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3)),Bs),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ab),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ac),Ba))))
             => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(aa_lis7578488618070684478t_bool(aa_int4199521047403114475t_bool(aa_int5490438224660835352t_bool(aa_fun6863469173970246151t_bool(P3,A3),Aa),B3),Bs),Ab),Ac),Ba))
               => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(aa_typ7307212363976137678t_bool(aa_int6753763498455105403t_bool(aa_int118421709588503720t_bool(aa_fun8301434453466920087t_bool(R3,Ab),Ac),Ba),Bb),Ad),Ae),Bc))
                 => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(aa_lis7578488618070684478t_bool(aa_int4199521047403114475t_bool(aa_int5490438224660835352t_bool(aa_fun6863469173970246151t_bool(P3,A3),Aa),B3),append_typerep(Bs,aa_lis9041531584263668358yperep(cons_typerep(Bb),nil_typerep))),Ad),Ae),Bc)) ) ) )
         => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun2967821446744691017t_bool(aa_lis7578488618070684478t_bool(aa_int4199521047403114475t_bool(aa_int5490438224660835352t_bool(aa_fun6863469173970246151t_bool(P3,Ax2),Ay2),Az2),X2a),Cx),Cy),Cz)) ) ) ) )).

% rtrancl3p_induct3
fof(fact_474_rtrancl3p__induct3,axiom,(
    ! [R3,Ax2,Ay2,Az2,X2a,Cx,Cy,Cz,P3] :
      ( pp(aa_Pro7591400126937138665t_bool(rtranc4013231012727985807yperep(cOMBB_9108069416537923362nt_int(cOMBB_5951983665369491986yperep(produc6627716702706253960t_bool),cOMBB_4653876195357876810nt_int(cOMBB_3498058466423397720yperep(cOMBB_8013967700487213420e_term(produc8560705615207772305t_bool)),produc4393254493027025410t_bool(cOMBB_3184552694563685984e_term(produc2403897821427536139t_bool,R3)))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ay2),Az2)),X2a),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Cx),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Cy),Cz))))
     => ( ! [A3,Aa,B3] : pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(aa_lis2915701633071851114t_bool(aa_int8010135659330731287t_bool(aa_int6541360370215867204t_bool(aa_fun4903620715250965599t_bool(P3,A3),Aa),B3),nil_typerep),A3),Aa),B3))
       => ( ! [A3,Aa,B3,Bs,Ab,Ac,Ba,Bb,Ad,Ae,Bc] :
              ( pp(aa_Pro7591400126937138665t_bool(rtranc4013231012727985807yperep(cOMBB_9108069416537923362nt_int(cOMBB_5951983665369491986yperep(produc6627716702706253960t_bool),cOMBB_4653876195357876810nt_int(cOMBB_3498058466423397720yperep(cOMBB_8013967700487213420e_term(produc8560705615207772305t_bool)),produc4393254493027025410t_bool(cOMBB_3184552694563685984e_term(produc2403897821427536139t_bool,R3)))),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Aa),B3)),Bs),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ab),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Ac),Ba))))
             => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(aa_lis2915701633071851114t_bool(aa_int8010135659330731287t_bool(aa_int6541360370215867204t_bool(aa_fun4903620715250965599t_bool(P3,A3),Aa),B3),Bs),Ab),Ac),Ba))
               => ( pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(aa_typ4048471301251518202t_bool(aa_int7021653199906655399t_bool(aa_int9177333886640407508t_bool(aa_fun9140844013146832111t_bool(R3,Ab),Ac),Ba),Bb),Ad),Ae),Bc))
                 => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(aa_lis2915701633071851114t_bool(aa_int8010135659330731287t_bool(aa_int6541360370215867204t_bool(aa_fun4903620715250965599t_bool(P3,A3),Aa),B3),append_typerep(Bs,aa_lis9041531584263668358yperep(cons_typerep(Bb),nil_typerep))),Ad),Ae),Bc)) ) ) )
         => pp(aa_int_bool(aa_int_fun_int_bool(aa_fun3090123613162288245t_bool(aa_lis2915701633071851114t_bool(aa_int8010135659330731287t_bool(aa_int6541360370215867204t_bool(aa_fun4903620715250965599t_bool(P3,Ax2),Ay2),Az2),X2a),Cx),Cy),Cz)) ) ) ) )).

% rtrancl3p_induct3
fof(fact_475_snd__comp__apfst,axiom,(
    ! [F] : comp_P7610810914149544718atural(produc6591912806276919810atural,produc4623092060929046819atural(F)) = produc6591912806276919810atural )).

% snd_comp_apfst
fof(fact_476_snd__comp__apfst,axiom,(
    ! [F] : comp_P4267156721827287172list_f(produc8710481132536983823list_f,produc5173547218785033201list_f(F)) = produc8710481132536983823list_f )).

% snd_comp_apfst
fof(fact_477_fst__comp__apfst,axiom,(
    ! [F] : comp_P3990188960041576470nteger(produc3971164842776949671nteger,produc3186735841308740863nteger(F)) = comp_f5781897744313322404nteger(F,produc3971164842776949671nteger) )).

% fst_comp_apfst
fof(fact_478_fst__comp__apfst,axiom,(
    ! [F] : comp_P3963986752856745612nteger(produc3971164842776949671nteger,produc3068984984575431029nteger(F)) = comp_f2313621508578202660nteger(F,produc5986598495681327645nteger) )).

% fst_comp_apfst
fof(fact_479_fst__comp__apfst,axiom,(
    ! [F] : comp_P8739097636480170179atural(produc1168782837711296254atural,produc8499700979911337623atural(F)) = comp_f120087647446688761atural(F,produc1168782837711296254atural) )).

% fst_comp_apfst
fof(fact_480_fst__comp__apfst,axiom,(
    ! [F] : comp_P4747203175050475926nteger(produc5986598495681327645nteger,produc3333295048669924213nteger(F)) = comp_f1391551884146842542nteger(F,produc3971164842776949671nteger) )).

% fst_comp_apfst
fof(fact_481_fst__comp__apfst,axiom,(
    ! [F] : comp_P8645197615446898700nteger(produc5986598495681327645nteger,produc1779435066467205099nteger(F)) = comp_f7894305650325292078nteger(F,produc5986598495681327645nteger) )).

% fst_comp_apfst
fof(fact_482_fst__comp__apfst,axiom,(
    ! [F] : comp_P8214188666173692375nt_int(produc6655012789309278474nt_int,produc797834107270070439nt_int(F)) = comp_f1609986638454120445nt_int(F,produc6655012789309278474nt_int) )).

% fst_comp_apfst
fof(fact_483_fst__comp__apfst,axiom,(
    ! [F] : comp_P9069730902323767043nt_int(produc6655012789309278474nt_int,produc5828266736486832595nt_int(F)) = comp_f3236101226726422781nt_int(F,produc2507970727455213110nt_int) )).

% fst_comp_apfst
fof(fact_484_fst__comp__apfst,axiom,(
    ! [F] : comp_P5352292203129765079nt_int(produc2507970727455213110nt_int,produc2152783933663180243nt_int(F)) = comp_f8676991769733914577nt_int(F,produc6655012789309278474nt_int) )).

% fst_comp_apfst
fof(fact_485_fst__comp__apfst,axiom,(
    ! [F] : comp_P5310741988796926467nt_int(produc2507970727455213110nt_int,produc652620917742595839nt_int(F)) = comp_f300797508955093201nt_int(F,produc2507970727455213110nt_int) )).

% fst_comp_apfst
fof(fact_486_rtrancl__induct,axiom,(
    ! [A,B,R,P] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),transi2905341329935302413cl_nat(R)))
     => ( pp(aa_nat_bool(P,A))
       => ( ! [Y3,Z2] :
              ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),Y3)),transi2905341329935302413cl_nat(R)))
             => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y3),Z2)),R))
               => ( pp(aa_nat_bool(P,Y3))
                 => pp(aa_nat_bool(P,Z2)) ) ) )
         => pp(aa_nat_bool(P,B)) ) ) ) )).

% rtrancl_induct
fof(fact_487_rtrancl__induct,axiom,(
    ! [A,B,R,P] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),transi8609417484261754244at_nat(R)))
     => ( pp(aa_Pro2232559814647311250t_bool(P,A))
       => ( ! [Y3,Z2] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),Y3)),transi8609417484261754244at_nat(R)))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Y3),Z2)),R))
               => ( pp(aa_Pro2232559814647311250t_bool(P,Y3))
                 => pp(aa_Pro2232559814647311250t_bool(P,Z2)) ) ) )
         => pp(aa_Pro2232559814647311250t_bool(P,B)) ) ) ) )).

% rtrancl_induct
fof(fact_488_imageI,axiom,(
    ! [X,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro262675715343573244at_nat(F,X)),image_5168914502847457605at_nat(F,A4))) ) )).

% imageI
fof(fact_489_imageI,axiom,(
    ! [X,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(F,X)),image_1119892238107900587at_nat(F,A4))) ) )).

% imageI
fof(fact_490_imageI,axiom,(
    ! [X,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro5901169740204579478at_nat(F,X)),image_6706873702294942047at_nat(F,A4))) ) )).

% imageI
fof(fact_491_imageI,axiom,(
    ! [X,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro7157000481330941564at_nat(F,X)),image_6321802852832981957at_nat(F,A4))) ) )).

% imageI
fof(fact_492_comp__cong,axiom,(
    ! [F,G,X,F3,G2,X6] :
      ( aa_Pro5496877705301569838_a_b_c(F,aa_Pro2582230449628027978list_f(G,X)) = aa_Pro5496877705301569838_a_b_c(F3,aa_Pro2582230449628027978list_f(G2,X6))
     => aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),X) = aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F3),G2),X6) ) )).

% comp_cong
fof(fact_493_comp__eq__elim,axiom,(
    ! [A,B,C2,D] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,A),B) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,C2),D)
     => ! [V2] : aa_Pro5496877705301569838_a_b_c(A,aa_Pro2582230449628027978list_f(B,V2)) = aa_Pro5496877705301569838_a_b_c(C2,aa_Pro2582230449628027978list_f(D,V2)) ) )).

% comp_eq_elim
fof(fact_494_singletonD,axiom,(
    ! [B,A] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),insert8211810215607154385at_nat(A,bot_bo2099793752762293965at_nat)))
     => B = A ) )).

% singletonD
fof(fact_495_singletonD,axiom,(
    ! [B,A] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),insert5050368324300391991at_nat(A,bot_bo5327735625951526323at_nat)))
     => B = A ) )).

% singletonD
fof(fact_496_comp__assoc,axiom,(
    ! [F,G,H] : comp_P1644921750638218854list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),H) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),comp_P4267156721827287172list_f(G,H)) )).

% comp_assoc
fof(fact_497_comp__assoc,axiom,(
    ! [F,G,H] : aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_l6492537726383095040list_f(F,G)),H) = comp_l8432902307485339590list_f(F,aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),H)) )).

% comp_assoc
fof(fact_498_comp__assoc,axiom,(
    ! [F,G,H] : aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(F,G)),H) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),comp_P2673361230361438154list_f(G,H)) )).

% comp_assoc
fof(fact_499_pair__lessI1,axiom,(
    ! [A,B,S,T2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,A),B))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T2))),fun_pair_less)) ) )).

% pair_lessI1
fof(fact_500_image__eq__imp__comp,axiom,(
    ! [F,A4,G,B5,H] :
      ( aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,F),A4) = aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,G),B5)
     => image_6608088440629302181_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,H),F),A4) = image_6608088440629302181_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,H),G),B5) ) )).

% image_eq_imp_comp
fof(fact_501_subrelI,axiom,(
    ! [R,S] :
      ( ! [X3,Y3] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3)),R))
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3)),S)) )
     => pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(R),S)) ) )).

% subrelI
fof(fact_502_subrelI,axiom,(
    ! [R,S] :
      ( ! [X3,Y3] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),Y3)),R))
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),Y3)),S)) )
     => pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(R),S)) ) )).

% subrelI
fof(fact_503_subrelI,axiom,(
    ! [R,S] :
      ( ! [X3,Y3] :
          ( gg_Pro3873016545244360254nteger(Y3)
         => ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)),R))
           => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)),S)) ) )
     => pp(aa_set3464050655127758210r_bool(aa_set4966068208888386948r_bool(ord_le5347933966117430903nteger,R),S)) ) )).

% subrelI
fof(fact_504_subrelI,axiom,(
    ! [R,S] :
      ( ! [X3,Y3] :
          ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3)),R))
         => pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3)),S)) )
     => pp(aa_set4207312397001245291l_bool(aa_set3747303085572403414l_bool(ord_le8467756462758155086atural,R),S)) ) )).

% subrelI
fof(fact_505_subrelI,axiom,(
    ! [R,S] :
      ( ! [X3,Y3] :
          ( gg_Pro3873016545244360254nteger(Y3)
         => ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3)),R))
           => pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3)),S)) ) )
     => pp(aa_set1981577615330639756r_bool(aa_set2923558947593635992r_bool(ord_le3337582088779512301nteger,R),S)) ) )).

% subrelI
fof(fact_506_subrelI,axiom,(
    ! [R,S] :
      ( ! [X3,Y3] :
          ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3)),R))
         => pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3)),S)) )
     => pp(aa_set462754579954174303t_bool(aa_set9008649754896260286t_bool(ord_le5172437211506631514nt_int,R),S)) ) )).

% subrelI
fof(fact_507_subrelI,axiom,(
    ! [R,S] :
      ( ! [X3,Y3] :
          ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3)),R))
         => pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3)),S)) )
     => pp(aa_set6451871791712458035t_bool(aa_set4292432735413367398t_bool(ord_le172202941055982214nt_int,R),S)) ) )).

% subrelI
fof(fact_508_pair__leqI2,axiom,(
    ! [A,B,S,T2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),B))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,S),T2))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T2))),fun_pair_leq)) ) ) )).

% pair_leqI2
fof(fact_509_image__comp,axiom,(
    ! [F,G,R] : image_6684545758539136421_a_b_c(F,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,G),R)) = image_6608088440629302181_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),R) )).

% image_comp
fof(fact_510_pair__leqI1,axiom,(
    ! [A,B,S,T2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,A),B))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T2))),fun_pair_leq)) ) )).

% pair_leqI1
fof(fact_511_Sup_OSUP__image,axiom,(
    ! [Sup,G,F,A4] : aa_set2668507740632656156_a_b_c(Sup,image_6684545758539136421_a_b_c(G,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,F),A4))) = aa_set2668507740632656156_a_b_c(Sup,image_6608088440629302181_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),F),A4)) )).

% Sup.SUP_image
fof(fact_512_Inf_OINF__image,axiom,(
    ! [Inf,G,F,A4] : aa_set2668507740632656156_a_b_c(Inf,image_6684545758539136421_a_b_c(G,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,F),A4))) = aa_set2668507740632656156_a_b_c(Inf,image_6608088440629302181_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),F),A4)) )).

% Inf.INF_image
fof(fact_513_fst__fstOp,axiom,(
    ! [Bc2,P,Q] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Bc2) = aa_Pro3255062042318636430e_term(comp_P3990188960041576470nteger(produc3971164842776949671nteger,bNF_fs5551184864110499297nteger(P,Q)),Bc2) )).

% fst_fstOp
fof(fact_514_fst__fstOp,axiom,(
    ! [Bc2,P,Q] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Bc2) = aa_Pro5217105177887748324e_term(comp_P8739097636480170179atural(produc1168782837711296254atural,bNF_fs4803784828902956000atural(P,Q)),Bc2) )).

% fst_fstOp
fof(fact_515_fst__fstOp,axiom,(
    ! [Bc2,P,Q] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Bc2) = aa_Pro7852915517588584206e_term(comp_P8645197615446898700nteger(produc5986598495681327645nteger,bNF_fs3780317907347579883nteger(P,Q)),Bc2) )).

% fst_fstOp
fof(fact_516_fst__fstOp,axiom,(
    ! [Bc2,P,Q] : aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Bc2) = aa_Pro1970863770526474220e_term(comp_P8214188666173692375nt_int(produc6655012789309278474nt_int,bNF_fs6111084528178183388nt_int(P,Q)),Bc2) )).

% fst_fstOp
fof(fact_517_fst__fstOp,axiom,(
    ! [Bc2,P,Q] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Bc2) = aa_Pro6937503462419145452e_term(comp_P5310741988796926467nt_int(produc2507970727455213110nt_int,bNF_fs2186792319726704816nt_int(P,Q)),Bc2) )).

% fst_fstOp
fof(fact_518_pair__lessI2,axiom,(
    ! [A,B,S,T2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),B))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,S),T2))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T2))),fun_pair_less)) ) ) )).

% pair_lessI2
fof(fact_519_snd__sndOp,axiom,(
    ! [Bc2,P,Q] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,Bc2) = aa_Pro3673693039631929973atural(comp_P7610810914149544718atural(produc6591912806276919810atural,bNF_sn8722645597740893163atural(P,Q)),Bc2) )).

% snd_sndOp
fof(fact_520_snd__sndOp,axiom,(
    ! [Bc2,P,Q] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Bc2) = aa_Pro2582230449628027978list_f(comp_P4267156721827287172list_f(produc8710481132536983823list_f,bNF_sn101281456809739049list_f(P,Q)),Bc2) )).

% snd_sndOp
fof(fact_521_cond__case__prod__eta,axiom,(
    ! [F,G] :
      ( ! [X3,Y3] : aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,X3),Y3) = aa_Pro1971126414814181170atural(G,aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,X3),Y3))
     => aa_fun4394021921911188166atural(produc8282080750456430313atural,F) = G ) )).

% cond_case_prod_eta
fof(fact_522_case__prodE,axiom,(
    ! [C2,P2] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,C2),P2))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)
             => ~ pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(C2,X3),Y3)) ) ) ) )).

% case_prodE
fof(fact_523_case__prodE,axiom,(
    ! [C2,P2] :
      ( pp(aa_Pro916321633901839137l_bool(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,C2),P2))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3)
           => ~ pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(C2,X3),Y3)) ) ) )).

% case_prodE
fof(fact_524_case__prodE,axiom,(
    ! [C2,P2] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,C2),P2))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3)
             => ~ pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(C2,X3),Y3)) ) ) ) )).

% case_prodE
fof(fact_525_case__prodE,axiom,(
    ! [C2,P2] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,C2),P2))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3)
           => ~ pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(C2,X3),Y3)) ) ) )).

% case_prodE
fof(fact_526_case__prodE,axiom,(
    ! [C2,P2] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,C2),P2))
     => ~ ! [X3,Y3] :
            ( P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3)
           => ~ pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(C2,X3),Y3)) ) ) )).

% case_prodE
fof(fact_527_pair__less__iff1,axiom,(
    ! [X,Y,Z] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Z))),fun_pair_less))
    <=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,Y),Z)) ) )).

% pair_less_iff1
fof(fact_528_Collect__split__mono__strong,axiom,(
    ! [X7,A4,Y5,P,Q] :
      ( X7 = image_3233457633125470167e_term(produc3971164842776949671nteger,A4)
     => ( Y5 = image_1855451871314733619nteger(produc7330894765516781285nteger,A4)
       => ( ! [X3] :
              ( member4312719604404396038e_term(X3,X7)
             => ! [Xa3] :
                  ( gg_Pro3873016545244360254nteger(Xa3)
                 => ( member157494554546826820nteger(Xa3,Y5)
                   => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,X3),Xa3))
                     => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(Q,X3),Xa3)) ) ) ) )
         => ( pp(aa_set3464050655127758210r_bool(aa_set4966068208888386948r_bool(ord_le5347933966117430903nteger,A4),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,P))))
           => pp(aa_set3464050655127758210r_bool(aa_set4966068208888386948r_bool(ord_le5347933966117430903nteger,A4),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,Q)))) ) ) ) ) )).

% Collect_split_mono_strong
fof(fact_529_Collect__split__mono__strong,axiom,(
    ! [X7,A4,Y5,P,Q] :
      ( X7 = image_8429719091235490605e_term(produc1168782837711296254atural,A4)
     => ( Y5 = image_4515539628264833842atural(produc3992340709582277180atural,A4)
       => ( ! [X3] :
              ( member3406593020217859077e_term(X3,X7)
             => ! [Xa3] :
                  ( member8280416476884352090atural(Xa3,Y5)
                 => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,X3),Xa3))
                   => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(Q,X3),Xa3)) ) ) )
         => ( pp(aa_set4207312397001245291l_bool(aa_set3747303085572403414l_bool(ord_le8467756462758155086atural,A4),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,P))))
           => pp(aa_set4207312397001245291l_bool(aa_set3747303085572403414l_bool(ord_le8467756462758155086atural,A4),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,Q)))) ) ) ) ) )).

% Collect_split_mono_strong
fof(fact_530_Collect__split__mono__strong,axiom,(
    ! [X7,A4,Y5,P,Q] :
      ( X7 = image_1842157394081550679e_term(produc5986598495681327645nteger,A4)
     => ( Y5 = image_7992156950738608189nteger(produc8810156367552308571nteger,A4)
       => ( ! [X3] :
              ( member4565687819040644368e_term(X3,X7)
             => ! [Xa3] :
                  ( gg_Pro3873016545244360254nteger(Xa3)
                 => ( member157494554546826820nteger(Xa3,Y5)
                   => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,X3),Xa3))
                     => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(Q,X3),Xa3)) ) ) ) )
         => ( pp(aa_set1981577615330639756r_bool(aa_set2923558947593635992r_bool(ord_le3337582088779512301nteger,A4),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,P))))
           => pp(aa_set1981577615330639756r_bool(aa_set2923558947593635992r_bool(ord_le3337582088779512301nteger,A4),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,Q)))) ) ) ) ) )).

% Collect_split_mono_strong
fof(fact_531_Collect__split__mono__strong,axiom,(
    ! [X7,A4,Y5,P,Q] :
      ( X7 = image_563853799432866357e_term(produc6655012789309278474nt_int,A4)
     => ( Y5 = image_8801024764147475502nt_int(produc7622839952223151176nt_int,A4)
       => ( ! [X3] :
              ( member2948136515907314945e_term(X3,X7)
             => ! [Xa3] :
                  ( member5262025264175285858nt_int(Xa3,Y5)
                 => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,X3),Xa3))
                   => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(Q,X3),Xa3)) ) ) )
         => ( pp(aa_set462754579954174303t_bool(aa_set9008649754896260286t_bool(ord_le5172437211506631514nt_int,A4),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,P))))
           => pp(aa_set462754579954174303t_bool(aa_set9008649754896260286t_bool(ord_le5172437211506631514nt_int,A4),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,Q)))) ) ) ) ) )).

% Collect_split_mono_strong
fof(fact_532_Collect__split__mono__strong,axiom,(
    ! [X7,A4,Y5,P,Q] :
      ( X7 = image_686817785882688821e_term(produc2507970727455213110nt_int,A4)
     => ( Y5 = image_3371747934834907138nt_int(produc726383008135262580nt_int,A4)
       => ( ! [X3] :
              ( member7723273712176309973e_term(X3,X7)
             => ! [Xa3] :
                  ( member5262025264175285858nt_int(Xa3,Y5)
                 => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,X3),Xa3))
                   => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(Q,X3),Xa3)) ) ) )
         => ( pp(aa_set6451871791712458035t_bool(aa_set4292432735413367398t_bool(ord_le172202941055982214nt_int,A4),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,P))))
           => pp(aa_set6451871791712458035t_bool(aa_set4292432735413367398t_bool(ord_le172202941055982214nt_int,A4),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,Q)))) ) ) ) ) )).

% Collect_split_mono_strong
fof(fact_533_Collect__split__mono__strong,axiom,(
    ! [X7,A4,Y5,P,Q] :
      ( X7 = image_8194678751871465133atural(produc497848011034438852atural,A4)
     => ( Y5 = image_3837677093542026988atural(produc6591912806276919810atural,A4)
       => ( ! [X3] :
              ( member_Code_natural(X3,X7)
             => ! [Xa3] :
                  ( member8280416476884352090atural(Xa3,Y5)
                 => ( pp(aa_Pro8754844875067278050l_bool(aa_Cod7054345612336956751l_bool(P,X3),Xa3))
                   => pp(aa_Pro8754844875067278050l_bool(aa_Cod7054345612336956751l_bool(Q,X3),Xa3)) ) ) )
         => ( pp(aa_set7459647962600473637l_bool(aa_set2046992081204100426l_bool(ord_le2202040463148982292atural,A4),collec1991479681304692691atural(produc5868410056131333498l_bool(P))))
           => pp(aa_set7459647962600473637l_bool(aa_set2046992081204100426l_bool(ord_le2202040463148982292atural,A4),collec1991479681304692691atural(produc5868410056131333498l_bool(Q)))) ) ) ) ) )).

% Collect_split_mono_strong
fof(fact_534_Collect__split__mono__strong,axiom,(
    ! [X7,A4,Y5,P,Q] :
      ( X7 = image_6251736531144035663action(produc3089225533250117581list_f,A4)
     => ( Y5 = aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,produc8710481132536983823list_f),A4)
       => ( ! [X3] :
              ( member4650752750499974146action(X3,X7)
             => ! [Xa3] :
                  ( member6304641671555014644list_f(Xa3,Y5)
                 => ( pp(aa_Pro4904543688695909180f_bool(aa_fin426239777789757162f_bool(P,X3),Xa3))
                   => pp(aa_Pro4904543688695909180f_bool(aa_fin426239777789757162f_bool(Q,X3),Xa3)) ) ) )
         => ( pp(aa_set5766309472476915338f_bool(aa_set3359789233003681502f_bool(ord_le3852096572277380649list_f,A4),collec2941370454899091988list_f(produc4709439930048449441f_bool(P))))
           => pp(aa_set5766309472476915338f_bool(aa_set3359789233003681502f_bool(ord_le3852096572277380649list_f,A4),collec2941370454899091988list_f(produc4709439930048449441f_bool(Q)))) ) ) ) ) )).

% Collect_split_mono_strong
fof(fact_535_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,bNF_Grp_nat_nat(A4,F)))))
     => aa_Pro4243173770044397973at_nat(comp_n2711240574518091068at_nat(F,product_fst_nat_nat),Z) = aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_536_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,bNF_Gr7275288873855648526at_nat(A4,F)))))
     => aa_Pro5901169740204579478at_nat(comp_P3189659738270478212at_nat(F,produc3213797794245857475at_nat),Z) = aa_Pro5901169740204579478at_nat(produc6408287024330202629at_nat,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_537_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,Z),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,bNF_Gr2194527004838278172nteger(A4,F)))))
     => comp_f7201406323132290986nteger(F,produc3971164842776949671nteger,Z) = aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_538_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,Z),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,bNF_Gr5054611065658580851atural(A4,F)))))
     => comp_f2906742050339453912atural(F,produc1168782837711296254atural,Z) = aa_Pro7386464516095682491atural(produc3992340709582277180atural,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_539_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,Z),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,bNF_Gr649054686773836434nteger(A4,F)))))
     => comp_f8192611244414835094nteger(F,produc5986598495681327645nteger,Z) = aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_540_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,Z),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,bNF_Gr7186825967973617023nt_int(A4,F)))))
     => comp_f2412628331973903856nt_int(F,produc6655012789309278474nt_int,Z) = aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_541_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,Z),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,bNF_Gr1003679413264351915nt_int(A4,F)))))
     => comp_f8541215233017858632nt_int(F,produc2507970727455213110nt_int,Z) = aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_542_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( member2108296798382401941atural(Z,collec1991479681304692691atural(produc5868410056131333498l_bool(bNF_Gr1183324042980456505atural(A4,F))))
     => comp_C3540846879249570404atural(F,produc497848011034438852atural,Z) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_543_Collect__case__prod__Grp__eqD,axiom,(
    ! [Z,A4,F] :
      ( member1992181931100238290list_f(Z,collec2941370454899091988list_f(produc4709439930048449441f_bool(bNF_Gr6286777782477588504list_f(A4,F))))
     => aa_Pro2582230449628027978list_f(comp_f5362652388678882620list_f(F,produc3089225533250117581list_f),Z) = aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Z) ) )).

% Collect_case_prod_Grp_eqD
fof(fact_544_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P3990188960041576470nteger(produc3971164842776949671nteger,produc63072358922508822nteger(F,G)) = comp_f5781897744313322404nteger(F,produc3971164842776949671nteger) )).

% fst_comp_map_prod
fof(fact_545_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P1036702775515704229nt_int(produc3971164842776949671nteger,produc8646943564923299783nteger(F,G)) = comp_f7225720785758864770nt_int(F,produc2507970727455213110nt_int) )).

% fst_comp_map_prod
fof(fact_546_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P2907937953479450228nteger(produc2507970727455213110nt_int,produc4728319346741315203nt_int(F,G)) = comp_f1565886119101697779nteger(F,produc3971164842776949671nteger) )).

% fst_comp_map_prod
fof(fact_547_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P5310741988796926467nt_int(produc2507970727455213110nt_int,produc8631014097479913524nt_int(F,G)) = comp_f300797508955093201nt_int(F,produc2507970727455213110nt_int) )).

% fst_comp_map_prod
fof(fact_548_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P2998951207316316269atural(produc3971164842776949671nteger,produc9188367097266839807nteger(F,G)) = comp_f7584298453894734714atural(F,produc1168782837711296254atural) )).

% fst_comp_map_prod
fof(fact_549_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P3963986752856745612nteger(produc3971164842776949671nteger,produc1437091937170647584nteger(F,G)) = comp_f2313621508578202660nteger(F,produc5986598495681327645nteger) )).

% fst_comp_map_prod
fof(fact_550_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P1205399366292975225nt_int(produc3971164842776949671nteger,produc1659241349444321267nteger(F,G)) = comp_f6521668100833223810nt_int(F,produc6655012789309278474nt_int) )).

% fst_comp_map_prod
fof(fact_551_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P7680642556388610156nteger(produc1168782837711296254atural,produc2817918400915399083atural(F,G)) = comp_f3311191160968420387nteger(F,produc3971164842776949671nteger) )).

% fst_comp_map_prod
fof(fact_552_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P3901399697021950971nt_int(produc1168782837711296254atural,produc3442593042707087196atural(F,G)) = comp_f7238851778800411137nt_int(F,produc2507970727455213110nt_int) )).

% fst_comp_map_prod
fof(fact_553_fst__comp__map__prod,axiom,(
    ! [F,G] : comp_P4747203175050475926nteger(produc5986598495681327645nteger,produc2464009018090205216nteger(F,G)) = comp_f1391551884146842542nteger(F,produc3971164842776949671nteger) )).

% fst_comp_map_prod
fof(fact_554_snd__comp__map__prod,axiom,(
    ! [F,G] : comp_P7610810914149544718atural(produc6591912806276919810atural,produc6172530018443213064atural(F,G)) = comp_P3067963646784605345atural(G,produc6591912806276919810atural) )).

% snd_comp_map_prod
fof(fact_555_snd__comp__map__prod,axiom,(
    ! [F,G] : comp_P754933049744969497list_f(produc6591912806276919810atural,produc6433193301019619911atural(F,G)) = comp_P4126295255191388280list_f(G,produc8710481132536983823list_f) )).

% snd_comp_map_prod
fof(fact_556_snd__comp__map__prod,axiom,(
    ! [F,G] : comp_P3912863319257206115atural(produc8710481132536983823list_f,produc9125308813900113731list_f(F,G)) = comp_P894719457104077291atural(G,produc6591912806276919810atural) )).

% snd_comp_map_prod
fof(fact_557_snd__comp__map__prod,axiom,(
    ! [F,G] : comp_P4267156721827287172list_f(produc8710481132536983823list_f,produc1848554412176970122list_f(F,G)) = comp_P2673361230361438154list_f(G,produc8710481132536983823list_f) )).

% snd_comp_map_prod
fof(fact_558_fstOp__def,axiom,(
    ! [P,Q,Ac2] : aa_Pro605336214283753216nteger(bNF_fs5551184864110499297nteger(P,Q),Ac2) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Ac2)),aa_Pro4693618923521437820nteger(bNF_pi4641210434737448211nteger(P,Q,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Ac2)),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Ac2))) )).

% fstOp_def
fof(fact_559_fstOp__def,axiom,(
    ! [P,Q,Ac2] : aa_Pro7626634194206414894atural(bNF_fs4803784828902956000atural(P,Q),Ac2) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Ac2)),aa_Pro4262726347734369532atural(bNF_pi6918074208948910866atural(P,Q,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Ac2)),aa_Pro7386464516095682491atural(produc3992340709582277180atural,Ac2))) )).

% fstOp_def
fof(fact_560_fstOp__def,axiom,(
    ! [P,Q,Ac2] : aa_Pro8016721334973800684nteger(bNF_fs3780317907347579883nteger(P,Q),Ac2) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Ac2)),aa_Pro4693618923521437820nteger(bNF_pi5894607287393534749nteger(P,Q,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Ac2)),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Ac2))) )).

% fstOp_def
fof(fact_561_fstOp__def,axiom,(
    ! [P,Q,Ac2] : aa_Pro7619707155024403014nt_int(bNF_fs6111084528178183388nt_int(P,Q),Ac2) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Ac2)),aa_Pro6970504127699319548nt_int(bNF_pi983947869366273038nt_int(P,Q,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Ac2)),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Ac2))) )).

% fstOp_def
fof(fact_562_fstOp__def,axiom,(
    ! [P,Q,Ac2] : aa_Pro7656415901706311326nt_int(bNF_fs2186792319726704816nt_int(P,Q),Ac2) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Ac2)),aa_Pro6970504127699319548nt_int(bNF_pi178345747010392034nt_int(P,Q,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Ac2)),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Ac2))) )).

% fstOp_def
fof(fact_563_rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Ax),Ay)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Bx),By))),transi8609417484261754244at_nat(R)))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Ax),Ay)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3))),transi8609417484261754244at_nat(R)))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Aa),Ba))),R))
               => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(P,A3),B3))
                 => pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Aa),Ba)) ) ) )
         => pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Bx),By)) ) ) ) )).

% rtrancl_induct2
fof(fact_564_rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)),transi4489791620539454750nteger(R))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),transi4489791620539454750nteger(R))
               => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)),R)
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Bx),By)) ) ) ) )).

% rtrancl_induct2
fof(fact_565_rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)),transi4246158250603548021atural(R))
     => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),transi4246158250603548021atural(R))
             => ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)),R)
               => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3))
                 => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Bx),By)) ) ) ) )).

% rtrancl_induct2
fof(fact_566_rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)),transi5211193796143977364nteger(R))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),transi5211193796143977364nteger(R))
               => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)),R)
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Bx),By)) ) ) ) )).

% rtrancl_induct2
fof(fact_567_rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)),transi928579105954741121nt_int(R))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),transi928579105954741121nt_int(R))
             => ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)),R)
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Bx),By)) ) ) ) )).

% rtrancl_induct2
fof(fact_568_rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)),transi9001910261832988845nt_int(R))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Ax),Ay))
       => ( ! [A3,B3,Aa,Ba] :
              ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),transi9001910261832988845nt_int(R))
             => ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)),R)
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Bx),By)) ) ) ) )).

% rtrancl_induct2
fof(fact_569_case__prodI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(F,A),B))
     => pp(aa_Pro7150874649148492216r_bool(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,F),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B))) ) )).

% case_prodI
fof(fact_570_case__prodI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(F,A),B))
     => pp(aa_Pro916321633901839137l_bool(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,F),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B))) ) )).

% case_prodI
fof(fact_571_case__prodI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(F,A),B))
     => pp(aa_Pro3640759179027349698r_bool(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,F),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B))) ) )).

% case_prodI
fof(fact_572_case__prodI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(F,A),B))
     => pp(aa_Pro5031108791230793749t_bool(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,F),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B))) ) )).

% case_prodI
fof(fact_573_case__prodI,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(F,A),B))
     => pp(aa_Pro7591400126937138665t_bool(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,F),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B))) ) )).

% case_prodI
fof(fact_574_pair__less__def,axiom,(
    fun_pair_less = lex_prod_nat_nat(less_than,less_than) )).

% pair_less_def
fof(fact_575_le__sup__iff,axiom,(
    ! [X,Y,Z] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y)),Z))
    <=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Z))
        & pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Y),Z)) ) ) )).

% le_sup_iff
fof(fact_576_sup_Obounded__iff,axiom,(
    ! [B,C2,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,B),C2)),A))
    <=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
        & pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),A)) ) ) )).

% sup.bounded_iff
fof(fact_577_rtrancl__tab_Oequation_I3_J,axiom,(
    ! [R3,Xa4,Xb2,Xc] : transi8137332151331134886at_nat(R3,Xa4,Xb2,Xc) = sup_su2981425912110785871t_unit(bind_P7133822938289884078t_unit(single5216280447982286995at_nat(produc3454366016999414071at_nat(Xa4,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Xb2),Xc))),produc7613932700751717743t_unit(cOMBK_3462217395813459000at_nat(aa_fun762978388704573670t_unit(produc4288560984398973711t_unit,aa_pre3988284201554867738t_unit(aa_fun8620934445070975814t_unit(cOMBC_1831313084446023480t_unit,aa_fun8179310490366260934t_unit(cOMBB_164136767961081285at_nat(cOMBC_1552180646880195170t_unit),aa_pre6878865595929844410t_unit(aa_fun8261945545960088710t_unit(cOMBC_5659729398678793432t_unit,aa_fun8639297843695411718t_unit(cOMBB_2513854330640417733at_nat(cOMBC_2112645637916996866t_unit),aa_fun1398212528012210538t_unit(cOMBB_5276851976296163209at_nat(cOMBB_8619469215816066475at_nat(if_pred_Product_unit)),fequal9188845342289841878at_nat))),single_Product_unit(product_Unity)))),bot_bo2717538794563056311t_unit))))),bind_P7133822938289884078t_unit(single5216280447982286995at_nat(produc3454366016999414071at_nat(Xa4,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Xb2),Xc))),produc7613932700751717743t_unit(cOMBB_725290839343848585at_nat(produc4288560984398973711t_unit,cOMBS_4175389943812038914t_unit(cOMBB_5451314004310722645at_nat(cOMBS_3161903135851905446t_unit,cOMBB_2981639810276598231at_nat(cOMBB_6021740294354723209at_nat(cOMBB_115759876198316351at_nat),cOMBB_3687923245201772409at_nat(cOMBB_3082412447133040017at_nat(bind_P7128388325418652648t_unit),cOMBB_5898222925619342159at_nat(cOMBB_5909589190342145515at_nat(if_pred),cOMBB_4426666140241859373at_nat(aa_fun2412459903328548336t_bool(cOMBB_3950327738894754075at_nat,fNot),cOMBB_4314901741678400945at_nat(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),set_Pr5648618587558075414at_nat)))))),cOMBB_8852436043916570701at_nat(cOMBB_6329840712220438825at_nat(cOMBB_852830008901541831at_nat(produc1731598583106934569t_unit)),cOMBC_7334429563222251924t_unit(cOMBB_5462122356127669157at_nat(cOMBS_4230836484273029706t_unit,cOMBB_1075901795510275469at_nat(cOMBB_1854007403303834855at_nat(cOMBC_5613538993853102528t_unit),cOMBB_258358684656524183at_nat(cOMBB_5103073487066619019at_nat(cOMBB_5679504191179243281at_nat(bind_P8554545925139817076t_unit)),cOMBB_2038197445915012777at_nat(cOMBB_8265912070450743159at_nat(transi882309894880223404at_nat(R3)),cOMBC_5135100225479720282at_nat(cons_P6512896166579812791at_nat))))),cOMBB_6391274120106964943at_nat(cOMBB_858827066190991205at_nat(aa_pre2607734555494874840t_unit(bind_P1979233827931663630t_unit,R3)),cOMBB_7887312347652333625at_nat(cOMBB_2065526613309619203at_nat(produc4288560984398973711t_unit),cOMBC_1833984069380548174t_unit(cOMBB_4765135231851555653at_nat(cOMBC_5275586973196154104t_unit,cOMBB_7178453367878975473at_nat(cOMBB_5189233098434810449at_nat(cOMBC_1831313084446023480t_unit),cOMBB_5458323460549197893at_nat(cOMBB_2113419532209094353at_nat(cOMBB_164136767961081285at_nat(cOMBC_1552180646880195170t_unit)),cOMBC_2019996620745495534t_unit(cOMBB_1053811261885026117at_nat(cOMBC_5328311016465078168t_unit,cOMBB_8260708853994407409at_nat(cOMBB_5476310215842033425at_nat(cOMBC_5659729398678793432t_unit),cOMBB_6412959268813628485at_nat(cOMBB_7465871554117472657at_nat(cOMBB_2513854330640417733at_nat(cOMBC_2112645637916996866t_unit)),cOMBB_5060330993596087689at_nat(cOMBB_4699236211449707007at_nat(cOMBB_5276851976296163209at_nat(cOMBB_8619469215816066475at_nat(if_pred_Product_unit))),cOMBC_213517001142981186t_bool(cOMBB_5471853805901070681at_nat(cOMBB_6298731734558261203at_nat,cOMBB_1317090727945068337at_nat(cOMBC_3379778804465295182t_bool,cOMBB_7968978829756819823at_nat(cOMBB_7619062392956744359at_nat(cOMBB_3950327738894754075at_nat),cOMBB_6079270709258741481at_nat(cOMBB_1143792199142760587at_nat(fconj),fequal9188845342289841878at_nat)))),fequal9188845342289841878at_nat))))),single_Product_unit(product_Unity))))),bot_bo2717538794563056311t_unit)))))))))) )).

% rtrancl_tab.equation(3)
fof(fact_578_rtrancl__tab_Oequation_I3_J,axiom,(
    ! [R3,Xa4,Xb2,Xc] : transi5680681622043916684at_nat(R3,Xa4,Xb2,Xc) = sup_su2981425912110785871t_unit(bind_P4922376816526270484t_unit(single2428174337336239661at_nat(produc7781176426044631377at_nat(Xa4,produc4662710985925991255at_nat(Xb2,Xc))),produc3209168420654000521t_unit(cOMBK_4083529787398425118at_nat(aa_fun4392527517299224678t_unit(produc5963772262439867279t_unit,aa_pre7525886857133037338t_unit(aa_fun8426866602407252166t_unit(cOMBC_3641583497095807544t_unit,aa_fun1489765999007759686t_unit(cOMBB_3023484951760934187at_nat(cOMBC_889979299708343368t_unit),aa_pre6399090365428005818t_unit(aa_fun7899406617516134918t_unit(cOMBC_1152749508414443480t_unit,aa_fun9057668640481527942t_unit(cOMBB_3402300324767598891at_nat(cOMBC_4002404201293077736t_unit),aa_fun7800316760529163626t_unit(cOMBB_3778376931805274659at_nat(cOMBB_1146216699205043729at_nat(if_pred_Product_unit)),fequal3254904519494148796at_nat))),single_Product_unit(product_Unity)))),bot_bo2717538794563056311t_unit))))),bind_P4922376816526270484t_unit(single2428174337336239661at_nat(produc7781176426044631377at_nat(Xa4,produc4662710985925991255at_nat(Xb2,Xc))),produc3209168420654000521t_unit(cOMBB_1697112226982122479at_nat(produc5963772262439867279t_unit,cOMBS_852849108698950684t_unit(cOMBB_1283755341968866465at_nat(cOMBS_468982351371082508t_unit,cOMBB_6690966668755164349at_nat(cOMBB_1855707829989582371at_nat(cOMBB_722061058032413605at_nat),cOMBB_881699588201662943at_nat(cOMBB_9184922037993172215at_nat(bind_P7128388325418652648t_unit),cOMBB_8866385252142140521at_nat(cOMBB_4063035190317856337at_nat(if_pred),cOMBB_426876527336951263at_nat(aa_fun387114033786370596t_bool(cOMBB_2433561337776822657at_nat,fNot),cOMBB_319504641231003415at_nat(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),set_Pr5518436109238095868at_nat)))))),cOMBB_8217109880266147123at_nat(cOMBB_1387502547487320591at_nat(cOMBB_188498006783075885at_nat(produc1731598583106934569t_unit)),cOMBC_1232740382984552954t_unit(cOMBB_4400092321824902565at_nat(cOMBS_6623718919662172080t_unit,cOMBB_4507197582062124019at_nat(cOMBB_918673876994245709at_nat(cOMBC_1225399753699113152t_unit),cOMBB_3040415379833955197at_nat(cOMBB_3860581143808473125at_nat(cOMBB_1013918345445279863at_nat(bind_P1979233827931663630t_unit)),cOMBB_507629349358754857at_nat(cOMBB_5861866454310774391at_nat(transi8068056145586740114at_nat(R3)),cOMBC_971145656680427968at_nat(cons_P8732206157123786781at_nat))))),cOMBB_7735310652399635689at_nat(cOMBB_4872979208479835979at_nat(bind_P5740067618745592206t_unit(R3)),cOMBB_1882989461695051679at_nat(cOMBB_1532903394140347113at_nat(produc5963772262439867279t_unit),cOMBC_2431071010728068942t_unit(cOMBB_4114533540521960107at_nat(cOMBC_3552359484409778910t_unit,cOMBB_999785620500825175at_nat(cOMBB_3855614887157447223at_nat(cOMBC_3641583497095807544t_unit),cOMBB_3879019967057479083at_nat(cOMBB_8991931639003983287at_nat(cOMBB_3023484951760934187at_nat(cOMBC_889979299708343368t_unit)),cOMBC_1386049509011911918t_unit(cOMBB_3220919535631662251at_nat(cOMBC_442156658242747262t_unit,cOMBB_761957234729320535at_nat(cOMBB_1887950562371458807at_nat(cOMBC_1152749508414443480t_unit),cOMBB_1420717140963188651at_nat(cOMBB_7995020808009318519at_nat(cOMBB_3402300324767598891at_nat(cOMBC_4002404201293077736t_unit)),cOMBB_828043341016091171at_nat(cOMBB_3757407158083035749at_nat(cOMBB_3778376931805274659at_nat(cOMBB_1146216699205043729at_nat(if_pred_Product_unit))),cOMBC_6749554223059728118t_bool(cOMBB_754071365825226635at_nat(cOMBB_56352309719135187at_nat,cOMBB_1082243486056276683at_nat(cOMBC_4876564424516006760t_bool,cOMBB_6497752990643608097at_nat(cOMBB_3313237432338228441at_nat(cOMBB_2433561337776822657at_nat),cOMBB_345633376158509955at_nat(cOMBB_6335558003536670961at_nat(fconj),fequal3254904519494148796at_nat)))),fequal3254904519494148796at_nat))))),single_Product_unit(product_Unity))))),bot_bo2717538794563056311t_unit)))))))))) )).

% rtrancl_tab.equation(3)
fof(fact_579_in__rel__def,axiom,(
    ! [R2,X,Y] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(fun_in_rel_nat_nat(R2),X),Y))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y)),R2)) ) )).

% in_rel_def
fof(fact_580_in__rel__def,axiom,(
    ! [R2,X,Y] :
      ( pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(fun_in3916733394112622082at_nat(R2),X),Y))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X),Y)),R2)) ) )).

% in_rel_def
fof(fact_581_in__rel__def,axiom,(
    ! [R2,X,Y] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(fun_in589827024711239208nteger(R2),X),Y))
    <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)),R2)) ) )).

% in_rel_def
fof(fact_582_in__rel__def,axiom,(
    ! [R2,X,Y] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(fun_in6785248504625566079atural(R2),X),Y))
    <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)),R2)) ) )).

% in_rel_def
fof(fact_583_in__rel__def,axiom,(
    ! [R2,X,Y] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(fun_in2379692125740821662nteger(R2),X),Y))
    <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)),R2)) ) )).

% in_rel_def
fof(fact_584_in__rel__def,axiom,(
    ! [R2,X,Y] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(fun_in8461163380030820235nt_int(R2),X),Y))
    <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)),R2)) ) )).

% in_rel_def
fof(fact_585_in__rel__def,axiom,(
    ! [R2,X,Y] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(fun_in702307684740539575nt_int(R2),X),Y))
    <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)),R2)) ) )).

% in_rel_def
fof(fact_586_rtrancl__tab_Oequation_I1_J,axiom,(
    ! [R3,Xa4,Xb2,Xc] : aa_Pro8506890182770087144t_unit(aa_Pro1289996471523352882t_unit(aa_lis2506519724559586180t_unit(transi7776283402896926368at_nat(R3),Xa4),Xb2),Xc) = sup_su2981425912110785871t_unit(bind_P7133822938289884078t_unit(single5216280447982286995at_nat(produc3454366016999414071at_nat(Xa4,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Xb2),Xc))),produc7613932700751717743t_unit(cOMBK_3462217395813459000at_nat(aa_fun762978388704573670t_unit(produc4288560984398973711t_unit,aa_pre3988284201554867738t_unit(aa_fun8620934445070975814t_unit(cOMBC_1831313084446023480t_unit,aa_fun8179310490366260934t_unit(cOMBB_164136767961081285at_nat(cOMBC_1552180646880195170t_unit),aa_pre6878865595929844410t_unit(aa_fun8261945545960088710t_unit(cOMBC_5659729398678793432t_unit,aa_fun8639297843695411718t_unit(cOMBB_2513854330640417733at_nat(cOMBC_2112645637916996866t_unit),aa_fun1398212528012210538t_unit(cOMBB_5276851976296163209at_nat(cOMBB_8619469215816066475at_nat(if_pred_Product_unit)),fequal9188845342289841878at_nat))),single_Product_unit(product_Unity)))),bot_bo2717538794563056311t_unit))))),bind_P7133822938289884078t_unit(single5216280447982286995at_nat(produc3454366016999414071at_nat(Xa4,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Xb2),Xc))),produc7613932700751717743t_unit(cOMBB_725290839343848585at_nat(produc4288560984398973711t_unit,cOMBS_4175389943812038914t_unit(cOMBB_5451314004310722645at_nat(cOMBS_3161903135851905446t_unit,cOMBB_2981639810276598231at_nat(cOMBB_6021740294354723209at_nat(cOMBB_115759876198316351at_nat),cOMBB_3687923245201772409at_nat(cOMBB_3082412447133040017at_nat(bind_P7128388325418652648t_unit),cOMBB_5898222925619342159at_nat(cOMBB_5909589190342145515at_nat(if_pred),cOMBB_4426666140241859373at_nat(aa_fun2412459903328548336t_bool(cOMBB_3950327738894754075at_nat,fNot),cOMBB_4314901741678400945at_nat(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),set_Pr5648618587558075414at_nat)))))),cOMBB_8852436043916570701at_nat(cOMBB_6329840712220438825at_nat(cOMBB_852830008901541831at_nat(produc1731598583106934569t_unit)),cOMBB_1893438810344559013at_nat(cOMBS_7740738590251242802t_unit(cOMBB_8050131321477566705at_nat(cOMBB_6816641055676022475at_nat,aa_fun4285381634782878046t_unit(cOMBB_5679504191179243281at_nat(bind_P8554545925139817076t_unit),R3))),cOMBC_2131939975131778154t_unit(cOMBB_1502820198456722369at_nat(cOMBC_3475263444157777506t_unit,cOMBB_6582776088936761025at_nat(cOMBB_1101662280078262423at_nat(cOMBC_257629196287008334t_unit),cOMBB_244467826459067329at_nat(cOMBB_645862290203618719at_nat(cOMBB_2130115195809794919at_nat(cOMBC_1545691546122322636t_unit)),cOMBB_7993243027322938317at_nat(cOMBB_2277941568467913617at_nat(cOMBB_7200171043471927027at_nat(cOMBB_3082412447133040017at_nat(bind_P7128388325418652648t_unit))),cOMBB_5760826963616815649at_nat(cOMBB_6710114948282586727at_nat(cOMBC_4661858004074810762t_unit),cOMBB_7322608964178846121at_nat(cOMBB_2384414550650649573at_nat(transi7776283402896926368at_nat(R3)),cOMBC_5135100225479720282at_nat(cons_P6512896166579812791at_nat))))))),aa_pre8602123596742896802t_unit(produc1731598583106934569t_unit,single_Product_unit(product_Unity)))))))))) )).

% rtrancl_tab.equation(1)
fof(fact_587_rtrancl__tab_Oequation_I1_J,axiom,(
    ! [R3,Xa4,Xb2,Xc] : aa_Pro1271188383344610766t_unit(aa_Pro4353053020390231602t_unit(aa_lis1417999792129105130t_unit(transi4223599960602944390at_nat(R3),Xa4),Xb2),Xc) = sup_su2981425912110785871t_unit(bind_P4922376816526270484t_unit(single2428174337336239661at_nat(produc7781176426044631377at_nat(Xa4,produc4662710985925991255at_nat(Xb2,Xc))),produc3209168420654000521t_unit(cOMBK_4083529787398425118at_nat(aa_fun4392527517299224678t_unit(produc5963772262439867279t_unit,aa_pre7525886857133037338t_unit(aa_fun8426866602407252166t_unit(cOMBC_3641583497095807544t_unit,aa_fun1489765999007759686t_unit(cOMBB_3023484951760934187at_nat(cOMBC_889979299708343368t_unit),aa_pre6399090365428005818t_unit(aa_fun7899406617516134918t_unit(cOMBC_1152749508414443480t_unit,aa_fun9057668640481527942t_unit(cOMBB_3402300324767598891at_nat(cOMBC_4002404201293077736t_unit),aa_fun7800316760529163626t_unit(cOMBB_3778376931805274659at_nat(cOMBB_1146216699205043729at_nat(if_pred_Product_unit)),fequal3254904519494148796at_nat))),single_Product_unit(product_Unity)))),bot_bo2717538794563056311t_unit))))),bind_P4922376816526270484t_unit(single2428174337336239661at_nat(produc7781176426044631377at_nat(Xa4,produc4662710985925991255at_nat(Xb2,Xc))),produc3209168420654000521t_unit(cOMBB_1697112226982122479at_nat(produc5963772262439867279t_unit,cOMBS_852849108698950684t_unit(cOMBB_1283755341968866465at_nat(cOMBS_468982351371082508t_unit,cOMBB_6690966668755164349at_nat(cOMBB_1855707829989582371at_nat(cOMBB_722061058032413605at_nat),cOMBB_881699588201662943at_nat(cOMBB_9184922037993172215at_nat(bind_P7128388325418652648t_unit),cOMBB_8866385252142140521at_nat(cOMBB_4063035190317856337at_nat(if_pred),cOMBB_426876527336951263at_nat(aa_fun387114033786370596t_bool(cOMBB_2433561337776822657at_nat,fNot),cOMBB_319504641231003415at_nat(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),set_Pr5518436109238095868at_nat)))))),cOMBB_8217109880266147123at_nat(cOMBB_1387502547487320591at_nat(cOMBB_188498006783075885at_nat(produc1731598583106934569t_unit)),cOMBB_4707605103177175077at_nat(cOMBS_1756900555139377458t_unit(cOMBB_9083452616230038999at_nat(cOMBB_6492268301515059403at_nat,aa_fun8280779118801906474t_unit(cOMBB_1013918345445279863at_nat(bind_P1979233827931663630t_unit),R3))),cOMBC_4063351036741475126t_unit(cOMBB_8143124021515221159at_nat(cOMBC_3383123544743041020t_unit,cOMBB_435512371231529639at_nat(cOMBB_1935306088440294345at_nat(cOMBC_7315994157396238746t_unit),cOMBB_6077392791958845607at_nat(cOMBB_6884808994264965945at_nat(cOMBB_7650539644633499085at_nat(cOMBC_5402529741865119846t_unit)),cOMBB_4795075098868226611at_nat(cOMBB_2530141228362346743at_nat(cOMBB_1561256065025312985at_nat(cOMBB_9184922037993172215at_nat(bind_P7128388325418652648t_unit))),cOMBB_4766623185494176647at_nat(cOMBB_7418897035603326669at_nat(cOMBC_8924442749102034186t_unit),cOMBB_8059422838563483177at_nat(cOMBB_2638579188562276581at_nat(transi4223599960602944390at_nat(R3)),cOMBC_971145656680427968at_nat(cons_P8732206157123786781at_nat))))))),aa_pre8602123596742896802t_unit(produc1731598583106934569t_unit,single_Product_unit(product_Unity)))))))))) )).

% rtrancl_tab.equation(1)
fof(fact_588_snd__map__prod,axiom,(
    ! [F,G,X] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro4026365172444991930atural(produc6172530018443213064atural(F,G),X)) = aa_Pro4262726347734369532atural(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X)) )).

% snd_map_prod
fof(fact_589_snd__map__prod,axiom,(
    ! [F,G,X] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro6945104852914167019atural(produc6433193301019619911atural(F,G),X)) = aa_Pro5675988011797720150atural(G,aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,X)) )).

% snd_map_prod
fof(fact_590_snd__map__prod,axiom,(
    ! [F,G,X] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro2654565744390766957list_f(produc9125308813900113731list_f(F,G),X)) = aa_Pro2163047984581542354list_f(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X)) )).

% snd_map_prod
fof(fact_591_snd__map__prod,axiom,(
    ! [F,G,X] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,aa_Pro7428252341792638716list_f(produc1848554412176970122list_f(F,G),X)) = aa_Pro777963009888889592list_f(G,aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,X)) )).

% snd_map_prod
fof(fact_592_finite__induct,axiom,(
    ! [F4,P] :
      ( pp(aa_set3135850010578026034t_bool(finite6177210948735845034at_nat,F4))
     => ( pp(aa_set3135850010578026034t_bool(P,bot_bo2099793752762293965at_nat))
       => ( ! [X3,F5] :
              ( pp(aa_set3135850010578026034t_bool(finite6177210948735845034at_nat,F5))
             => ( ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),F5))
               => ( pp(aa_set3135850010578026034t_bool(P,F5))
                 => pp(aa_set3135850010578026034t_bool(P,insert8211810215607154385at_nat(X3,F5))) ) ) )
         => pp(aa_set3135850010578026034t_bool(P,F4)) ) ) ) )).

% finite_induct
fof(fact_593_finite__induct,axiom,(
    ! [F4,P] :
      ( pp(aa_set1680211184867041100t_bool(finite4392333629123659920at_nat,F4))
     => ( pp(aa_set1680211184867041100t_bool(P,bot_bo5327735625951526323at_nat))
       => ( ! [X3,F5] :
              ( pp(aa_set1680211184867041100t_bool(finite4392333629123659920at_nat,F5))
             => ( ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),F5))
               => ( pp(aa_set1680211184867041100t_bool(P,F5))
                 => pp(aa_set1680211184867041100t_bool(P,insert5050368324300391991at_nat(X3,F5))) ) ) )
         => pp(aa_set1680211184867041100t_bool(P,F4)) ) ) ) )).

% finite_induct
fof(fact_594_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro605336214283753216nteger(produc63072358922508822nteger(F,G),X)) = aa_fun1274623470434842396e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X)) )).

% fst_map_prod
fof(fact_595_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro500179501102819087nteger(produc8646943564923299783nteger(F,G),X)) = aa_fun725494399760559339e_term(F,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X)) )).

% fst_map_prod
fof(fact_596_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro1767059176697221775nt_int(produc4728319346741315203nt_int(F,G),X)) = aa_fun7763722112327144939e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X)) )).

% fst_map_prod
fof(fact_597_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,aa_Pro7656415901706311326nt_int(produc8631014097479913524nt_int(F,G),X)) = aa_fun78455448157554618e_term(F,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X)) )).

% fst_map_prod
fof(fact_598_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro1881300264899033047nteger(produc9188367097266839807nteger(F,G),X)) = aa_fun2603856539051944475e_term(F,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,X)) )).

% fst_map_prod
fof(fact_599_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro2148824989012779638nteger(produc1437091937170647584nteger(F,G),X)) = aa_fun1784510506351320614e_term(F,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,X)) )).

% fst_map_prod
fof(fact_600_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,aa_Pro381531223449366499nteger(produc1659241349444321267nteger(F,G),X)) = aa_fun3263039873566730007e_term(F,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,X)) )).

% fst_map_prod
fof(fact_601_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro7907784746481409879atural(produc2817918400915399083atural(F,G),X)) = aa_fun2534482373496464155e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X)) )).

% fst_map_prod
fof(fact_602_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,aa_Pro2270378316210030438atural(produc3442593042707087196atural(F,G),X)) = aa_fun3119940262582087914e_term(F,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,X)) )).

% fst_map_prod
fof(fact_603_fst__map__prod,axiom,(
    ! [F,G,X] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,aa_Pro8872820292021839222nteger(produc2464009018090205216nteger(F,G),X)) = aa_fun3693577172319249446e_term(F,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,X)) )).

% fst_map_prod
fof(fact_604_min__def,axiom,(
    ! [A,B] :
      ( ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),B))
       => aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,A),B) = A )
      & ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),B))
       => aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,A),B) = B ) ) )).

% min_def
fof(fact_605_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R2))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(F,A)),aa_nat_nat(G,B))),image_5168914502847457605at_nat(produc6977886695330630970at_nat(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_606_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R2))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(F,A)),aa_nat7603221163087113075at_nat(G,B))),image_1119892238107900587at_nat(produc1153188318382123958at_nat(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_607_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),R2))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(F,A)),aa_Pro4243173770044397973at_nat(G,B))),image_6706873702294942047at_nat(produc5156754000680454454at_nat(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_608_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),R2))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_Pro262675715343573244at_nat(F,A)),aa_Pro262675715343573244at_nat(G,B))),image_6321802852832981957at_nat(produc7147751436741673334at_nat(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_609_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R2))
     => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_nat7421442283702589053e_term(F,A)),aa_nat8379393489429068301nteger(G,B))),image_2297897673477433117nteger(produc3672520456469720658nteger(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_610_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R2))
     => pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_nat6502569299123894604e_term(F,A)),aa_nat4424723855478970923nt_int(G,B))),image_3715811364571725484nt_int(produc3426805976037033185nt_int(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_611_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)),R2))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_fun8986063297134161277rm_nat(F,A)),aa_Pro2825113747721566255er_nat(G,B))),image_6839489575515704217at_nat(produc6906078524221674868er_nat(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_612_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)),R2))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_fun3169797829166518348rm_nat(F,A)),aa_Pro6801748904974264397nt_nat(G,B))),image_6550245242443049290at_nat(produc5121499143024131075nt_nat(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_613_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),R2))
     => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_Pro2719419399745674036e_term(F,A)),aa_Pro1630239690174064534nteger(G,B))),image_1338358960625775747nteger(produc3321244597150042068nteger(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_614_map__prod__imageI,axiom,(
    ! [A,B,R2,F,G] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R2))
     => pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,aa_nat3843621882417769084e_term(F,A)),aa_nat7278943374911817763atural(G,B))),image_6493797118160844660atural(produc5645457619127561641atural(F,G),R2))) ) )).

% map_prod_imageI
fof(fact_615_trancl__induct,axiom,(
    ! [A,B,R,P] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),transi6264000038957366511cl_nat(R)))
     => ( ! [Y3] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),Y3)),R))
           => pp(aa_nat_bool(P,Y3)) )
       => ( ! [Y3,Z2] :
              ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),Y3)),transi6264000038957366511cl_nat(R)))
             => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y3),Z2)),R))
               => ( pp(aa_nat_bool(P,Y3))
                 => pp(aa_nat_bool(P,Z2)) ) ) )
         => pp(aa_nat_bool(P,B)) ) ) ) )).

% trancl_induct
fof(fact_616_trancl__induct,axiom,(
    ! [A,B,R,P] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),transi243908449541399842at_nat(R)))
     => ( ! [Y3] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),Y3)),R))
           => pp(aa_Pro2232559814647311250t_bool(P,Y3)) )
       => ( ! [Y3,Z2] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),Y3)),transi243908449541399842at_nat(R)))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Y3),Z2)),R))
               => ( pp(aa_Pro2232559814647311250t_bool(P,Y3))
                 => pp(aa_Pro2232559814647311250t_bool(P,Z2)) ) ) )
         => pp(aa_Pro2232559814647311250t_bool(P,B)) ) ) ) )).

% trancl_induct
fof(fact_617_trancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Ax),Ay)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Bx),By))),transi243908449541399842at_nat(R)))
     => ( ! [A3,B3] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Ax),Ay)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3))),R))
           => pp(aa_nat_bool(aa_nat_fun_nat_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Ax),Ay)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3))),transi243908449541399842at_nat(R)))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Aa),Ba))),R))
               => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(P,A3),B3))
                 => pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Aa),Ba)) ) ) )
         => pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Bx),By)) ) ) ) )).

% trancl_induct2
fof(fact_618_trancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)),transi4177963382248473088nteger(R))
     => ( ! [A3,B3] :
            ( gg_Pro3873016545244360254nteger(B3)
           => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),R)
             => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3)) ) )
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),transi4177963382248473088nteger(R))
               => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)),R)
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Bx),By)) ) ) ) )).

% trancl_induct2
fof(fact_619_trancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)),transi312628918080326231atural(R))
     => ( ! [A3,B3] :
            ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),R)
           => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),transi312628918080326231atural(R))
             => ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)),R)
               => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3))
                 => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Bx),By)) ) ) ) )).

% trancl_induct2
fof(fact_620_trancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)),transi1277664463620755574nteger(R))
     => ( ! [A3,B3] :
            ( gg_Pro3873016545244360254nteger(B3)
           => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),R)
             => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3)) ) )
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),transi1277664463620755574nteger(R))
               => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)),R)
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Aa),Ba)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Bx),By)) ) ) ) )).

% trancl_induct2
fof(fact_621_trancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)),transi425565986406895715nt_int(R))
     => ( ! [A3,B3] :
            ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),R)
           => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),transi425565986406895715nt_int(R))
             => ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)),R)
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Bx),By)) ) ) ) )).

% trancl_induct2
fof(fact_622_trancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)),transi1908933091705503119nt_int(R))
     => ( ! [A3,B3] :
            ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),R)
           => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3)) )
       => ( ! [A3,B3,Aa,Ba] :
              ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),transi1908933091705503119nt_int(R))
             => ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)),R)
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Aa),Ba)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Bx),By)) ) ) ) )).

% trancl_induct2
fof(fact_623_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( member6033505038158179318at_nat(produc5496787636967163197at_nat(A,B),produc7465995907834253422at_nat(A4,B5))
    <=> ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),A4))
        & pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),aa_Pro1853492592809407170at_nat(B5,A))) ) ) )).

% mem_Sigma_iff
fof(fact_624_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( member3919319858682911658at_nat(produc1860397064299428849at_nat(A,B),produc3829605335166519074at_nat(A4,B5))
    <=> ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),A4))
        & pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),aa_Pro6658729501382055926at_nat(B5,A))) ) ) )).

% mem_Sigma_iff
fof(fact_625_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( member8062223511168850704at_nat(produc4662710985925991255at_nat(A,B),produc18557253517588744at_nat(A4,B5))
    <=> ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),A4))
        & pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),aa_Pro6784719962651702620at_nat(B5,A))) ) ) )).

% mem_Sigma_iff
fof(fact_626_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),produc457027306803732586at_nat(A4,B5)))
    <=> ( member_nat(A,A4)
        & member_nat(B,aa_nat_set_nat(B5,A)) ) ) )).

% mem_Sigma_iff
fof(fact_627_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),produc2761391749766926216at_nat(A4,B5)))
    <=> ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),A4))
        & pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),aa_Pro2745879313366468188at_nat(B5,A))) ) ) )).

% mem_Sigma_iff
fof(fact_628_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)),produc2216217370482886178nteger(A4,B5)))
    <=> ( member4312719604404396038e_term(A,A4)
        & member157494554546826820nteger(B,aa_fun4819535994926776846nteger(B5,A)) ) ) )).

% mem_Sigma_iff
fof(fact_629_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)),produc8686794092750807417atural(A4,B5)))
    <=> ( member3406593020217859077e_term(A,A4)
        & member8280416476884352090atural(B,aa_fun2737572712774520421atural(B5,A)) ) ) )).

% mem_Sigma_iff
fof(fact_630_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)),produc4281237713866063000nteger(A4,B5)))
    <=> ( member4565687819040644368e_term(A,A4)
        & member157494554546826820nteger(B,aa_fun5004681828450369668nteger(B5,A)) ) ) )).

% mem_Sigma_iff
fof(fact_631_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)),produc2283267782316988293nt_int(A4,B5)))
    <=> ( member2948136515907314945e_term(A,A4)
        & member5262025264175285858nt_int(B,aa_fun5857771435611940977nt_int(B5,A)) ) ) )).

% mem_Sigma_iff
fof(fact_632_mem__Sigma__iff,axiom,(
    ! [A,B,A4,B5] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)),produc2461002308163165361nt_int(A4,B5)))
    <=> ( member7723273712176309973e_term(A,A4)
        & member5262025264175285858nt_int(B,aa_fun324629106390277533nt_int(B5,A)) ) ) )).

% mem_Sigma_iff
fof(fact_633_case__prod__Pair,axiom,(
    produc9069023536360486177nteger(produc4282985567423050387nteger) = id_Pro5889504707146570544nteger )).

% case_prod_Pair
fof(fact_634_case__prod__Pair,axiom,(
    produc602513715219876175atural(produc2566709293081654762atural) = id_Pro2313341630963819399atural )).

% case_prod_Pair
fof(fact_635_case__prod__Pair,axiom,(
    produc5888382909295257357nteger(produc7384524951051686153nteger) = id_Pro3278377176504248742nteger )).

% case_prod_Pair
fof(fact_636_case__prod__Pair,axiom,(
    produc7428976581010258791nt_int(produc1560874099174258678nt_int) = id_Pro4598293453917596051nt_int )).

% case_prod_Pair
fof(fact_637_case__prod__Pair,axiom,(
    produc3712466714231214015nt_int(produc4852315488734385442nt_int) = id_Pro4189599326890251967nt_int )).

% case_prod_Pair
fof(fact_638_converse__rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Ax),Ay)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Bx),By))),transi8609417484261754244at_nat(R)))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Aa),Ba))),R))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Aa),Ba)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Bx),By))),transi8609417484261754244at_nat(R)))
               => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Aa),Ba))
                 => pp(aa_nat_bool(aa_nat_fun_nat_bool(P,A3),B3)) ) ) )
         => pp(aa_nat_bool(aa_nat_fun_nat_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtrancl_induct2
fof(fact_639_converse__rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Ax),Ay),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)),transi4489791620539454750nteger(R))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba)),R)
               => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Aa),Ba),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Bx),By)),transi4489791620539454750nteger(R))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Aa),Ba))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,A3),B3)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtrancl_induct2
fof(fact_640_converse__rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Ax),Ay),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)),transi4246158250603548021atural(R))
     => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba)),R)
             => ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Aa),Ba),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Bx),By)),transi4246158250603548021atural(R))
               => ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Aa),Ba))
                 => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtrancl_induct2
fof(fact_641_converse__rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Ax),Ay),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)),transi5211193796143977364nteger(R))
     => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( ( gg_Pro3873016545244360254nteger(B3)
                & gg_Pro3873016545244360254nteger(Ba) )
             => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba)),R)
               => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Aa),Ba),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Bx),By)),transi5211193796143977364nteger(R))
                 => ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Aa),Ba))
                   => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,A3),B3)) ) ) ) )
         => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtrancl_induct2
fof(fact_642_converse__rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Ax),Ay),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)),transi928579105954741121nt_int(R))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba)),R)
             => ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Aa),Ba),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Bx),By)),transi928579105954741121nt_int(R))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Aa),Ba))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtrancl_induct2
fof(fact_643_converse__rtrancl__induct2,axiom,(
    ! [Ax,Ay,Bx,By,R,P] :
      ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Ax),Ay),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)),transi9001910261832988845nt_int(R))
     => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Bx),By))
       => ( ! [A3,B3,Aa,Ba] :
              ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba)),R)
             => ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Aa),Ba),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Bx),By)),transi9001910261832988845nt_int(R))
               => ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Aa),Ba))
                 => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,A3),B3)) ) ) )
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(P,Ax),Ay)) ) ) ) )).

% converse_rtrancl_induct2
fof(fact_644_snd__o__Pair__conv__id,axiom,(
    ! [A] : comp_P2099343613683088644nteger(produc7330894765516781285nteger,aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A)) = id_Pro2309048762231606924nteger )).

% snd_o_Pair_conv_id
fof(fact_645_snd__o__Pair__conv__id,axiom,(
    ! [A] : comp_P7599747047401362267atural(produc3992340709582277180atural,aa_fun5152780764703512272atural(produc2566709293081654762atural,A)) = id_Pro1208598647714356386atural )).

% snd_o_Pair_conv_id
fof(fact_646_snd__o__Pair__conv__id,axiom,(
    ! [A] : comp_P3622171552362713722nteger(produc8810156367552308571nteger,aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A)) = id_Pro2309048762231606924nteger )).

% snd_o_Pair_conv_id
fof(fact_647_snd__o__Pair__conv__id,axiom,(
    ! [A] : comp_P7225169503418027367nt_int(produc7622839952223151176nt_int,aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A)) = id_Pro4381231610383771306nt_int )).

% snd_o_Pair_conv_id
fof(fact_648_snd__o__Pair__conv__id,axiom,(
    ! [A] : comp_P1788129801601894547nt_int(produc726383008135262580nt_int,aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A)) = id_Pro4381231610383771306nt_int )).

% snd_o_Pair_conv_id
fof(fact_649_snd__o__Pair__conv__id,axiom,(
    ! [A] : comp_P5917919802303437345atural(produc6591912806276919810atural,produc6639722614265839536atural(A)) = id_Pro1208598647714356386atural )).

% snd_o_Pair_conv_id
fof(fact_650_snd__o__Pair__conv__id,axiom,(
    ! [A] : comp_P5708296701725499586list_f(produc8710481132536983823list_f,produc8331056147679645153list_f(A)) = id_Pro1034130279814846892list_f )).

% snd_o_Pair_conv_id
fof(fact_651_insertE,axiom,(
    ! [A,B,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),insert8211810215607154385at_nat(B,A4)))
     => ( A != B
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),A4)) ) ) )).

% insertE
fof(fact_652_insertE,axiom,(
    ! [A,B,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),insert5050368324300391991at_nat(B,A4)))
     => ( A != B
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),A4)) ) ) )).

% insertE
fof(fact_653_converse__rtrancl__induct,axiom,(
    ! [A,B,R,P] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),transi2905341329935302413cl_nat(R)))
     => ( pp(aa_nat_bool(P,B))
       => ( ! [Y3,Z2] :
              ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y3),Z2)),R))
             => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Z2),B)),transi2905341329935302413cl_nat(R)))
               => ( pp(aa_nat_bool(P,Z2))
                 => pp(aa_nat_bool(P,Y3)) ) ) )
         => pp(aa_nat_bool(P,A)) ) ) ) )).

% converse_rtrancl_induct
fof(fact_654_converse__rtrancl__induct,axiom,(
    ! [A,B,R,P] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),transi8609417484261754244at_nat(R)))
     => ( pp(aa_Pro2232559814647311250t_bool(P,B))
       => ( ! [Y3,Z2] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Y3),Z2)),R))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Z2),B)),transi8609417484261754244at_nat(R)))
               => ( pp(aa_Pro2232559814647311250t_bool(P,Z2))
                 => pp(aa_Pro2232559814647311250t_bool(P,Y3)) ) ) )
         => pp(aa_Pro2232559814647311250t_bool(P,A)) ) ) ) )).

% converse_rtrancl_induct
fof(fact_655_UnI2,axiom,(
    ! [C2,B5,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),sup_su6327502436637775413at_nat(A4,B5))) ) )).

% UnI2
fof(fact_656_UnI2,axiom,(
    ! [C2,B5,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),sup_su718114333110466843at_nat(A4,B5))) ) )).

% UnI2
fof(fact_657_UnI1,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),sup_su6327502436637775413at_nat(A4,B5))) ) )).

% UnI1
fof(fact_658_UnI1,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),sup_su718114333110466843at_nat(A4,B5))) ) )).

% UnI1
fof(fact_659_map__prod_Ocompositionality,axiom,(
    ! [F,G,H,I2,Prod] : aa_Pro6385926395568392904_a_b_c(produc4841148139688540918_a_b_c(F,G),aa_Pro2547187584818457648list_f(produc5505274914705194486list_f(H,I2),Prod)) = aa_Pro5463588683361700988_a_b_c(produc8198191332872049718_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),H),aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),I2)),Prod) )).

% map_prod.compositionality
fof(fact_660_map__prod__compose,axiom,(
    ! [F1,F22,G1,G22] : produc8198191332872049718_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F1),F22),aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G1),G22)) = comp_P7472824288426439864list_f(produc4841148139688540918_a_b_c(F1,G1),produc5505274914705194486list_f(F22,G22)) )).

% map_prod_compose
fof(fact_661_map__prod_Ocomp,axiom,(
    ! [F,G,H,I2] : comp_P7472824288426439864list_f(produc4841148139688540918_a_b_c(F,G),produc5505274914705194486list_f(H,I2)) = produc8198191332872049718_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),H),aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),I2)) )).

% map_prod.comp
fof(fact_662_same__fstI,axiom,(
    ! [P,X,Y6,Y,R2] :
      ( pp(aa_nat_bool(P,X))
     => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y6),Y)),aa_nat7062706319057040595at_nat(R2,X)))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y6)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y))),same_fst_nat_nat(P,R2))) ) ) )).

% same_fstI
fof(fact_663_same__fstI,axiom,(
    ! [P,X,Y6,Y,R2] :
      ( pp(aa_fun8257100190732734890m_bool(P,X))
     => ( member335077259223437328nteger(produc4911887526399440471nteger(Y6,Y),aa_fun81865306170080090nteger(R2,X))
       => member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y6),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)),same_f5965724374525896190nteger(P,R2)) ) ) )).

% same_fstI
fof(fact_664_same__fstI,axiom,(
    ! [P,X,Y6,Y,R2] :
      ( pp(aa_fun545845183243510123m_bool(P,X))
     => ( member3756964795865971088atural(aa_Pro1971126414814181170atural(aa_Pro1220262147015971502atural(produc4480994950612372183atural,Y6),Y),aa_fun1335025524541816987atural(R2,X))
       => member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y6),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)),same_f3520066702339580245atural(P,R2)) ) ) )).

% same_fstI
fof(fact_665_same__fstI,axiom,(
    ! [P,X,Y6,Y,R2] :
      ( pp(aa_fun8146989869410979616m_bool(P,X))
     => ( member335077259223437328nteger(produc4911887526399440471nteger(Y6,Y),aa_fun1454769430281748688nteger(R2,X))
       => member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y6),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)),same_f8337882360309611636nteger(P,R2)) ) ) )).

% same_fstI
fof(fact_666_same__fstI,axiom,(
    ! [P,X,Y6,Y,R2] :
      ( pp(aa_fun1922592006021787503m_bool(P,X))
     => ( member8566619992076573584nt_int(produc3646306378393792727nt_int(Y6,Y),aa_fun7649007877488042143nt_int(R2,X))
       => member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y6),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)),same_f2683036784933431137nt_int(P,R2)) ) ) )).

% same_fstI
fof(fact_667_same__fstI,axiom,(
    ! [P,X,Y6,Y,R2] :
      ( pp(aa_fun1066343515980309147m_bool(P,X))
     => ( member8566619992076573584nt_int(produc3646306378393792727nt_int(Y6,Y),aa_fun4713629944198702027nt_int(R2,X))
       => member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y6),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)),same_f7203479228769520781nt_int(P,R2)) ) ) )).

% same_fstI
fof(fact_668_image__subsetI,axiom,(
    ! [A4,F,B5] :
      ( ! [X3] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro262675715343573244at_nat(F,X3)),B5)) )
     => pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(image_5168914502847457605at_nat(F,A4)),B5)) ) )).

% image_subsetI
fof(fact_669_image__subsetI,axiom,(
    ! [A4,F,B5] :
      ( ! [X3] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(F,X3)),B5)) )
     => pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(image_1119892238107900587at_nat(F,A4)),B5)) ) )).

% image_subsetI
fof(fact_670_image__subsetI,axiom,(
    ! [A4,F,B5] :
      ( ! [X3] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro5901169740204579478at_nat(F,X3)),B5)) )
     => pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(image_6706873702294942047at_nat(F,A4)),B5)) ) )).

% image_subsetI
fof(fact_671_image__subsetI,axiom,(
    ! [A4,F,B5] :
      ( ! [X3] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro7157000481330941564at_nat(F,X3)),B5)) )
     => pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(image_6321802852832981957at_nat(F,A4)),B5)) ) )).

% image_subsetI
fof(fact_672_case__prodI2,axiom,(
    ! [P2,C2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => ( P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)
           => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(C2,A3),B3)) ) )
     => pp(aa_Pro7150874649148492216r_bool(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,C2),P2)) ) )).

% case_prodI2
fof(fact_673_case__prodI2,axiom,(
    ! [P2,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)
         => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(C2,A3),B3)) )
     => pp(aa_Pro916321633901839137l_bool(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,C2),P2)) ) )).

% case_prodI2
fof(fact_674_case__prodI2,axiom,(
    ! [P2,C2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => ( P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)
           => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(C2,A3),B3)) ) )
     => pp(aa_Pro3640759179027349698r_bool(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,C2),P2)) ) )).

% case_prodI2
fof(fact_675_case__prodI2,axiom,(
    ! [P2,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)
         => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(C2,A3),B3)) )
     => pp(aa_Pro5031108791230793749t_bool(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,C2),P2)) ) )).

% case_prodI2
fof(fact_676_case__prodI2,axiom,(
    ! [P2,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)
         => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(C2,A3),B3)) )
     => pp(aa_Pro7591400126937138665t_bool(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,C2),P2)) ) )).

% case_prodI2
fof(fact_677_converse__rtranclE2,axiom,(
    ! [Xa,Xb,Za,Zb,R] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xa),Xb)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Za),Zb))),transi8609417484261754244at_nat(R)))
     => ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xa),Xb) != aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Za),Zb)
       => ~ ! [A3,B3] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xa),Xb)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3))),R))
             => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B3)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Za),Zb))),transi8609417484261754244at_nat(R))) ) ) ) )).

% converse_rtranclE2
fof(fact_678_converse__rtranclE2,axiom,(
    ! [Xa,Xb,Za,Zb,R] :
      ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Xa),Xb),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Za),Zb)),transi4489791620539454750nteger(R))
     => ( aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Xa),Xb) != aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Za),Zb)
       => ~ ! [A3,B3] :
              ( gg_Pro3873016545244360254nteger(B3)
             => ( member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Xa),Xb),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)),R)
               => ~ member7931448637355168588nteger(produc8767237661199492699nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Za),Zb)),transi4489791620539454750nteger(R)) ) ) ) ) )).

% converse_rtranclE2
fof(fact_679_converse__rtranclE2,axiom,(
    ! [Xa,Xb,Za,Zb,R] :
      ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Xa),Xb),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Za),Zb)),transi4246158250603548021atural(R))
     => ( aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Xa),Xb) != aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Za),Zb)
       => ~ ! [A3,B3] :
              ( member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Xa),Xb),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)),R)
             => ~ member1519122167407479034atural(produc6389658630381836169atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,Za),Zb)),transi4246158250603548021atural(R)) ) ) ) )).

% converse_rtranclE2
fof(fact_680_converse__rtranclE2,axiom,(
    ! [Xa,Xb,Za,Zb,R] :
      ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Xa),Xb),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Za),Zb)),transi5211193796143977364nteger(R))
     => ( aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Xa),Xb) != aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Za),Zb)
       => ~ ! [A3,B3] :
              ( gg_Pro3873016545244360254nteger(B3)
             => ( member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Xa),Xb),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)),R)
               => ~ member5037371425510568504nteger(produc6779745771149221959nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Za),Zb)),transi5211193796143977364nteger(R)) ) ) ) ) )).

% converse_rtranclE2
fof(fact_681_converse__rtranclE2,axiom,(
    ! [Xa,Xb,Za,Zb,R] :
      ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Xa),Xb),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Za),Zb)),transi928579105954741121nt_int(R))
     => ( aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Xa),Xb) != aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Za),Zb)
       => ~ ! [A3,B3] :
              ( member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Xa),Xb),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)),R)
             => ~ member5015713543875923218nt_int(produc5372120124174279073nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Za),Zb)),transi928579105954741121nt_int(R)) ) ) ) )).

% converse_rtranclE2
fof(fact_682_converse__rtranclE2,axiom,(
    ! [Xa,Xb,Za,Zb,R] :
      ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Xa),Xb),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Za),Zb)),transi9001910261832988845nt_int(R))
     => ( aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Xa),Xb) != aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Za),Zb)
       => ~ ! [A3,B3] :
              ( member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Xa),Xb),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)),R)
             => ~ member7649561347739665258nt_int(produc5207114200681655801nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Za),Zb)),transi9001910261832988845nt_int(R)) ) ) ) )).

% converse_rtranclE2
fof(fact_683_pred__prod__inject,axiom,(
    ! [P1,P22,A,B] :
      ( pp(aa_Pro7150874649148492216r_bool(basic_8786148452290946551nteger(P1,P22),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)))
    <=> ( pp(aa_fun8257100190732734890m_bool(P1,A))
        & pp(aa_Pro5843519176478241656r_bool(P22,B)) ) ) )).

% pred_prod_inject
fof(fact_684_pred__prod__inject,axiom,(
    ! [P1,P22,A,B] :
      ( pp(aa_Pro916321633901839137l_bool(basic_7419279857980033358atural(P1,P22),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)))
    <=> ( pp(aa_fun545845183243510123m_bool(P1,A))
        & pp(aa_Pro8754844875067278050l_bool(P22,B)) ) ) )).

% pred_prod_inject
fof(fact_685_pred__prod__inject,axiom,(
    ! [P1,P22,A,B] :
      ( pp(aa_Pro3640759179027349698r_bool(basic_3013723479095288941nteger(P1,P22),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)))
    <=> ( pp(aa_fun8146989869410979616m_bool(P1,A))
        & pp(aa_Pro5843519176478241656r_bool(P22,B)) ) ) )).

% pred_prod_inject
fof(fact_686_pred__prod__inject,axiom,(
    ! [P1,P22,A,B] :
      ( pp(aa_Pro5031108791230793749t_bool(basic_4875947187853015898nt_int(P1,P22),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)))
    <=> ( pp(aa_fun1922592006021787503m_bool(P1,A))
        & pp(aa_Pro4501881432599481050t_bool(P22,B)) ) ) )).

% pred_prod_inject
fof(fact_687_pred__prod__inject,axiom,(
    ! [P1,P22,A,B] :
      ( pp(aa_Pro7591400126937138665t_bool(basic_2796480923355871366nt_int(P1,P22),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)))
    <=> ( pp(aa_fun1066343515980309147m_bool(P1,A))
        & pp(aa_Pro4501881432599481050t_bool(P22,B)) ) ) )).

% pred_prod_inject
fof(fact_688_inf__sup__ord_I4_J,axiom,(
    ! [Y,X] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Y),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y))) )).

% inf_sup_ord(4)
fof(fact_689_inf__sup__ord_I3_J,axiom,(
    ! [X,Y] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y))) )).

% inf_sup_ord(3)
fof(fact_690_le__supE,axiom,(
    ! [A,B,X] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B)),X))
     => ~ ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),X))
         => ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),X)) ) ) )).

% le_supE
fof(fact_691_converse__rtranclE,axiom,(
    ! [X,Z,R] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Z)),transi2905341329935302413cl_nat(R)))
     => ( X != Z
       => ~ ! [Y3] :
              ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y3)),R))
             => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y3),Z)),transi2905341329935302413cl_nat(R))) ) ) ) )).

% converse_rtranclE
fof(fact_692_converse__rtranclE,axiom,(
    ! [X,Z,R] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X),Z)),transi8609417484261754244at_nat(R)))
     => ( X != Z
       => ~ ! [Y3] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X),Y3)),R))
             => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Y3),Z)),transi8609417484261754244at_nat(R))) ) ) ) )).

% converse_rtranclE
fof(fact_693_le__supI,axiom,(
    ! [A,X,B] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),X))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),X))
       => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B)),X)) ) ) )).

% le_supI
fof(fact_694_sup__ge1,axiom,(
    ! [X,Y] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y))) )).

% sup_ge1
fof(fact_695_max_Ocobounded1,axiom,(
    ! [A,B] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,A),B))) )).

% max.cobounded1
fof(fact_696_sup__ge2,axiom,(
    ! [Y,X] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Y),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y))) )).

% sup_ge2
fof(fact_697_Id__onI,axiom,(
    ! [A,A4] :
      ( member_nat(A,A4)
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),A)),id_on_nat(A4))) ) )).

% Id_onI
fof(fact_698_Id__onI,axiom,(
    ! [A,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),A)),id_on_2554058798563519774at_nat(A4))) ) )).

% Id_onI
fof(fact_699_Id__onI,axiom,(
    ! [A,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),A4))
     => member8062223511168850704at_nat(produc4662710985925991255at_nat(A,A),id_on_7917584626360399108at_nat(A4)) ) )).

% Id_onI
fof(fact_700_le__supI1,axiom,(
    ! [X,A,B] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),A))
     => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B))) ) )).

% le_supI1
fof(fact_701_le__supI2,axiom,(
    ! [X,B,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),B))
     => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B))) ) )).

% le_supI2
fof(fact_702_sup_Omono,axiom,(
    ! [C2,A,D,B] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),A))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,D),B))
       => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,C2),D)),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B))) ) ) )).

% sup.mono
fof(fact_703_sup__mono,axiom,(
    ! [A,C2,B,D] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),C2))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),D))
       => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B)),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,C2),D))) ) ) )).

% sup_mono
fof(fact_704_extract__Cons__code,axiom,(
    ! [P3,X8,Xs2] :
      ( ( pp(aa_typerep_bool(P3,X8))
       => extract_typerep(P3,aa_lis9041531584263668358yperep(cons_typerep(X8),Xs2)) = aa_Pro3095640615015971554yperep(some_P4742658530298911237yperep,aa_Pro7670417329144945031yperep(aa_lis1893350635152483124yperep(produc2255752811254757084yperep,nil_typerep),aa_lis2760345450568550903yperep(aa_typ5684556066063664508yperep(produc8398273619233227473yperep,X8),Xs2))) )
      & ( ~ pp(aa_typerep_bool(P3,X8))
       => extract_typerep(P3,aa_lis9041531584263668358yperep(cons_typerep(X8),Xs2)) = case_o7657976496830776113yperep(none_P7642766325015749769yperep,produc362396003296346243yperep(cOMBB_5168154828206786744yperep(produc7628607474913760352yperep,cOMBB_1373007174243688340yperep(cOMBB_7462520177858535266yperep(cOMBB_2780684560723742384yperep(some_P4742658530298911237yperep)),cOMBC_104451899224933796yperep(cOMBB_1472777779343922656yperep(cOMBB_3333493938215720265yperep,cOMBB_2455524263481968736yperep(cOMBB_4651361748934511235yperep,cOMBB_4432475366804139056yperep(produc2255752811254757084yperep,cons_typerep(X8)))),produc8398273619233227473yperep)))),extract_typerep(P3,Xs2)) ) ) )).

% extract_Cons_code
fof(fact_705_sup__least,axiom,(
    ! [Y,X,Z] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Y),X))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Z),X))
       => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,Y),Z)),X)) ) ) )).

% sup_least
fof(fact_706_max_Ocobounded2,axiom,(
    ! [B,A] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,A),B))) )).

% max.cobounded2
fof(fact_707_le__iff__sup,axiom,(
    ! [X,Y] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
    <=> aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y) = Y ) )).

% le_iff_sup
fof(fact_708_eventually__prod__filter,axiom,(
    ! [P,F4,G3] :
      ( eventu7017221307461876569nteger(P,prod_f7084514368817594935nteger(F4,G3))
    <=> ? [Pf,Pg] :
          ( eventu2800091161264929639e_term(Pf,F4)
          & eventu3177686391277443747nteger(Pg,G3)
          & ! [X5,Y7] :
              ( gg_Pro3873016545244360254nteger(Y7)
             => ( pp(aa_fun8257100190732734890m_bool(Pf,X5))
               => ( pp(aa_Pro5843519176478241656r_bool(Pg,Y7))
                 => pp(aa_Pro7150874649148492216r_bool(P,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X5),Y7))) ) ) ) ) ) )).

% eventually_prod_filter
fof(fact_709_eventually__prod__filter,axiom,(
    ! [P,F4,G3] :
      ( eventu6837902473195465648atural(P,prod_f2713837840308233614atural(F4,G3))
    <=> ? [Pf,Pg] :
          ( eventu7758845596214632294e_term(Pf,F4)
          & eventu2077236276760193209atural(Pg,G3)
          & ! [X5,Y7] :
              ( pp(aa_fun545845183243510123m_bool(Pf,X5))
             => ( pp(aa_Pro8754844875067278050l_bool(Pg,Y7))
               => pp(aa_Pro916321633901839137l_bool(P,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X5),Y7))) ) ) ) ) )).

% eventually_prod_filter
fof(fact_710_eventually__prod__filter,axiom,(
    ! [P,F4,G3] :
      ( eventu7802938018735894991nteger(P,prod_f7531653498278265005nteger(F4,G3))
    <=> ? [Pf,Pg] :
          ( eventu8917940395037417585e_term(Pf,F4)
          & eventu3177686391277443747nteger(Pg,G3)
          & ! [X5,Y7] :
              ( gg_Pro3873016545244360254nteger(Y7)
             => ( pp(aa_fun8146989869410979616m_bool(Pf,X5))
               => ( pp(aa_Pro5843519176478241656r_bool(Pg,Y7))
                 => pp(aa_Pro3640759179027349698r_bool(P,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X5),Y7))) ) ) ) ) ) )).

% eventually_prod_filter
fof(fact_711_eventually__prod__filter,axiom,(
    ! [P,F4,G3] :
      ( eventu307347211962195388nt_int(P,prod_f8173137906491709338nt_int(F4,G3))
    <=> ? [Pf,Pg] :
          ( eventu895538643436465250e_term(Pf,F4)
          & eventu7082874808314849985nt_int(Pg,G3)
          & ! [X5,Y7] :
              ( pp(aa_fun1922592006021787503m_bool(Pf,X5))
             => ( pp(aa_Pro4501881432599481050t_bool(Pg,Y7))
               => pp(aa_Pro5031108791230793749t_bool(P,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X5),Y7))) ) ) ) ) )).

% eventually_prod_filter
fof(fact_712_eventually__prod__filter,axiom,(
    ! [P,F4,G3] :
      ( eventu7048762671450333928nt_int(P,prod_f7987156664389932230nt_int(F4,G3))
    <=> ? [Pf,Pg] :
          ( eventu1668121777649010230e_term(Pf,F4)
          & eventu7082874808314849985nt_int(Pg,G3)
          & ! [X5,Y7] :
              ( pp(aa_fun1066343515980309147m_bool(Pf,X5))
             => ( pp(aa_Pro4501881432599481050t_bool(Pg,Y7))
               => pp(aa_Pro7591400126937138665t_bool(P,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X5),Y7))) ) ) ) ) )).

% eventually_prod_filter
fof(fact_713_sup_OorderE,axiom,(
    ! [B,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
     => A = aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B) ) )).

% sup.orderE
fof(fact_714_sup_OorderI,axiom,(
    ! [A,B] :
      ( A = aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B)
     => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A)) ) )).

% sup.orderI
fof(fact_715_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(F,A),B)),image_5168914502847457605at_nat(produc2626176000494625587at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_716_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_nat4793067608094048217at_nat(aa_nat7268726946926703970at_nat(F,A),B)),image_1119892238107900587at_nat(produc2382474379627796377at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_717_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro262675715343573244at_nat(aa_Pro8023792847356852296at_nat(F,A),B)),image_6706873702294942047at_nat(produc2982569246487150357at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_718_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( member8280416476884352090atural(aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,A),B),A4)
     => member3756964795865971088atural(aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,A),B),image_561289856197260795atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),A4)) ) )).

% pair_imageI
fof(fact_719_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(F,A),B)),image_6321802852832981957at_nat(produc6744312701629110395at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_720_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro3266150703211780578at_nat(aa_fun3128034053082001686at_nat(F,A),B)),image_6839489575515704217at_nat(produc5911954151858848833at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_721_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro925629398452685892at_nat(aa_fun4289629018356122055at_nat(F,A),B)),image_6550245242443049290at_nat(produc4874494332988030706at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_722_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro7438219776462629832at_nat(aa_fun7391465224403525244at_nat(F,A),B)),image_7138342034938629887at_nat(produc8691174144381840295at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_723_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro1119995659335004236at_nat(aa_fun7944865808426953471at_nat(F,A),B)),image_7721245015989624450at_nat(produc29583747307394090at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_724_pair__imageI,axiom,(
    ! [A,B,A4,F] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)),A4))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro3266150703211780578at_nat(aa_fun8366759590679884576at_nat(F,A),B)),image_1464889339719274915at_nat(produc5411878480578179659at_nat(F),A4))) ) )).

% pair_imageI
fof(fact_725_sup__unique,axiom,(
    ! [F,X,Y] :
      ( ! [X3,Y3] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X3),aa_nat_nat(aa_nat_fun_nat_nat(F,X3),Y3)))
     => ( ! [X3,Y3] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Y3),aa_nat_nat(aa_nat_fun_nat_nat(F,X3),Y3)))
       => ( ! [X3,Y3,Z2] :
              ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Y3),X3))
             => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Z2),X3))
               => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(F,Y3),Z2)),X3)) ) )
         => aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y) = aa_nat_nat(aa_nat_fun_nat_nat(F,X),Y) ) ) ) )).

% sup_unique
fof(fact_726_sup_Oabsorb1,axiom,(
    ! [B,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
     => aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B) = A ) )).

% sup.absorb1
fof(fact_727_sup_Oabsorb2,axiom,(
    ! [A,B] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),B))
     => aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B) = B ) )).

% sup.absorb2
fof(fact_728_sup__absorb1,axiom,(
    ! [Y,X] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,Y),X))
     => aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y) = X ) )).

% sup_absorb1
fof(fact_729_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro8072183222952159042at_nat(aa_fun3804858034681916022at_nat(C2,A),B)))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc3716618507110716833at_nat(C2,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)))) ) )).

% mem_case_prodI
fof(fact_730_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro5330295685620130472at_nat(aa_fun3098381869635060060at_nat(C2,A),B)))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc7846996071466247815at_nat(C2,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)))) ) )).

% mem_case_prodI
fof(fact_731_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro5065032141757191596at_nat(aa_fun4407674144259686495at_nat(C2,A),B)))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc5220494214129680778at_nat(C2,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)))) ) )).

% mem_case_prodI
fof(fact_732_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro1602350909037546002at_nat(aa_fun7997644143818749381at_nat(C2,A),B)))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc5085394703842144496at_nat(C2,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)))) ) )).

% mem_case_prodI
fof(fact_733_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro8072183222952159042at_nat(aa_fun1202306444933629056at_nat(C2,A),B)))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc5409226724224080811at_nat(C2,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)))) ) )).

% mem_case_prodI
fof(fact_734_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro5330295685620130472at_nat(aa_fun730111718248227942at_nat(C2,A),B)))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc8326432594814252433at_nat(C2,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)))) ) )).

% mem_case_prodI
fof(fact_735_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro6675321895958450596at_nat(aa_fun4621462025247951699at_nat(C2,A),B)))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc9029412504376103038at_nat(C2,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)))) ) )).

% mem_case_prodI
fof(fact_736_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro7094643338862014986at_nat(aa_fun4694523806444339897at_nat(C2,A),B)))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc8326714205345120740at_nat(C2,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)))) ) )).

% mem_case_prodI
fof(fact_737_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro6675321895958450596at_nat(aa_fun2120632890448033575at_nat(C2,A),B)))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc9025042679509388370at_nat(C2,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)))) ) )).

% mem_case_prodI
fof(fact_738_mem__case__prodI,axiom,(
    ! [Z,C2,A,B] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro7094643338862014986at_nat(aa_fun5513736782981554317at_nat(C2,A),B)))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc7603330299348430776at_nat(C2,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)))) ) )).

% mem_case_prodI
fof(fact_739_sup__absorb2,axiom,(
    ! [X,Y] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X),Y))
     => aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,X),Y) = Y ) )).

% sup_absorb2
fof(fact_740_sup_OboundedE,axiom,(
    ! [B,C2,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,B),C2)),A))
     => ~ ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
         => ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),A)) ) ) )).

% sup.boundedE
fof(fact_741_case__prod__eta,axiom,(
    ! [F6] : aa_fun4394021921911188166atural(produc8282080750456430313atural,cOMBB_614124024834170628atural(aa_fun874564436610370672atural(cOMBB_2184716832515491012atural,F6),produc3574140220909816553atural)) = F6 )).

% case_prod_eta
fof(fact_742_sup_OboundedI,axiom,(
    ! [B,A,C2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
     => ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),A))
       => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,B),C2)),A)) ) ) )).

% sup.boundedI
fof(fact_743_snd__diag__snd,axiom,(
    comp_P230220204662055659atural(produc7455300194457530885atural,comp_P4943825737035310295atural(cOMBS_6118738780513179056atural(produc4480994950612372183atural,cOMBI_5557065343485138948atural),produc6591912806276919810atural)) = produc6591912806276919810atural )).

% snd_diag_snd
fof(fact_744_snd__diag__snd,axiom,(
    comp_P2690847479783168146list_f(produc5351416724170879361list_f,comp_P8324358310098339598list_f(cOMBS_8232698859660808296list_f(produc7497196274192653651list_f,cOMBI_7289307674472069322list_f),produc8710481132536983823list_f)) = produc8710481132536983823list_f )).

% snd_diag_snd
fof(fact_745_fst__diag__fst,axiom,(
    comp_P8426903182859094766nteger(produc4113325574681568099e_term,comp_f2272477551872351438nteger(cOMBS_3798557623796943976e_term(produc4524505180950781815e_term,cOMBI_114885526001389276e_term),produc3971164842776949671nteger)) = produc3971164842776949671nteger )).

% fst_diag_fst
fof(fact_746_fst__diag__fst,axiom,(
    comp_P516494326397839938atural(produc3155209471897782881e_term,comp_f4100555839605008484atural(cOMBS_1951816572909101928e_term(produc2490241672432993909e_term,cOMBI_448422350011333339e_term),produc1168782837711296254atural)) = produc1168782837711296254atural )).

% fst_diag_fst
fof(fact_747_fst__diag__fst,axiom,(
    comp_P2159505048964989570nteger(produc3827397385110091639e_term,comp_f1812561028672012238nteger(cOMBS_512701030858872424e_term(produc3162429585645302667e_term,cOMBI_1607517148834118630e_term),produc5986598495681327645nteger)) = produc5986598495681327645nteger )).

% fst_diag_fst
fof(fact_748_fst__diag__fst,axiom,(
    comp_P6068656315390496578nt_int(produc5940789772782627929e_term,comp_f3293818662242405484nt_int(cOMBS_7586185255124916072e_term(produc3936376198816598125e_term,cOMBI_276860953521691607e_term),produc6655012789309278474nt_int)) = produc6655012789309278474nt_int )).

% fst_diag_fst
fof(fact_749_fst__diag__fst,axiom,(
    comp_P2508933227626186218nt_int(produc3729210308364921857e_term,comp_f8720440732809935468nt_int(cOMBS_3107017480751799144e_term(produc6842831835191658517e_term,cOMBI_2333703903009992107e_term),produc2507970727455213110nt_int)) = produc2507970727455213110nt_int )).

% fst_diag_fst
fof(fact_750_case__prodE2,axiom,(
    ! [Q,P,Z] :
      ( pp(aa_Pro8832322792688638508l_bool(Q,aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,P),Z)))
     => ~ ! [X3,Y3] :
            ( Z = aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,X3),Y3)
           => ~ pp(aa_Pro8832322792688638508l_bool(Q,aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(P,X3),Y3))) ) ) )).

% case_prodE2
fof(fact_751_case__prodD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro7150874649148492216r_bool(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,F),aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)))
     => pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(F,A),B)) ) )).

% case_prodD
fof(fact_752_case__prodD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro916321633901839137l_bool(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,F),aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)))
     => pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(F,A),B)) ) )).

% case_prodD
fof(fact_753_case__prodD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro3640759179027349698r_bool(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,F),aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)))
     => pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(F,A),B)) ) )).

% case_prodD
fof(fact_754_case__prodD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro5031108791230793749t_bool(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,F),aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)))
     => pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(F,A),B)) ) )).

% case_prodD
fof(fact_755_case__prodD,axiom,(
    ! [F,A,B] :
      ( pp(aa_Pro7591400126937138665t_bool(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,F),aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)))
     => pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(F,A),B)) ) )).

% case_prodD
fof(fact_756_iterate_Opelims,axiom,(
    ! [X,Xa,Xb,Y] :
      ( aa_fun3790775640809306146nteger(iterat5815644986751842463nteger(X,Xa),Xb) = Y
     => ( accp_P3788254003418167145e_term(iterat316102677715376060nteger,produc3639547750066272408e_term(X,produc7905318178607843665e_term(Xa,Xb)))
       => ~ ( ( ( X = zero_z2226904508553997617atural
               => Y = aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Xb) )
              & ( X != zero_z2226904508553997617atural
               => Y = produc4177196607378122295nteger(aa_fun3790775640809306146nteger(Xa,Xb),iterat5815644986751842463nteger(aa_Cod4272041906116450446atural(minus_7197305767214868737atural(X),one_one_Code_natural),Xa)) ) )
           => ~ accp_P3788254003418167145e_term(iterat316102677715376060nteger,produc3639547750066272408e_term(X,produc7905318178607843665e_term(Xa,Xb))) ) ) ) )).

% iterate.pelims
fof(fact_757_iterate_Opelims,axiom,(
    ! [X,Xa,Xb,Y] :
      ( aa_fun5152780764703512272atural(iterat6014495176605441014atural(X,Xa),Xb) = Y
     => ( accp_P1872360919815867286e_term(iterat3908108939669193491atural,produc850367766445998917e_term(X,produc1584688653639713662e_term(Xa,Xb)))
       => ~ ( ( ( X = zero_z2226904508553997617atural
               => Y = aa_fun5152780764703512272atural(produc2566709293081654762atural,Xb) )
              & ( X != zero_z2226904508553997617atural
               => Y = produc1785006893989240271atural(aa_fun5152780764703512272atural(Xa,Xb),iterat6014495176605441014atural(aa_Cod4272041906116450446atural(minus_7197305767214868737atural(X),one_one_Code_natural),Xa)) ) )
           => ~ accp_P1872360919815867286e_term(iterat3908108939669193491atural,produc850367766445998917e_term(X,produc1584688653639713662e_term(Xa,Xb))) ) ) ) )).

% iterate.pelims
fof(fact_758_iterate_Opelims,axiom,(
    ! [X,Xa,Xb,Y] :
      ( aa_fun4101202993852558094nteger(iterat1608938797720696597nteger(X,Xa),Xb) = Y
     => ( accp_P3784717846775054431e_term(iterat8725924597639224882nteger,produc4365180053099629710e_term(X,produc8438918668315419207e_term(Xa,Xb)))
       => ~ ( ( ( X = zero_z2226904508553997617atural
               => Y = aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Xb) )
              & ( X != zero_z2226904508553997617atural
               => Y = produc1837771498964596771nteger(aa_fun4101202993852558094nteger(Xa,Xb),iterat1608938797720696597nteger(aa_Cod4272041906116450446atural(minus_7197305767214868737atural(X),one_one_Code_natural),Xa)) ) )
           => ~ accp_P3784717846775054431e_term(iterat8725924597639224882nteger,produc4365180053099629710e_term(X,produc8438918668315419207e_term(Xa,Xb))) ) ) ) )).

% iterate.pelims
fof(fact_759_iterate_Opelims,axiom,(
    ! [X,Xa,Xb,Y] :
      ( aa_fun1388719692539776744nt_int(iterat6430475438738959874nt_int(X,Xa),Xb) = Y
     => ( accp_P6524376445600399018e_term(iterat8849169842107216159nt_int,produc4718806292800870489e_term(X,produc6537576720041977490e_term(Xa,Xb)))
       => ~ ( ( ( X = zero_z2226904508553997617atural
               => Y = aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,Xb) )
              & ( X != zero_z2226904508553997617atural
               => Y = produc4792007316326371295nt_int(aa_fun1388719692539776744nt_int(Xa,Xb),iterat6430475438738959874nt_int(aa_Cod4272041906116450446atural(minus_7197305767214868737atural(X),one_one_Code_natural),Xa)) ) )
           => ~ accp_P6524376445600399018e_term(iterat8849169842107216159nt_int,produc4718806292800870489e_term(X,produc6537576720041977490e_term(Xa,Xb))) ) ) ) )).

% iterate.pelims
fof(fact_760_iterate_Opelims,axiom,(
    ! [X,Xa,Xb,Y] :
      ( aa_fun7940596247606734144nt_int(iterat5309834586725673774nt_int(X,Xa),Xb) = Y
     => ( accp_P2443355490216151254e_term(iterat569110748504860235nt_int,produc4994578978181236869e_term(X,produc7735940333619011774e_term(Xa,Xb)))
       => ~ ( ( ( X = zero_z2226904508553997617atural
               => Y = aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Xb) )
              & ( X != zero_z2226904508553997617atural
               => Y = produc7538727770948494391nt_int(aa_fun7940596247606734144nt_int(Xa,Xb),iterat5309834586725673774nt_int(aa_Cod4272041906116450446atural(minus_7197305767214868737atural(X),one_one_Code_natural),Xa)) ) )
           => ~ accp_P2443355490216151254e_term(iterat569110748504860235nt_int,produc4994578978181236869e_term(X,produc7735940333619011774e_term(Xa,Xb))) ) ) ) )).

% iterate.pelims
fof(fact_761_sup_Oorder__iff,axiom,(
    ! [B,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
    <=> A = aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B) ) )).

% sup.order_iff
fof(fact_762_top__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(top_to7157997983867680761t_bool,X4),Xa2))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Xa2)),top_to4669805908274784177at_nat)) ) )).

% top_empty_eq2
fof(fact_763_top__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(top_to5737982718198795773t_bool,X4),Xa2))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X4),Xa2)),top_to8454300755403694231at_nat)) ) )).

% top_empty_eq2
fof(fact_764_top__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(top_to3690524595604944923r_bool,X4),Xa2))
    <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X4),Xa2)),top_to3823906760630574279nteger)) ) )).

% top_empty_eq2
fof(fact_765_top__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(top_to1894867223586757508l_bool,X4),Xa2))
    <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X4),Xa2)),top_to6594682765904251294atural)) ) )).

% top_empty_eq2
fof(fact_766_top__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(top_to5714095241469362981r_bool,X4),Xa2))
    <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X4),Xa2)),top_to1464508391925608509nteger)) ) )).

% top_empty_eq2
fof(fact_767_top__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(top_to3603260791386930296t_bool,X4),Xa2))
    <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X4),Xa2)),top_to6478485262153701802nt_int)) ) )).

% top_empty_eq2
fof(fact_768_top__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(top_to2163609019492969036t_bool,X4),Xa2))
    <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X4),Xa2)),top_to8792140074891071702nt_int)) ) )).

% top_empty_eq2
fof(fact_769_sup_Ocobounded1,axiom,(
    ! [A,B] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B))) )).

% sup.cobounded1
fof(fact_770_case__prod__Pair__iden,axiom,(
    ! [P2] : aa_Pro605336214283753216nteger(produc9069023536360486177nteger(produc4282985567423050387nteger),P2) = P2 )).

% case_prod_Pair_iden
fof(fact_771_case__prod__Pair__iden,axiom,(
    ! [P2] : aa_Pro7626634194206414894atural(produc602513715219876175atural(produc2566709293081654762atural),P2) = P2 )).

% case_prod_Pair_iden
fof(fact_772_case__prod__Pair__iden,axiom,(
    ! [P2] : aa_Pro8016721334973800684nteger(produc5888382909295257357nteger(produc7384524951051686153nteger),P2) = P2 )).

% case_prod_Pair_iden
fof(fact_773_case__prod__Pair__iden,axiom,(
    ! [P2] : aa_Pro7619707155024403014nt_int(produc7428976581010258791nt_int(produc1560874099174258678nt_int),P2) = P2 )).

% case_prod_Pair_iden
fof(fact_774_case__prod__Pair__iden,axiom,(
    ! [P2] : aa_Pro7656415901706311326nt_int(produc3712466714231214015nt_int(produc4852315488734385442nt_int),P2) = P2 )).

% case_prod_Pair_iden
fof(fact_775_sup_Ocobounded2,axiom,(
    ! [B,A] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B))) )).

% sup.cobounded2
fof(fact_776_sup_Oabsorb__iff1,axiom,(
    ! [B,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,B),A))
    <=> aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B) = A ) )).

% sup.absorb_iff1
fof(fact_777_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => ( P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)
           => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro8072183222952159042at_nat(aa_fun3804858034681916022at_nat(C2,A3),B3))) ) )
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc3716618507110716833at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_778_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => ( P2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A3),B3)
           => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro5330295685620130472at_nat(aa_fun3098381869635060060at_nat(C2,A3),B3))) ) )
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc7846996071466247815at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_779_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro5065032141757191596at_nat(aa_fun4407674144259686495at_nat(C2,A3),B3))) )
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc5220494214129680778at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_780_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A3),B3)
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro1602350909037546002at_nat(aa_fun7997644143818749381at_nat(C2,A3),B3))) )
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc5085394703842144496at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_781_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => ( P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)
           => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro8072183222952159042at_nat(aa_fun1202306444933629056at_nat(C2,A3),B3))) ) )
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc5409226724224080811at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_782_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( gg_Pro3873016545244360254nteger(B3)
         => ( P2 = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A3),B3)
           => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro5330295685620130472at_nat(aa_fun730111718248227942at_nat(C2,A3),B3))) ) )
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc8326432594814252433at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_783_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro6675321895958450596at_nat(aa_fun4621462025247951699at_nat(C2,A3),B3))) )
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc9029412504376103038at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_784_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A3),B3)
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro7094643338862014986at_nat(aa_fun4694523806444339897at_nat(C2,A3),B3))) )
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc8326714205345120740at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_785_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),aa_Pro6675321895958450596at_nat(aa_fun2120632890448033575at_nat(C2,A3),B3))) )
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),produc9025042679509388370at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_786_mem__case__prodI2,axiom,(
    ! [P2,Z,C2] :
      ( ! [A3,B3] :
          ( P2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A3),B3)
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),aa_Pro7094643338862014986at_nat(aa_fun5513736782981554317at_nat(C2,A3),B3))) )
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),produc7603330299348430776at_nat(C2,P2))) ) )).

% mem_case_prodI2
fof(fact_787_sup_Oabsorb__iff2,axiom,(
    ! [A,B] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,A),B))
    <=> aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B) = B ) )).

% sup.absorb_iff2
fof(fact_788_sup_OcoboundedI1,axiom,(
    ! [C2,A,B] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),A))
     => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B))) ) )).

% sup.coboundedI1
fof(fact_789_sup_OcoboundedI2,axiom,(
    ! [C2,B,A] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),B))
     => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,C2),aa_nat_nat(aa_nat_fun_nat_nat(sup_sup_nat,A),B))) ) )).

% sup.coboundedI2
fof(fact_790_pred__equals__eq2,axiom,(
    ! [R2,S3] :
      ( ! [X5,Xa5] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X5),Xa5)),R2))
        <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X5),Xa5)),S3)) )
    <=> R2 = S3 ) )).

% pred_equals_eq2
fof(fact_791_pred__equals__eq2,axiom,(
    ! [R2,S3] :
      ( ! [X5,Xa5] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X5),Xa5)),R2))
        <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X5),Xa5)),S3)) )
    <=> R2 = S3 ) )).

% pred_equals_eq2
fof(fact_792_pred__equals__eq2,axiom,(
    ! [R2,S3] :
      ( ! [X5,Xa5] :
          ( gg_Pro3873016545244360254nteger(Xa5)
         => ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X5),Xa5)),R2))
          <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X5),Xa5)),S3)) ) )
    <=> R2 = S3 ) )).

% pred_equals_eq2
fof(fact_793_pred__equals__eq2,axiom,(
    ! [R2,S3] :
      ( ! [X5,Xa5] :
          ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X5),Xa5)),R2))
        <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X5),Xa5)),S3)) )
    <=> R2 = S3 ) )).

% pred_equals_eq2
fof(fact_794_pred__equals__eq2,axiom,(
    ! [R2,S3] :
      ( ! [X5,Xa5] :
          ( gg_Pro3873016545244360254nteger(Xa5)
         => ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X5),Xa5)),R2))
          <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X5),Xa5)),S3)) ) )
    <=> R2 = S3 ) )).

% pred_equals_eq2
fof(fact_795_pred__equals__eq2,axiom,(
    ! [R2,S3] :
      ( ! [X5,Xa5] :
          ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X5),Xa5)),R2))
        <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X5),Xa5)),S3)) )
    <=> R2 = S3 ) )).

% pred_equals_eq2
fof(fact_796_pred__equals__eq2,axiom,(
    ! [R2,S3] :
      ( ! [X5,Xa5] :
          ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X5),Xa5)),R2))
        <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X5),Xa5)),S3)) )
    <=> R2 = S3 ) )).

% pred_equals_eq2
fof(fact_797_Collect__case__prod__Grp__in,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,bNF_Grp_nat_nat(A4,F)))))
     => member_nat(aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Z),A4) ) )).

% Collect_case_prod_Grp_in
fof(fact_798_Collect__case__prod__Grp__in,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,bNF_Gr7275288873855648526at_nat(A4,F)))))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro5901169740204579478at_nat(produc3213797794245857475at_nat,Z)),A4)) ) )).

% Collect_case_prod_Grp_in
fof(fact_799_Collect__case__prod__Grp__in,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,Z),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,bNF_Gr2194527004838278172nteger(A4,F)))))
     => member4312719604404396038e_term(aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Z),A4) ) )).

% Collect_case_prod_Grp_in
fof(fact_800_Collect__case__prod__Grp__in,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,Z),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,bNF_Gr5054611065658580851atural(A4,F)))))
     => member3406593020217859077e_term(aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Z),A4) ) )).

% Collect_case_prod_Grp_in
fof(fact_801_Collect__case__prod__Grp__in,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,Z),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,bNF_Gr649054686773836434nteger(A4,F)))))
     => member4565687819040644368e_term(aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Z),A4) ) )).

% Collect_case_prod_Grp_in
fof(fact_802_Collect__case__prod__Grp__in,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,Z),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,bNF_Gr7186825967973617023nt_int(A4,F)))))
     => member2948136515907314945e_term(aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Z),A4) ) )).

% Collect_case_prod_Grp_in
fof(fact_803_Collect__case__prod__Grp__in,axiom,(
    ! [Z,A4,F] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,Z),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,bNF_Gr1003679413264351915nt_int(A4,F)))))
     => member7723273712176309973e_term(aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Z),A4) ) )).

% Collect_case_prod_Grp_in
fof(fact_804_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),image_5168914502847457605at_nat(produc6977886695330630970at_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(F,X3)),aa_nat_nat(G,Y3))
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_805_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),image_6706873702294942047at_nat(produc5156754000680454454at_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(F,X3)),aa_Pro4243173770044397973at_nat(G,Y3))
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_806_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),image_1119892238107900587at_nat(produc1153188318382123958at_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(F,X3)),aa_nat7603221163087113075at_nat(G,Y3))
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_807_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),image_6321802852832981957at_nat(produc7147751436741673334at_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_Pro262675715343573244at_nat(F,X3)),aa_Pro262675715343573244at_nat(G,Y3))
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_808_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),image_6839489575515704217at_nat(produc6906078524221674868er_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( C2 = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_fun8986063297134161277rm_nat(F,X3)),aa_Pro2825113747721566255er_nat(G,Y3))
             => ~ pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)),R2)) ) ) ) )).

% prod_fun_imageE
fof(fact_809_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),image_6550245242443049290at_nat(produc5121499143024131075nt_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_fun3169797829166518348rm_nat(F,X3)),aa_Pro6801748904974264397nt_nat(G,Y3))
           => ~ pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_810_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,C2),image_2297897673477433117nteger(produc3672520456469720658nteger(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,aa_nat7421442283702589053e_term(F,X3)),aa_nat8379393489429068301nteger(G,Y3))
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_811_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,C2),image_3715811364571725484nt_int(produc3426805976037033185nt_int(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,aa_nat6502569299123894604e_term(F,X3)),aa_nat4424723855478970923nt_int(G,Y3))
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_812_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),image_7138342034938629887at_nat(produc5034069981938506240at_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( gg_Pro3873016545244360254nteger(Y3)
           => ( C2 = aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_fun7497178531316255508at_nat(F,X3)),aa_Pro3266150703211780578at_nat(G,Y3))
             => ~ pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)),R2)) ) ) ) )).

% prod_fun_imageE
fof(fact_813_prod__fun__imageE,axiom,(
    ! [C2,F,G,R2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),image_7721245015989624450at_nat(produc5686221710152343755al_nat(F,G),R2)))
     => ~ ! [X3,Y3] :
            ( C2 = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_fun2132847734345915772rm_nat(F,X3)),aa_Pro1523461786693152325al_nat(G,Y3))
           => ~ pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3)),R2)) ) ) )).

% prod_fun_imageE
fof(fact_814_fst__def,axiom,(
    ! [Prod3] : aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Prod3) = produc2648250679809704239e_term(cOMBK_5794734647290304348nteger,Prod3) )).

% fst_def
fof(fact_815_fst__def,axiom,(
    ! [Prod3] : aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Prod3) = produc2887384820467351429e_term(cOMBK_6064020867355542195atural,Prod3) )).

% fst_def
fof(fact_816_fst__def,axiom,(
    ! [Prod3] : aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Prod3) = produc549836512099736239e_term(cOMBK_1658464488470797778nteger,Prod3) )).

% fst_def
fof(fact_817_fst__def,axiom,(
    ! [Prod3] : aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Prod3) = produc9024580578639451789e_term(cOMBK_1216995286146592959nt_int,Prod3) )).

% fst_def
fof(fact_818_fst__def,axiom,(
    ! [Prod3] : aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Prod3) = produc2509169454971777421e_term(cOMBK_1145910323346499051nt_int,Prod3) )).

% fst_def
fof(fact_819_fst__diag__snd,axiom,(
    comp_P230220204662055659atural(produc1537665297809786051atural,comp_P4943825737035310295atural(cOMBS_6118738780513179056atural(produc4480994950612372183atural,cOMBI_5557065343485138948atural),produc6591912806276919810atural)) = produc6591912806276919810atural )).

% fst_diag_snd
fof(fact_820_fst__diag__snd,axiom,(
    comp_P2690847479783168146list_f(produc8633839776129222975list_f,comp_P8324358310098339598list_f(cOMBS_8232698859660808296list_f(produc7497196274192653651list_f,cOMBI_7289307674472069322list_f),produc8710481132536983823list_f)) = produc8710481132536983823list_f )).

% fst_diag_snd
fof(fact_821_snd__diag__fst,axiom,(
    comp_P8426903182859094766nteger(produc2783631417955504037e_term,comp_f2272477551872351438nteger(cOMBS_3798557623796943976e_term(produc4524505180950781815e_term,cOMBI_114885526001389276e_term),produc3971164842776949671nteger)) = produc3971164842776949671nteger )).

% snd_diag_fst
fof(fact_822_snd__diag__fst,axiom,(
    comp_P516494326397839938atural(produc1290259334558652067e_term,comp_f4100555839605008484atural(cOMBS_1951816572909101928e_term(produc2490241672432993909e_term,cOMBI_448422350011333339e_term),produc1168782837711296254atural)) = produc1168782837711296254atural )).

% snd_diag_fst
fof(fact_823_snd__diag__fst,axiom,(
    comp_P2159505048964989570nteger(produc1962447247770960825e_term,comp_f1812561028672012238nteger(cOMBS_512701030858872424e_term(produc3162429585645302667e_term,cOMBI_1607517148834118630e_term),produc5986598495681327645nteger)) = produc5986598495681327645nteger )).

% snd_diag_fst
fof(fact_824_snd__diag__fst,axiom,(
    comp_P6068656315390496578nt_int(produc2441032106448865435e_term,comp_f3293818662242405484nt_int(cOMBS_7586185255124916072e_term(produc3936376198816598125e_term,cOMBI_276860953521691607e_term),produc6655012789309278474nt_int)) = produc6655012789309278474nt_int )).

% snd_diag_fst
fof(fact_825_snd__diag__fst,axiom,(
    comp_P2508933227626186218nt_int(produc6229830494782171203e_term,comp_f8720440732809935468nt_int(cOMBS_3107017480751799144e_term(produc6842831835191658517e_term,cOMBI_2333703903009992107e_term),produc2507970727455213110nt_int)) = produc2507970727455213110nt_int )).

% snd_diag_fst
fof(fact_826_snd__def,axiom,(
    ! [Prod3] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod3) = produc6302656368764539796atural(cOMBK_3223473554123672507atural(cOMBI_5557065343485138948atural),Prod3) )).

% snd_def
fof(fact_827_snd__def,axiom,(
    ! [Prod3] : aa_Pro2582230449628027978list_f(produc8710481132536983823list_f,Prod3) = aa_Pro2582230449628027978list_f(produc6078222734141437267list_f(cOMBK_2699287799416521394action(cOMBI_7289307674472069322list_f)),Prod3) )).

% snd_def
fof(fact_828_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn6260290346630637511nteger(P,Q,Ac2) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,bNF_pi863345106417414871nteger(P,Q,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Ac2),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Ac2))),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Ac2)) )).

% sndOp_def
fof(fact_829_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn6446443032420197949nteger(P,Q,Ac2) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,bNF_pi7905361734986379597nteger(P,Q,aa_Pro3255062042318636430e_term(produc3971164842776949671nteger,Ac2),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Ac2))),aa_Pro8576478981779400380nteger(produc7330894765516781285nteger,Ac2)) )).

% sndOp_def
fof(fact_830_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn4516007541741027679atural(P,Q,Ac2) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,bNF_pi3519353736597965935atural(P,Q,aa_Pro5217105177887748324e_term(produc1168782837711296254atural,Ac2),aa_Pro7386464516095682491atural(produc3992340709582277180atural,Ac2))),aa_Pro7386464516095682491atural(produc3992340709582277180atural,Ac2)) )).

% sndOp_def
fof(fact_831_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn6182132968325704765nteger(P,Q,Ac2) = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,bNF_pi7641051670891886413nteger(P,Q,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Ac2),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Ac2))),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Ac2)) )).

% sndOp_def
fof(fact_832_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn7019113665151670963nteger(P,Q,Ac2) = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,bNF_pi6022459860008609219nteger(P,Q,aa_Pro7852915517588584206e_term(produc5986598495681327645nteger,Ac2),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Ac2))),aa_Pro1639709801714681030nteger(produc8810156367552308571nteger,Ac2)) )).

% sndOp_def
fof(fact_833_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn120784391647550319nt_int(P,Q,Ac2) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,bNF_pi860585480193402495nt_int(P,Q,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Ac2),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Ac2))),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Ac2)) )).

% sndOp_def
fof(fact_834_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn3094666680845897883nt_int(P,Q,Ac2) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,bNF_pi3232219509897108395nt_int(P,Q,aa_Pro1970863770526474220e_term(produc6655012789309278474nt_int,Ac2),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Ac2))),aa_Pro5955847883112758455nt_int(produc7622839952223151176nt_int,Ac2)) )).

% sndOp_def
fof(fact_835_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn6770149483669550235nt_int(P,Q,Ac2) = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,bNF_pi6907702312720760747nt_int(P,Q,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Ac2),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Ac2))),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Ac2)) )).

% sndOp_def
fof(fact_836_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn7810373729934461383nt_int(P,Q,Ac2) = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,bNF_pi1175755751645598935nt_int(P,Q,aa_Pro6937503462419145452e_term(produc2507970727455213110nt_int,Ac2),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Ac2))),aa_Pro3662026205427353739nt_int(produc726383008135262580nt_int,Ac2)) )).

% sndOp_def
fof(fact_837_sndOp__def,axiom,(
    ! [P,Q,Ac2] : bNF_sn516747824238275877atural(P,Q,Ac2) = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,bNF_pi3997839005731006517atural(P,Q,aa_Pro5806155842103967332atural(produc497848011034438852atural,Ac2),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Ac2))),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Ac2)) )).

% sndOp_def
fof(fact_838_prod_Omap__comp,axiom,(
    ! [G1,G22,F1,F22,V] : aa_Pro6385926395568392904_a_b_c(produc4841148139688540918_a_b_c(G1,G22),aa_Pro2547187584818457648list_f(produc5505274914705194486list_f(F1,F22),V)) = aa_Pro5463588683361700988_a_b_c(produc8198191332872049718_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G1),F1),aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G22),F22)),V) )).

% prod.map_comp
fof(fact_839_relChain__def,axiom,(
    ! [R,As] :
      ( bNF_Ca968750328013420230at_nat(R,As)
    <=> ! [I3,J] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,I3),J)),R))
         => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(As,I3)),aa_nat_nat(As,J))) ) ) )).

% relChain_def
fof(fact_840_relChain__def,axiom,(
    ! [R,As] :
      ( bNF_Ca8308629720386654381at_nat(R,As)
    <=> ! [I3,J] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,I3),J)),R))
         => pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_Pro4243173770044397973at_nat(As,I3)),aa_Pro4243173770044397973at_nat(As,J))) ) ) )).

% relChain_def
fof(fact_841_map__prod__def,axiom,(
    ! [F6,G4] : produc4718505701431157174atural(F6,G4) = aa_fun4394021921911188166atural(produc8282080750456430313atural,cOMBC_9156281758219505925atural(cOMBB_3531993188910419714atural(cOMBB_2184716832515491012atural,aa_fun1155053613087964036atural(cOMBB_3012511739362972014atural(produc4480994950612372183atural),F6)),G4)) )).

% map_prod_def
fof(fact_842_pred__subset__eq2,axiom,(
    ! [R4,S4] :
      ( ord_le4899916226251588169t_bool(cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),R4),cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),S4))
    <=> pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(R4),S4)) ) )).

% pred_subset_eq2
fof(fact_843_pred__subset__eq2,axiom,(
    ! [R4,S4] :
      ( ord_le2087689725136068685t_bool(cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),R4),cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),S4))
    <=> pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(R4),S4)) ) )).

% pred_subset_eq2
fof(fact_844_pred__subset__eq2,axiom,(
    ! [R4,S4] :
      ( ord_le7456723041722595787r_bool(cOMBC_1701604444625769262r_bool(cOMBB_2051620022066736427e_term(cOMBC_1849943191596060938r_bool,cOMBB_2794114419360077275e_term(cOMBB_7221559756505762377nteger(member4581088367259704696nteger),produc4282985567423050387nteger)),R4),cOMBC_1701604444625769262r_bool(cOMBB_2051620022066736427e_term(cOMBC_1849943191596060938r_bool,cOMBB_2794114419360077275e_term(cOMBB_7221559756505762377nteger(member4581088367259704696nteger),produc4282985567423050387nteger)),S4))
    <=> pp(aa_set3464050655127758210r_bool(aa_set4966068208888386948r_bool(ord_le5347933966117430903nteger,R4),S4)) ) )).

% pred_subset_eq2
fof(fact_845_pred__subset__eq2,axiom,(
    ! [R4,S4] :
      ( ord_le6524715543917452596l_bool(cOMBC_8519344746081138158l_bool(cOMBB_2417629582155303358e_term(cOMBC_1922632389518567517l_bool,cOMBB_7937736296159719194e_term(cOMBB_6132650689756367373atural(member5458643631506449871atural),produc2566709293081654762atural)),R4),cOMBC_8519344746081138158l_bool(cOMBB_2417629582155303358e_term(cOMBC_1922632389518567517l_bool,cOMBB_7937736296159719194e_term(cOMBB_6132650689756367373atural(member5458643631506449871atural),produc2566709293081654762atural)),S4))
    <=> pp(aa_set4207312397001245291l_bool(aa_set3747303085572403414l_bool(ord_le8467756462758155086atural,R4),S4)) ) )).

% pred_subset_eq2
fof(fact_846_pred__subset__eq2,axiom,(
    ! [R4,S4] :
      ( ord_le1120571524945282261r_bool(cOMBC_2430318800797357742r_bool(cOMBB_680426673656512949e_term(cOMBC_1164745642197396244r_bool,cOMBB_5316222305875338853e_term(cOMBB_3072517373778436405nteger(member6423679177046879214nteger),produc7384524951051686153nteger)),R4),cOMBC_2430318800797357742r_bool(cOMBB_680426673656512949e_term(cOMBC_1164745642197396244r_bool,cOMBB_5316222305875338853e_term(cOMBB_3072517373778436405nteger(member6423679177046879214nteger),produc7384524951051686153nteger)),S4))
    <=> pp(aa_set1981577615330639756r_bool(aa_set2923558947593635992r_bool(ord_le3337582088779512301nteger,R4),S4)) ) )).

% pred_subset_eq2
fof(fact_847_pred__subset__eq2,axiom,(
    ! [R4,S4] :
      ( ord_le1486933126236225064t_bool(cOMBC_4650738552150274286t_bool(cOMBB_9203412279331060138e_term(cOMBC_3685975587475309385t_bool,cOMBB_2463357054279533846e_term(cOMBB_1737989579323207725nt_int(member690604328116145115nt_int),produc1560874099174258678nt_int)),R4),cOMBC_4650738552150274286t_bool(cOMBB_9203412279331060138e_term(cOMBC_3685975587475309385t_bool,cOMBB_2463357054279533846e_term(cOMBB_1737989579323207725nt_int(member690604328116145115nt_int),produc1560874099174258678nt_int)),S4))
    <=> pp(aa_set462754579954174303t_bool(aa_set9008649754896260286t_bool(ord_le5172437211506631514nt_int,R4),S4)) ) )).

% pred_subset_eq2
fof(fact_848_pred__subset__eq2,axiom,(
    ! [R4,S4] :
      ( ord_le4148652360786930684t_bool(cOMBC_1018679855623880686t_bool(cOMBB_944033637513888382e_term(cOMBC_2995058810049920797t_bool,cOMBB_7430342728797892074e_term(cOMBB_952788161300084357nt_int(member500491123954006279nt_int),produc4852315488734385442nt_int)),R4),cOMBC_1018679855623880686t_bool(cOMBB_944033637513888382e_term(cOMBC_2995058810049920797t_bool,cOMBB_7430342728797892074e_term(cOMBB_952788161300084357nt_int(member500491123954006279nt_int),produc4852315488734385442nt_int)),S4))
    <=> pp(aa_set6451871791712458035t_bool(aa_set4292432735413367398t_bool(ord_le172202941055982214nt_int,R4),S4)) ) )).

% pred_subset_eq2
fof(fact_849_conditional__action_Oset__cases,axiom,(
    ! [E,A] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,E),condit6429450166605921294at_nat(A)))
     => A = condit7601234554295360766at_nat(E) ) )).

% conditional_action.set_cases
fof(fact_850_conditional__action_Oset__cases,axiom,(
    ! [E,A] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,E),condit5307000522679409652at_nat(A)))
     => A = condit965456907942171876at_nat(E) ) )).

% conditional_action.set_cases
fof(fact_851_fun_Omap__transfer,axiom,(
    ! [Rb2,Sd] : bNF_re8567837540591029085_a_b_c(bNF_re2373559492235539289_a_b_c(Rb2,Sd),bNF_re930906875496827237_a_b_c(bNF_re5276636924349840729list_f(fequal99650277583572734list_f,Rb2),bNF_re7641334924310632669_a_b_c(fequal99650277583572734list_f,Sd)),comp_P4767578765025054880list_f,comp_P4767578765025054880list_f) )).

% fun.map_transfer
fof(fact_852_case__prod__beta_H,axiom,(
    ! [F,X4] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),X4) = aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,produc1773691148792264405atural(X4)),produc8662200840462671639atural(X4)) )).

% case_prod_beta'
fof(fact_853_conditional__action_Oset__intros,axiom,(
    ! [X1] : pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X1),condit6429450166605921294at_nat(condit7601234554295360766at_nat(X1)))) )).

% conditional_action.set_intros
fof(fact_854_conditional__action_Oset__intros,axiom,(
    ! [X1] : pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X1),condit5307000522679409652at_nat(condit965456907942171876at_nat(X1)))) )).

% conditional_action.set_intros
fof(fact_855_total__on__def,axiom,(
    ! [A4,R] :
      ( pp(aa_set3135850010578026034t_bool(total_on_nat(A4),R))
    <=> ! [X5] :
          ( member_nat(X5,A4)
         => ! [Xa5] :
              ( member_nat(Xa5,A4)
             => ( X5 != Xa5
               => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X5),Xa5)),R))
                  | pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xa5),X5)),R)) ) ) ) ) ) )).

% total_on_def
fof(fact_856_total__on__def,axiom,(
    ! [A4,R] :
      ( pp(aa_set1680211184867041100t_bool(total_3592101749530773125at_nat(A4),R))
    <=> ! [X5] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X5),A4))
         => ! [Xa5] :
              ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Xa5),A4))
             => ( X5 != Xa5
               => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X5),Xa5)),R))
                  | pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Xa5),X5)),R)) ) ) ) ) ) )).

% total_on_def
fof(fact_857_fst__convol,axiom,(
    ! [F,G] : aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,produc3535155421234910955list_f),bNF_co7330362693151061550list_f(F,G)) = F )).

% fst_convol
fof(fact_858_fun_Omap__comp,axiom,(
    ! [G,F,V] : comp_l8432902307485339590list_f(G,aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),V)) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_l6492537726383095040list_f(G,F)),V) )).

% fun.map_comp
fof(fact_859_fun_Omap__comp,axiom,(
    ! [G,F,V] : aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),comp_P4267156721827287172list_f(F,V)) = comp_P1644921750638218854list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),F),V) )).

% fun.map_comp
fof(fact_860_fun_Omap__comp,axiom,(
    ! [G,F,V] : aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),comp_P2673361230361438154list_f(F,V)) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(G,F)),V) )).

% fun.map_comp
fof(fact_861_map__prod__o__convol,axiom,(
    ! [H1,H2,F,G] : comp_P2679607744079208442list_f(produc4841148139688540918_a_b_c(H1,H2),bNF_co5807002252975134268list_f(F,G)) = bNF_co7315529798985115712_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,H1),F),aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,H2),G)) )).

% map_prod_o_convol
fof(fact_862_convol__expand__snd_H,axiom,(
    ! [F,G,H] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,produc3535155421234910955list_f),F) = G
     => ( H = comp_P3270879886602560258list_f(produc7287154213363835177list_f,F)
      <=> bNF_co7330362693151061550list_f(G,H) = F ) ) )).

% convol_expand_snd'
fof(fact_863_convol__expand__snd,axiom,(
    ! [F,G] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,produc3535155421234910955list_f),F) = G
     => bNF_co7330362693151061550list_f(G,comp_P3270879886602560258list_f(produc7287154213363835177list_f,F)) = F ) )).

% convol_expand_snd
fof(fact_864_convol__o,axiom,(
    ! [F,G,H] : comp_P3349191292975441602list_f(bNF_co3276643461748138758_a_b_c(F,G),H) = bNF_co7315529798985115712_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),H),aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),H)) )).

% convol_o
fof(fact_865_conditional__action_Omap__comp,axiom,(
    ! [G,F,V] : condit3995630822656669714_a_b_c(G,aa_con6974328736262822752list_f(condit4069896782405135150list_f(F),V)) = condit1468111593096988280_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),F),V) )).

% conditional_action.map_comp
fof(fact_866_conditional__action_Opred__cong,axiom,(
    ! [X,Ya,P,Pa] :
      ( X = Ya
     => ( ! [Z2] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z2),condit6429450166605921294at_nat(Ya)))
           => ( pp(aa_Pro2232559814647311250t_bool(P,Z2))
            <=> pp(aa_Pro2232559814647311250t_bool(Pa,Z2)) ) )
       => ( condit2957664943879695485at_nat(P,X)
        <=> condit2957664943879695485at_nat(Pa,Ya) ) ) ) )).

% conditional_action.pred_cong
fof(fact_867_conditional__action_Opred__cong,axiom,(
    ! [X,Ya,P,Pa] :
      ( X = Ya
     => ( ! [Z2] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z2),condit5307000522679409652at_nat(Ya)))
           => ( pp(aa_Pro6098352494050694700t_bool(P,Z2))
            <=> pp(aa_Pro6098352494050694700t_bool(Pa,Z2)) ) )
       => ( condit2125367562630040035at_nat(P,X)
        <=> condit2125367562630040035at_nat(Pa,Ya) ) ) ) )).

% conditional_action.pred_cong
fof(fact_868_rewriteL__comp__comp,axiom,(
    ! [F,G,L,H] :
      ( comp_l6492537726383095040list_f(F,G) = L
     => comp_l8432902307485339590list_f(F,aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),H)) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L),H) ) )).

% rewriteL_comp_comp
fof(fact_869_rewriteL__comp__comp,axiom,(
    ! [F,G,L,H] :
      ( comp_P5271726855292207526list_f(F,G) = L
     => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),comp_P2673361230361438154list_f(G,H)) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L),H) ) )).

% rewriteL_comp_comp
fof(fact_870_rewriteL__comp__comp,axiom,(
    ! [F,G,L,H] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G) = L
     => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),comp_P4267156721827287172list_f(G,H)) = comp_P1644921750638218854list_f(L,H) ) )).

% rewriteL_comp_comp
fof(fact_871_pair__in__Id__conv,axiom,(
    ! [A,B] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),id_nat))
    <=> A = B ) )).

% pair_in_Id_conv
fof(fact_872_pair__in__Id__conv,axiom,(
    ! [A,B] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),id_Pro2258643101195443293at_nat))
    <=> A = B ) )).

% pair_in_Id_conv
fof(fact_873_typerep__conditional__action__def,axiom,(
    ! [T] : typere4123026268246276339action(T) = typerep(literal2(fFalse,fTrue,fTrue,fFalse,fFalse,fFalse,fTrue,literal2(fTrue,fTrue,fTrue,fFalse,fTrue,fFalse,fTrue,literal2(fTrue,fTrue,fFalse,fFalse,fTrue,fFalse,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,fTrue,literal2(fTrue,fFalse,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,fTrue,literal2(fTrue,fFalse,fTrue,fFalse,fFalse,fTrue,fTrue,literal2(fFalse,fTrue,fTrue,fTrue,fFalse,fTrue,fFalse,literal2(fTrue,fTrue,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fFalse,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fFalse,fTrue,fTrue,literal2(fTrue,fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,fTrue,literal2(fTrue,fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fFalse,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fFalse,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fFalse,fFalse,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fTrue,fTrue,fTrue,fFalse,fTrue,literal2(fTrue,fFalse,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fFalse,fFalse,fFalse,fTrue,fTrue,literal2(fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,fTrue,literal2(fTrue,fFalse,fFalse,fTrue,fFalse,fTrue,fTrue,literal2(fTrue,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,literal2(fFalse,fTrue,fTrue,fTrue,fFalse,fTrue,fTrue,zero_zero_literal)))))))))))))))))))))))))),aa_lis9041531584263668358yperep(cons_typerep(typere7107042215916526635action(type_lock_action)),nil_typerep)) )).

% typerep_conditional_action_def
fof(fact_874_rewriteR__comp__comp,axiom,(
    ! [G,H,R,F] :
      ( comp_P4267156721827287172list_f(G,H) = R
     => comp_P1644921750638218854list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),H) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),R) ) )).

% rewriteR_comp_comp
fof(fact_875_rewriteR__comp__comp,axiom,(
    ! [G,H,R,F] :
      ( comp_P2673361230361438154list_f(G,H) = R
     => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(F,G)),H) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),R) ) )).

% rewriteR_comp_comp
fof(fact_876_rewriteR__comp__comp,axiom,(
    ! [G,H,R,F] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),H) = R
     => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_l6492537726383095040list_f(F,G)),H) = comp_l8432902307485339590list_f(F,R) ) )).

% rewriteR_comp_comp
fof(fact_877_refl__on__def,axiom,(
    ! [A5,R3] :
      ( pp(aa_set3135850010578026034t_bool(refl_on_nat(A5),R3))
    <=> ( pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(R3),produc457027306803732586at_nat(A5,cOMBK_set_nat_nat(A5))))
        & ! [X5] :
            ( member_nat(X5,A5)
           => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X5),X5)),R3)) ) ) ) )).

% refl_on_def
fof(fact_878_refl__on__def,axiom,(
    ! [A5,R3] :
      ( pp(aa_set1680211184867041100t_bool(refl_o7122697186039111552at_nat(A5),R3))
    <=> ( pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(R3),produc2761391749766926216at_nat(A5,cOMBK_4933461867592223342at_nat(A5))))
        & ! [X5] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X5),A5))
           => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X5),X5)),R3)) ) ) ) )).

% refl_on_def
fof(fact_879_conditional__action_Opred__mono__strong,axiom,(
    ! [P,X,Pa] :
      ( condit2957664943879695485at_nat(P,X)
     => ( ! [Z2] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z2),condit6429450166605921294at_nat(X)))
           => ( pp(aa_Pro2232559814647311250t_bool(P,Z2))
             => pp(aa_Pro2232559814647311250t_bool(Pa,Z2)) ) )
       => condit2957664943879695485at_nat(Pa,X) ) ) )).

% conditional_action.pred_mono_strong
fof(fact_880_conditional__action_Opred__mono__strong,axiom,(
    ! [P,X,Pa] :
      ( condit2125367562630040035at_nat(P,X)
     => ( ! [Z2] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z2),condit5307000522679409652at_nat(X)))
           => ( pp(aa_Pro6098352494050694700t_bool(P,Z2))
             => pp(aa_Pro6098352494050694700t_bool(Pa,Z2)) ) )
       => condit2125367562630040035at_nat(Pa,X) ) ) )).

% conditional_action.pred_mono_strong
fof(fact_881_rewriteL__comp__comp2,axiom,(
    ! [F,G,L1,L2,H,R] :
      ( comp_l6492537726383095040list_f(F,G) = comp_P5271726855292207526list_f(L1,L2)
     => ( comp_P2673361230361438154list_f(L2,H) = R
       => comp_l8432902307485339590list_f(F,aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),H)) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L1),R) ) ) )).

% rewriteL_comp_comp2
fof(fact_882_rewriteL__comp__comp2,axiom,(
    ! [F,G,L1,L2,H,R] :
      ( comp_P5271726855292207526list_f(F,G) = comp_l6492537726383095040list_f(L1,L2)
     => ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L2),H) = R
       => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),comp_P2673361230361438154list_f(G,H)) = comp_l8432902307485339590list_f(L1,R) ) ) )).

% rewriteL_comp_comp2
fof(fact_883_rewriteL__comp__comp2,axiom,(
    ! [F,G,L1,L2,H,R] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L1),L2)
     => ( comp_P4267156721827287172list_f(L2,H) = R
       => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),comp_P4267156721827287172list_f(G,H)) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L1),R) ) ) )).

% rewriteL_comp_comp2
fof(fact_884_rewriteR__comp__comp2,axiom,(
    ! [G,H,R1,R22,F,L] :
      ( comp_P4267156721827287172list_f(G,H) = comp_P2673361230361438154list_f(R1,R22)
     => ( comp_P5271726855292207526list_f(F,R1) = L
       => comp_P1644921750638218854list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),G),H) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L),R22) ) ) )).

% rewriteR_comp_comp2
fof(fact_885_rewriteR__comp__comp2,axiom,(
    ! [G,H,R1,R22,F,L] :
      ( comp_P2673361230361438154list_f(G,H) = comp_P4267156721827287172list_f(R1,R22)
     => ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),R1) = L
       => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(F,G)),H) = comp_P1644921750638218854list_f(L,R22) ) ) )).

% rewriteR_comp_comp2
fof(fact_886_rewriteR__comp__comp2,axiom,(
    ! [G,H,R1,R22,F,L] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),H) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,R1),R22)
     => ( comp_l6492537726383095040list_f(F,R1) = L
       => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_l6492537726383095040list_f(F,G)),H) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,L),R22) ) ) )).

% rewriteR_comp_comp2
fof(fact_887_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( member6033505038158179318at_nat(C2,produc7465995907834253422at_nat(A4,B5))
     => ~ ! [X3] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
           => ! [Y3] :
                ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Y3),aa_Pro1853492592809407170at_nat(B5,X3)))
               => C2 != produc5496787636967163197at_nat(X3,Y3) ) ) ) )).

% SigmaE
fof(fact_888_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( member3919319858682911658at_nat(C2,produc3829605335166519074at_nat(A4,B5))
     => ~ ! [X3] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
           => ! [Y3] :
                ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Y3),aa_Pro6658729501382055926at_nat(B5,X3)))
               => C2 != produc1860397064299428849at_nat(X3,Y3) ) ) ) )).

% SigmaE
fof(fact_889_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( member8062223511168850704at_nat(C2,produc18557253517588744at_nat(A4,B5))
     => ~ ! [X3] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
           => ! [Y3] :
                ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Y3),aa_Pro6784719962651702620at_nat(B5,X3)))
               => C2 != produc4662710985925991255at_nat(X3,Y3) ) ) ) )).

% SigmaE
fof(fact_890_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),produc457027306803732586at_nat(A4,B5)))
     => ~ ! [X3] :
            ( member_nat(X3,A4)
           => ! [Y3] :
                ( member_nat(Y3,aa_nat_set_nat(B5,X3))
               => C2 != aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3) ) ) ) )).

% SigmaE
fof(fact_891_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),produc2761391749766926216at_nat(A4,B5)))
     => ~ ! [X3] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
           => ! [Y3] :
                ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Y3),aa_Pro2745879313366468188at_nat(B5,X3)))
               => C2 != aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),Y3) ) ) ) )).

% SigmaE
fof(fact_892_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,C2),produc2216217370482886178nteger(A4,B5)))
     => ~ ! [X3] :
            ( member4312719604404396038e_term(X3,A4)
           => ! [Y3] :
                ( gg_Pro3873016545244360254nteger(Y3)
               => ( member157494554546826820nteger(Y3,aa_fun4819535994926776846nteger(B5,X3))
                 => C2 != aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3) ) ) ) ) )).

% SigmaE
fof(fact_893_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,C2),produc8686794092750807417atural(A4,B5)))
     => ~ ! [X3] :
            ( member3406593020217859077e_term(X3,A4)
           => ! [Y3] :
                ( member8280416476884352090atural(Y3,aa_fun2737572712774520421atural(B5,X3))
               => C2 != aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3) ) ) ) )).

% SigmaE
fof(fact_894_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,C2),produc4281237713866063000nteger(A4,B5)))
     => ~ ! [X3] :
            ( member4565687819040644368e_term(X3,A4)
           => ! [Y3] :
                ( gg_Pro3873016545244360254nteger(Y3)
               => ( member157494554546826820nteger(Y3,aa_fun5004681828450369668nteger(B5,X3))
                 => C2 != aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3) ) ) ) ) )).

% SigmaE
fof(fact_895_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,C2),produc2283267782316988293nt_int(A4,B5)))
     => ~ ! [X3] :
            ( member2948136515907314945e_term(X3,A4)
           => ! [Y3] :
                ( member5262025264175285858nt_int(Y3,aa_fun5857771435611940977nt_int(B5,X3))
               => C2 != aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3) ) ) ) )).

% SigmaE
fof(fact_896_SigmaE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,C2),produc2461002308163165361nt_int(A4,B5)))
     => ~ ! [X3] :
            ( member7723273712176309973e_term(X3,A4)
           => ! [Y3] :
                ( member5262025264175285858nt_int(Y3,aa_fun324629106390277533nt_int(B5,X3))
               => C2 != aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3) ) ) ) )).

% SigmaE
fof(fact_897_comp__transfer,axiom,(
    ! [B5,C3,A4] : bNF_re8567837540591029085_a_b_c(bNF_re2373559492235539289_a_b_c(B5,C3),bNF_re930906875496827237_a_b_c(bNF_re5276636924349840729list_f(A4,B5),bNF_re7641334924310632669_a_b_c(A4,C3)),comp_P4767578765025054880list_f,comp_P4767578765025054880list_f) )).

% comp_transfer
fof(fact_898_o__rsp_I1_J,axiom,(
    ! [R23,R32,R12] : bNF_re8567837540591029085_a_b_c(bNF_re2373559492235539289_a_b_c(R23,R32),bNF_re930906875496827237_a_b_c(bNF_re5276636924349840729list_f(R12,R23),bNF_re7641334924310632669_a_b_c(R12,R32)),comp_P4767578765025054880list_f,comp_P4767578765025054880list_f) )).

% o_rsp(1)
fof(fact_899_o__rsp_I2_J,axiom,(
    ! [R12] : bNF_re8567837540591029085_a_b_c(fequal867972973346882202_a_b_c,bNF_re930906875496827237_a_b_c(bNF_re5276636924349840729list_f(R12,fequal8058590983366049736list_f),bNF_re7641334924310632669_a_b_c(R12,fequal170887312758788190_a_b_c)),comp_P4767578765025054880list_f,comp_P4767578765025054880list_f) )).

% o_rsp(2)
fof(fact_900_next_Osimps,axiom,(
    ! [V,W] : next(aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,V),W)) = aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Cod4272041906116450446atural(plus_p4538020629002901425atural(aa_Cod4272041906116450446atural(minus_shift(numera5444537566228673987atural(bit0(bit1(bit0(bit1(bit0(bit1(bit0(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(one))))))))))))))))))))))))))))))),aa_Cod4272041906116450446atural(minus_shift(numera5444537566228673987atural(bit1(bit1(bit0(bit1(bit0(bit1(bit0(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(one))))))))))))))))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(modulo8411746178871703098atural(V),numera5444537566228673987atural(bit0(bit0(bit1(bit0(bit0(bit1(bit0(bit1(bit1(bit0(bit0(bit0(bit1(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit0(bit1(bit1(bit1(bit0(bit0(bit1(bit0(bit0(bit0(bit1(bit1(bit1(bit0(bit0(one)))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(divide5121882707175180666atural(V),numera5444537566228673987atural(bit0(bit0(bit1(bit0(bit0(bit1(bit0(bit1(bit1(bit0(bit0(bit0(bit1(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit1(bit1(bit0(bit0(bit1(bit1(bit0(bit1(bit1(bit1(bit1(bit1(bit0(one))))))))))))))))),aa_Cod4272041906116450446atural(plus_p4538020629002901425atural(aa_Cod4272041906116450446atural(minus_shift(numera5444537566228673987atural(bit1(bit1(bit1(bit0(bit0(bit0(bit0(bit0(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(one))))))))))))))))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(modulo8411746178871703098atural(W),numera5444537566228673987atural(bit0(bit1(bit1(bit0(bit0(bit1(bit0(bit0(bit0(bit1(bit1(bit1(bit0(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit0(bit0(bit1(bit0(bit1(bit1(bit1(bit1(bit0(bit1(bit1(bit1(bit1(bit0(bit0(one)))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(divide5121882707175180666atural(W),numera5444537566228673987atural(bit0(bit1(bit1(bit0(bit0(bit1(bit0(bit0(bit0(bit1(bit1(bit1(bit0(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit1(bit1(bit1(bit1(bit0(bit0(bit1(bit1(bit0(bit1(bit1(one))))))))))))))),one_one_Code_natural))),one_one_Code_natural)),aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(produc3574140220909816553atural,aa_Cod4272041906116450446atural(minus_shift(numera5444537566228673987atural(bit1(bit1(bit0(bit1(bit0(bit1(bit0(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(one))))))))))))))))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(modulo8411746178871703098atural(V),numera5444537566228673987atural(bit0(bit0(bit1(bit0(bit0(bit1(bit0(bit1(bit1(bit0(bit0(bit0(bit1(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit0(bit1(bit1(bit1(bit0(bit0(bit1(bit0(bit0(bit0(bit1(bit1(bit1(bit0(bit0(one)))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(divide5121882707175180666atural(V),numera5444537566228673987atural(bit0(bit0(bit1(bit0(bit0(bit1(bit0(bit1(bit1(bit0(bit0(bit0(bit1(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit1(bit1(bit0(bit0(bit1(bit1(bit0(bit1(bit1(bit1(bit1(bit1(bit0(one))))))))))))))))),aa_Cod4272041906116450446atural(minus_shift(numera5444537566228673987atural(bit1(bit1(bit1(bit0(bit0(bit0(bit0(bit0(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(one))))))))))))))))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(modulo8411746178871703098atural(W),numera5444537566228673987atural(bit0(bit1(bit1(bit0(bit0(bit1(bit0(bit0(bit0(bit1(bit1(bit1(bit0(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit0(bit0(bit1(bit0(bit1(bit1(bit1(bit1(bit0(bit1(bit1(bit1(bit1(bit0(bit0(one)))))))))))))))))),aa_Cod4272041906116450446atural(times_2397367101498566445atural(aa_Cod4272041906116450446atural(divide5121882707175180666atural(W),numera5444537566228673987atural(bit0(bit1(bit1(bit0(bit0(bit1(bit0(bit0(bit0(bit1(bit1(bit1(bit0(bit0(bit1(one)))))))))))))))))),numera5444537566228673987atural(bit1(bit1(bit1(bit1(bit0(bit0(bit1(bit1(bit0(bit1(bit1(one)))))))))))))))) )).

% next.simps
fof(fact_901_comp__eq__id__dest,axiom,(
    ! [A,B,C2,V] :
      ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,A),B) = comp_l8432902307485339590list_f(id_lis6780652146352037754_a_b_c,C2)
     => aa_Pro5496877705301569838_a_b_c(A,aa_Pro2582230449628027978list_f(B,V)) = aa_Pro5002280679056845916_a_b_c(C2,V) ) )).

% comp_eq_id_dest
fof(fact_902_bot__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(bot_bo6560894463593755925t_bool,X4),Xa2))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Xa2)),bot_bo2099793752762293965at_nat)) ) )).

% bot_empty_eq2
fof(fact_903_bot__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(bot_bo5325672116769796377t_bool,X4),Xa2))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X4),Xa2)),bot_bo5327735625951526323at_nat)) ) )).

% bot_empty_eq2
fof(fact_904_bot__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(bot_bo1209944405316066303r_bool,X4),Xa2))
    <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X4),Xa2)),bot_bo360956144901883563nteger)) ) )).

% bot_empty_eq2
fof(fact_905_bot__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(bot_bo3419215632864370536l_bool,X4),Xa2))
    <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X4),Xa2)),bot_bo1826939979638051714atural)) ) )).

% bot_empty_eq2
fof(fact_906_bot__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(bot_bo7238443650746976009r_bool,X4),Xa2))
    <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X4),Xa2)),bot_bo5920137642514184737nteger)) ) )).

% bot_empty_eq2
fof(fact_907_bot__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(bot_bo9220524098407837788t_bool,X4),Xa2))
    <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X4),Xa2)),bot_bo5853814528170464142nt_int)) ) )).

% bot_empty_eq2
fof(fact_908_bot__empty__eq2,axiom,(
    ! [X4,Xa2] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(bot_bo6140462223577857584t_bool,X4),Xa2))
    <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X4),Xa2)),bot_bo1891714543702108858nt_int)) ) )).

% bot_empty_eq2
fof(fact_909_GrD1,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Fx)),bNF_Gr_nat_nat(A4,F)))
     => member_nat(X,A4) ) )).

% GrD1
fof(fact_910_GrD1,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X),Fx)),bNF_Gr4088865321246080482at_nat(A4,F)))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4)) ) )).

% GrD1
fof(fact_911_GrD1,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Fx)),bNF_Gr819940013078457928nteger(A4,F)))
     => member4312719604404396038e_term(X,A4) ) )).

% GrD1
fof(fact_912_GrD1,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Fx)),bNF_Gr4109916457782409631atural(A4,F)))
     => member3406593020217859077e_term(X,A4) ) )).

% GrD1
fof(fact_913_GrD1,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Fx)),bNF_Gr8927732115752441022nteger(A4,F)))
     => member4565687819040644368e_term(X,A4) ) )).

% GrD1
fof(fact_914_GrD1,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Fx)),bNF_Gr4088698144404748203nt_int(A4,F)))
     => member2948136515907314945e_term(X,A4) ) )).

% GrD1
fof(fact_915_GrD1,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Fx)),bNF_Gr2187260864437095639nt_int(A4,F)))
     => member7723273712176309973e_term(X,A4) ) )).

% GrD1
fof(fact_916_GrD2,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Fx)),bNF_Gr_nat_nat(A4,F)))
     => aa_nat_nat(F,X) = Fx ) )).

% GrD2
fof(fact_917_GrD2,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X),Fx)),bNF_Gr4088865321246080482at_nat(A4,F)))
     => aa_Pro262675715343573244at_nat(F,X) = Fx ) )).

% GrD2
fof(fact_918_GrD2,axiom,(
    ! [X,Fx,A4,F] :
      ( gg_Pro3873016545244360254nteger(Fx)
     => ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Fx)),bNF_Gr819940013078457928nteger(A4,F)))
       => aa_fun7803427576885940654nteger(F,X) = Fx ) ) )).

% GrD2
fof(fact_919_GrD2,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Fx)),bNF_Gr4109916457782409631atural(A4,F)))
     => aa_fun8721795956770458885atural(F,X) = Fx ) )).

% GrD2
fof(fact_920_GrD2,axiom,(
    ! [X,Fx,A4,F] :
      ( gg_Pro3873016545244360254nteger(Fx)
     => ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Fx)),bNF_Gr8927732115752441022nteger(A4,F)))
       => aa_fun4316239577885714468nteger(F,X) = Fx ) ) )).

% GrD2
fof(fact_921_GrD2,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Fx)),bNF_Gr4088698144404748203nt_int(A4,F)))
     => aa_fun5094604504124609297nt_int(F,X) = Fx ) )).

% GrD2
fof(fact_922_GrD2,axiom,(
    ! [X,Fx,A4,F] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Fx)),bNF_Gr2187260864437095639nt_int(A4,F)))
     => aa_fun8086837178233993277nt_int(F,X) = Fx ) )).

% GrD2
fof(fact_923_fstOp__in,axiom,(
    ! [Ac2,P,Q] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Ac2),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,relcompp_nat_nat_nat(P,Q)))))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro262675715343573244at_nat(bNF_fs6799373675401686564at_nat(P,Q),Ac2)),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,P)))) ) )).

% fstOp_in
fof(fact_924_fstOp__in,axiom,(
    ! [Ac2,P,Q] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Ac2),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,relcom282571730187242960at_nat(P,Q)))))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro7157000481330941564at_nat(bNF_fs8257191039976258191at_nat(P,Q),Ac2)),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,P)))) ) )).

% fstOp_in
fof(fact_925_bsqr__max2,axiom,(
    ! [R,A1,A22,B1,B22] :
      ( pp(aa_set1680211184867041100t_bool(order_8331247224601271455at_nat(field_4706345496283612622at_nat(R)),R))
     => ( member8062223511168850704at_nat(produc4662710985925991255at_nat(aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A1),A22),aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,B1),B22)),bNF_We3318688506120914846at_nat(R))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_Pro262675715343573244at_nat(aa_Pro8023792847356852296at_nat(bNF_We6793920340776068943at_nat(R),A1),A22)),aa_Pro262675715343573244at_nat(aa_Pro8023792847356852296at_nat(bNF_We6793920340776068943at_nat(R),B1),B22))),R)) ) ) )).

% bsqr_max2
fof(fact_926_bsqr__max2,axiom,(
    ! [R,A1,A22,B1,B22] :
      ( pp(aa_set3135850010578026034t_bool(order_2888998067076097458on_nat(field_nat(R)),R))
     => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A1),A22)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B1),B22))),bNF_We1732890022510290291qr_nat(R)))
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(bNF_We2380939065524664066x2_nat(R),A1),A22)),aa_nat_nat(aa_nat_fun_nat_nat(bNF_We2380939065524664066x2_nat(R),B1),B22))),R)) ) ) )).

% bsqr_max2
fof(fact_927_sndOp__in,axiom,(
    ! [Ac2,P,Q] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Ac2),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,relcompp_nat_nat_nat(P,Q)))))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_Pro262675715343573244at_nat(bNF_sn8916957246138178918at_nat(P,Q),Ac2)),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,Q)))) ) )).

% sndOp_in
fof(fact_928_sndOp__in,axiom,(
    ! [Ac2,P,Q] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Ac2),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,relcom282571730187242960at_nat(P,Q)))))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro7157000481330941564at_nat(bNF_sn5923954573255187405at_nat(P,Q),Ac2)),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,Q)))) ) )).

% sndOp_in
fof(fact_929_convol__mem__GrpI,axiom,(
    ! [X,A4,G] :
      ( member_nat(X,A4)
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(bNF_co805650143699787099at_nat(id_nat2,G),X)),collec3392354462482085612at_nat(aa_fun2126031879273811846t_bool(produc8955392012077580105t_bool,bNF_Grp_nat_nat(A4,G))))) ) )).

% convol_mem_GrpI
fof(fact_930_convol__mem__GrpI,axiom,(
    ! [X,A4,G] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(bNF_co3897469944465340696at_nat(id_Pro7559728917991913458at_nat,G),X)),collec7088162979684241874at_nat(aa_fun4814288003198759460t_bool(produc6738493412065443883t_bool,bNF_Gr7275288873855648526at_nat(A4,G))))) ) )).

% convol_mem_GrpI
fof(fact_931_conditional__action_Orel__cong,axiom,(
    ! [X,Ya,Y,Xa,R2,Ra2] :
      ( X = Ya
     => ( Y = Xa
       => ( ! [Z2,Yb] :
              ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z2),condit6429450166605921294at_nat(Ya)))
             => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Yb),condit6429450166605921294at_nat(Xa)))
               => ( pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(R2,Z2),Yb))
                <=> pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(Ra2,Z2),Yb)) ) ) )
         => ( condit3216346422009540699at_nat(R2,X,Y)
          <=> condit3216346422009540699at_nat(Ra2,Ya,Xa) ) ) ) ) )).

% conditional_action.rel_cong
fof(fact_932_conditional__action_Orel__cong,axiom,(
    ! [X,Ya,Y,Xa,R2,Ra2] :
      ( X = Ya
     => ( Y = Xa
       => ( ! [Z2,Yb] :
              ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z2),condit6429450166605921294at_nat(Ya)))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Yb),condit5307000522679409652at_nat(Xa)))
               => ( pp(aa_Pro6098352494050694700t_bool(aa_Pro1130215055808060792t_bool(R2,Z2),Yb))
                <=> pp(aa_Pro6098352494050694700t_bool(aa_Pro1130215055808060792t_bool(Ra2,Z2),Yb)) ) ) )
         => ( condit8505942925542983873at_nat(R2,X,Y)
          <=> condit8505942925542983873at_nat(Ra2,Ya,Xa) ) ) ) ) )).

% conditional_action.rel_cong
fof(fact_933_conditional__action_Orel__cong,axiom,(
    ! [X,Ya,Y,Xa,R2,Ra2] :
      ( X = Ya
     => ( Y = Xa
       => ( ! [Z2,Yb] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z2),condit5307000522679409652at_nat(Ya)))
             => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Yb),condit6429450166605921294at_nat(Xa)))
               => ( pp(aa_Pro2232559814647311250t_bool(aa_Pro5393284600793951044t_bool(R2,Z2),Yb))
                <=> pp(aa_Pro2232559814647311250t_bool(aa_Pro5393284600793951044t_bool(Ra2,Z2),Yb)) ) ) )
         => ( condit4869552352875249525at_nat(R2,X,Y)
          <=> condit4869552352875249525at_nat(Ra2,Ya,Xa) ) ) ) ) )).

% conditional_action.rel_cong
fof(fact_934_conditional__action_Orel__cong,axiom,(
    ! [X,Ya,Y,Xa,R2,Ra2] :
      ( X = Ya
     => ( Y = Xa
       => ( ! [Z2,Yb] :
              ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z2),condit5307000522679409652at_nat(Ya)))
             => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Yb),condit5307000522679409652at_nat(Xa)))
               => ( pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(R2,Z2),Yb))
                <=> pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(Ra2,Z2),Yb)) ) ) )
         => ( condit7775146776940579035at_nat(R2,X,Y)
          <=> condit7775146776940579035at_nat(Ra2,Ya,Xa) ) ) ) ) )).

% conditional_action.rel_cong
fof(fact_935_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro4243173770044397973at_nat(F,X)
     => ( C2 = aa_Pro4243173770044397973at_nat(G,X)
       => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),C2)),bNF_Gr8954129895687480649at_nat(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_936_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro262675715343573244at_nat(F,X)
     => ( C2 = aa_Pro262675715343573244at_nat(G,X)
       => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,B),C2)),bNF_Gr8808630244184418791at_nat(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_937_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro7677444533209344123at_nat(F,X)
     => ( C2 = aa_Pro7677444533209344123at_nat(G,X)
       => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),C2)),bNF_Gr97278709799963567at_nat(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_938_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro5901169740204579478at_nat(F,X)
     => ( C2 = aa_Pro5901169740204579478at_nat(G,X)
       => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,B),C2)),bNF_Gr978357984662150989at_nat(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_939_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro2719419399745674036e_term(F,X)
     => ( C2 = aa_Pro1630239690174064534nteger(G,X)
       => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
         => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,B),C2)),bNF_Gr3212922122627294083nteger(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_940_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro2439870806855506435e_term(F,X)
     => ( C2 = aa_Pro6307550444590206900nt_int(G,X)
       => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
         => pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,B),C2)),bNF_Gr2059983526449137170nt_int(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_941_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro6687596243742734362e_term(F,X)
     => ( C2 = aa_Pro4916877589482262832nteger(G,X)
       => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4))
         => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,B),C2)),bNF_Gr9051781505272334237nteger(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_942_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro4825181188267525939e_term(F,X)
     => ( C2 = aa_Pro529789575656813996atural(G,X)
       => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
         => pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,B),C2)),bNF_Gr3511109801205458650atural(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_943_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro5984275987090311230e_term(F,X)
     => ( C2 = aa_Pro1630239690174064534nteger(G,X)
       => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
         => pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,B),C2)),bNF_Gr8328925459175490041nteger(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_944_image2__eqI,axiom,(
    ! [B,F,X,C2,G,A4] :
      ( B = aa_Pro3480981206584215599e_term(F,X)
     => ( C2 = aa_Pro6307550444590206900nt_int(G,X)
       => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4))
         => pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,B),C2)),bNF_Gr8682135708586076390nt_int(A4,F,G))) ) ) ) )).

% image2_eqI
fof(fact_945_FieldI2,axiom,(
    ! [I2,J2,R2] :
      ( member8062223511168850704at_nat(produc4662710985925991255at_nat(I2,J2),R2)
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,J2),field_3044959742847878580at_nat(R2))) ) )).

% FieldI2
fof(fact_946_FieldI2,axiom,(
    ! [I2,J2,R2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,I2),J2)),R2))
     => member_nat(J2,field_nat(R2)) ) )).

% FieldI2
fof(fact_947_FieldI2,axiom,(
    ! [I2,J2,R2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,I2),J2)),R2))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,J2),field_4706345496283612622at_nat(R2))) ) )).

% FieldI2
fof(fact_948_range__snd,axiom,(
    image_3837677093542026988atural(produc6591912806276919810atural,top_to8002910594584184420atural) = top_to5116171525255943265atural )).

% range_snd
fof(fact_949_range__snd,axiom,(
    aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,produc8710481132536983823list_f),top_to1815313666553408473list_f) = top_to3090985321854968643list_f )).

% range_snd
fof(fact_950_range__fst,axiom,(
    image_3233457633125470167e_term(produc3971164842776949671nteger,top_to3823906760630574279nteger) = top_to1895123461162442325e_term )).

% range_fst
fof(fact_951_range__fst,axiom,(
    image_8429719091235490605e_term(produc1168782837711296254atural,top_to6594682765904251294atural) = top_to1183274166523996884e_term )).

% range_fst
fof(fact_952_range__fst,axiom,(
    image_1842157394081550679e_term(produc5986598495681327645nteger,top_to1464508391925608509nteger) = top_to8226323274179483231e_term )).

% range_fst
fof(fact_953_range__fst,axiom,(
    image_563853799432866357e_term(produc6655012789309278474nt_int,top_to6478485262153701802nt_int) = top_to3080956855971038672e_term )).

% range_fst
fof(fact_954_range__fst,axiom,(
    image_686817785882688821e_term(produc2507970727455213110nt_int,top_to8792140074891071702nt_int) = top_to4576415366476676516e_term )).

% range_fst
fof(fact_955_conditional__action_Orel__mono__strong,axiom,(
    ! [R2,X,Y,Ra2] :
      ( condit3216346422009540699at_nat(R2,X,Y)
     => ( ! [Z2,Yb] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z2),condit6429450166605921294at_nat(X)))
           => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Yb),condit6429450166605921294at_nat(Y)))
             => ( pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(R2,Z2),Yb))
               => pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(Ra2,Z2),Yb)) ) ) )
       => condit3216346422009540699at_nat(Ra2,X,Y) ) ) )).

% conditional_action.rel_mono_strong
fof(fact_956_conditional__action_Orel__mono__strong,axiom,(
    ! [R2,X,Y,Ra2] :
      ( condit8505942925542983873at_nat(R2,X,Y)
     => ( ! [Z2,Yb] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z2),condit6429450166605921294at_nat(X)))
           => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Yb),condit5307000522679409652at_nat(Y)))
             => ( pp(aa_Pro6098352494050694700t_bool(aa_Pro1130215055808060792t_bool(R2,Z2),Yb))
               => pp(aa_Pro6098352494050694700t_bool(aa_Pro1130215055808060792t_bool(Ra2,Z2),Yb)) ) ) )
       => condit8505942925542983873at_nat(Ra2,X,Y) ) ) )).

% conditional_action.rel_mono_strong
fof(fact_957_conditional__action_Orel__mono__strong,axiom,(
    ! [R2,X,Y,Ra2] :
      ( condit4869552352875249525at_nat(R2,X,Y)
     => ( ! [Z2,Yb] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z2),condit5307000522679409652at_nat(X)))
           => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Yb),condit6429450166605921294at_nat(Y)))
             => ( pp(aa_Pro2232559814647311250t_bool(aa_Pro5393284600793951044t_bool(R2,Z2),Yb))
               => pp(aa_Pro2232559814647311250t_bool(aa_Pro5393284600793951044t_bool(Ra2,Z2),Yb)) ) ) )
       => condit4869552352875249525at_nat(Ra2,X,Y) ) ) )).

% conditional_action.rel_mono_strong
fof(fact_958_conditional__action_Orel__mono__strong,axiom,(
    ! [R2,X,Y,Ra2] :
      ( condit7775146776940579035at_nat(R2,X,Y)
     => ( ! [Z2,Yb] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z2),condit5307000522679409652at_nat(X)))
           => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Yb),condit5307000522679409652at_nat(Y)))
             => ( pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(R2,Z2),Yb))
               => pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(Ra2,Z2),Yb)) ) ) )
       => condit7775146776940579035at_nat(Ra2,X,Y) ) ) )).

% conditional_action.rel_mono_strong
fof(fact_959_FieldI1,axiom,(
    ! [I2,J2,R2] :
      ( member8062223511168850704at_nat(produc4662710985925991255at_nat(I2,J2),R2)
     => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,I2),field_3044959742847878580at_nat(R2))) ) )).

% FieldI1
fof(fact_960_FieldI1,axiom,(
    ! [I2,J2,R2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,I2),J2)),R2))
     => member_nat(I2,field_nat(R2)) ) )).

% FieldI1
fof(fact_961_FieldI1,axiom,(
    ! [I2,J2,R2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,I2),J2)),R2))
     => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,I2),field_4706345496283612622at_nat(R2))) ) )).

% FieldI1
fof(fact_962_conditional__action_Orel__refl__strong,axiom,(
    ! [X,Ra2] :
      ( ! [Z2] :
          ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Z2),condit6429450166605921294at_nat(X)))
         => pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(Ra2,Z2),Z2)) )
     => condit3216346422009540699at_nat(Ra2,X,X) ) )).

% conditional_action.rel_refl_strong
fof(fact_963_conditional__action_Orel__refl__strong,axiom,(
    ! [X,Ra2] :
      ( ! [Z2] :
          ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Z2),condit5307000522679409652at_nat(X)))
         => pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(Ra2,Z2),Z2)) )
     => condit7775146776940579035at_nat(Ra2,X,X) ) )).

% conditional_action.rel_refl_strong
fof(fact_964_converse__iff,axiom,(
    ! [A,B,R] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),converse_nat_nat(R)))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),A)),R)) ) )).

% converse_iff
fof(fact_965_converse__iff,axiom,(
    ! [A,B,R] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),conver5251360641855610363at_nat(R)))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,B),A)),R)) ) )).

% converse_iff
fof(fact_966_converse__iff,axiom,(
    ! [A,B,R] :
      ( member3123075103536333008e_term(produc1348435034978110643e_term(A,B),conver4495126127411442799nteger(R))
    <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,B),A)),R)) ) )).

% converse_iff
fof(fact_967_converse__iff,axiom,(
    ! [A,B,R] :
      ( member181435700844474941e_term(produc712526726438796704e_term(A,B),conver7226732764181260030nt_int(R))
    <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,B),A)),R)) ) )).

% converse_iff
fof(fact_968_converse__iff,axiom,(
    ! [A,B,R] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)),conver1560575594966503055e_term(R)))
    <=> member3123075103536333008e_term(produc1348435034978110643e_term(B,A),R) ) )).

% converse_iff
fof(fact_969_converse__iff,axiom,(
    ! [A,B,R] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)),conver3086944001885671292e_term(R)))
    <=> member181435700844474941e_term(produc712526726438796704e_term(B,A),R) ) )).

% converse_iff
fof(fact_970_converse__iff,axiom,(
    ! [A,B,R] :
      ( member6576571850643990885e_term(produc8292168106141693128e_term(A,B),conver5405359343046645702atural(R))
    <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,B),A)),R)) ) )).

% converse_iff
fof(fact_971_converse__iff,axiom,(
    ! [A,B,R] :
      ( member3214315348813689050e_term(produc8269329332333466045e_term(A,B),conver999802964161901285nteger(R))
    <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,B),A)),R)) ) )).

% converse_iff
fof(fact_972_converse__iff,axiom,(
    ! [A,B,R] :
      ( member5531304980329882217e_term(produc5954221522141377484e_term(A,B),conver2149993463103547858nt_int(R))
    <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,B),A)),R)) ) )).

% converse_iff
fof(fact_973_converse__iff,axiom,(
    ! [A,B,R] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)),conver1907446119251908260e_term(R)))
    <=> member6576571850643990885e_term(produc8292168106141693128e_term(B,A),R) ) )).

% converse_iff
fof(fact_974_Id__on__iff,axiom,(
    ! [X,Y,A4] :
      ( member8062223511168850704at_nat(produc4662710985925991255at_nat(X,Y),id_on_7917584626360399108at_nat(A4))
    <=> ( X = Y
        & pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X),A4)) ) ) )).

% Id_on_iff
fof(fact_975_Id__on__iff,axiom,(
    ! [X,Y,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y)),id_on_nat(A4)))
    <=> ( X = Y
        & member_nat(X,A4) ) ) )).

% Id_on_iff
fof(fact_976_Id__on__iff,axiom,(
    ! [X,Y,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X),Y)),id_on_2554058798563519774at_nat(A4)))
    <=> ( X = Y
        & pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X),A4)) ) ) )).

% Id_on_iff
fof(fact_977_Id__on__eqI,axiom,(
    ! [A,B,A4] :
      ( A = B
     => ( member_nat(A,A4)
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),id_on_nat(A4))) ) ) )).

% Id_on_eqI
fof(fact_978_Id__on__eqI,axiom,(
    ! [A,B,A4] :
      ( A = B
     => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,A),A4))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),id_on_2554058798563519774at_nat(A4))) ) ) )).

% Id_on_eqI
fof(fact_979_Id__on__eqI,axiom,(
    ! [A,B,A4] :
      ( A = B
     => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,A),A4))
       => member8062223511168850704at_nat(produc4662710985925991255at_nat(A,B),id_on_7917584626360399108at_nat(A4)) ) ) )).

% Id_on_eqI
fof(fact_980_Id__onE,axiom,(
    ! [C2,A4] :
      ( member8062223511168850704at_nat(C2,id_on_7917584626360399108at_nat(A4))
     => ~ ! [X3] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4))
           => C2 != produc4662710985925991255at_nat(X3,X3) ) ) )).

% Id_onE
fof(fact_981_Id__onE,axiom,(
    ! [C2,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),id_on_nat(A4)))
     => ~ ! [X3] :
            ( member_nat(X3,A4)
           => C2 != aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),X3) ) ) )).

% Id_onE
fof(fact_982_Id__onE,axiom,(
    ! [C2,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),id_on_2554058798563519774at_nat(A4)))
     => ~ ! [X3] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4))
           => C2 != aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),X3) ) ) )).

% Id_onE
fof(fact_983_prod__set__simps_I2_J,axiom,(
    ! [X,Y] : basic_5024967099532918245nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = insert4913895101485356395nteger(Y,bot_bo4276436098303576167nteger) )).

% prod_set_simps(2)
fof(fact_984_prod__set__simps_I2_J,axiom,(
    ! [X,Y] : basic_2645386396694270268atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)) = insert3813444986968105857atural(Y,bot_bo7028766096215927677atural) )).

% prod_set_simps(2)
fof(fact_985_prod__set__simps_I2_J,axiom,(
    ! [X,Y] : basic_7463202054664301659nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = insert4913895101485356395nteger(Y,bot_bo4276436098303576167nteger) )).

% prod_set_simps(2)
fof(fact_986_prod__set__simps_I2_J,axiom,(
    ! [X,Y] : basic_6884646532157533000nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = insert5033312907999012233nt_int(Y,bot_bo1796632182523588997nt_int) )).

% prod_set_simps(2)
fof(fact_987_prod__set__simps_I2_J,axiom,(
    ! [X,Y] : basic_652739332891048052nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = insert5033312907999012233nt_int(Y,bot_bo1796632182523588997nt_int) )).

% prod_set_simps(2)
fof(fact_988_surj__fun__eq,axiom,(
    ! [F,X7,G1,G22] :
      ( aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,F),X7) = top_to3090985321854968643list_f
     => ( ! [X3] :
            ( member1992181931100238290list_f(X3,X7)
           => aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G1),F),X3) = aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G22),F),X3) )
       => G1 = G22 ) ) )).

% surj_fun_eq
fof(fact_989_prod__set__simps_I1_J,axiom,(
    ! [X,Y] : basic_2576585934186803619nteger(aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X),Y)) = insert190971643640263327e_term(X,bot_bo7261247930815417913e_term) )).

% prod_set_simps(1)
fof(fact_990_prod__set__simps_I1_J,axiom,(
    ! [X,Y] : basic_3829793649824281850atural(aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X),Y)) = insert5978560002646234782e_term(X,bot_bo9191057816668355256e_term) )).

% prod_set_simps(1)
fof(fact_991_prod__set__simps_I1_J,axiom,(
    ! [X,Y] : basic_8647609307794313241nteger(aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X),Y)) = insert7137654801469020073e_term(X,bot_bo7010734887469065795e_term) )).

% prod_set_simps(1)
fof(fact_992_prod__set__simps_I1_J,axiom,(
    ! [X,Y] : basic_2860316216444040966nt_int(aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X),Y)) = insert2106057668996072346e_term(X,bot_bo5496473946294314420e_term) )).

% prod_set_simps(1)
fof(fact_993_prod__set__simps_I1_J,axiom,(
    ! [X,Y] : basic_1678460015461602354nt_int(aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X),Y)) = insert5784700836022525294e_term(X,bot_bo8374228283394309512e_term) )).

% prod_set_simps(1)
fof(fact_994_comp__surj,axiom,(
    ! [F,G] :
      ( aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,F),top_to1815313666553408473list_f) = top_to3090985321854968643list_f
     => ( image_6684545758539136421_a_b_c(G,top_to3090985321854968643list_f) = top_to66987640601337145_a_b_c
       => image_6608088440629302181_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),F),top_to1815313666553408473list_f) = top_to66987640601337145_a_b_c ) ) )).

% comp_surj
fof(fact_995_IdE,axiom,(
    ! [P2] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,P2),id_nat))
     => ~ ! [X3] : P2 != aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),X3) ) )).

% IdE
fof(fact_996_IdE,axiom,(
    ! [P2] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,P2),id_Pro2258643101195443293at_nat))
     => ~ ! [X3] : P2 != aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),X3) ) )).

% IdE
fof(fact_997_fun_Oset__map,axiom,(
    ! [F,V] : image_6608088440629302181_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),V),top_to1815313666553408473list_f) = image_6684545758539136421_a_b_c(F,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,V),top_to1815313666553408473list_f)) )).

% fun.set_map
fof(fact_998_fun_Omap__cong,axiom,(
    ! [X,Ya,F,G] :
      ( X = Ya
     => ( ! [Z2] :
            ( member6304641671555014644list_f(Z2,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,Ya),top_to1815313666553408473list_f))
           => aa_Pro5496877705301569838_a_b_c(F,Z2) = aa_Pro5496877705301569838_a_b_c(G,Z2) )
       => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),X) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),Ya) ) ) )).

% fun.map_cong
fof(fact_999_IdI,axiom,(
    ! [A] : pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),A)),id_nat)) )).

% IdI
fof(fact_1000_IdI,axiom,(
    ! [A] : pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),A)),id_Pro2258643101195443293at_nat)) )).

% IdI
fof(fact_1001_fun_Omap__cong0,axiom,(
    ! [X,F,G] :
      ( ! [Z2] :
          ( member6304641671555014644list_f(Z2,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,X),top_to1815313666553408473list_f))
         => aa_Pro5496877705301569838_a_b_c(F,Z2) = aa_Pro5496877705301569838_a_b_c(G,Z2) )
     => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),X) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,G),X) ) )).

% fun.map_cong0
fof(fact_1002_fun_Oinj__map__strong,axiom,(
    ! [X,Xa,F,Fa] :
      ( ! [Z2,Za2] :
          ( member6304641671555014644list_f(Z2,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,X),top_to1815313666553408473list_f))
         => ( member6304641671555014644list_f(Za2,aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(image_4621308865571145409list_f,Xa),top_to1815313666553408473list_f))
           => ( aa_Pro5496877705301569838_a_b_c(F,Z2) = aa_Pro5496877705301569838_a_b_c(Fa,Za2)
             => Z2 = Za2 ) ) )
     => ( aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),X) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,Fa),Xa)
       => X = Xa ) ) )).

% fun.inj_map_strong
fof(fact_1003_IdD,axiom,(
    ! [A,B] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),id_nat))
     => A = B ) )).

% IdD
fof(fact_1004_IdD,axiom,(
    ! [A,B] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),id_Pro2258643101195443293at_nat))
     => A = B ) )).

% IdD
fof(fact_1005_fun_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( bNF_re6046208945862828881list_f(fequal99650277583572734list_f,R4,A7,B6)
    <=> ? [Z3] :
          ( member1263764406532965826list_f(Z3,collec3619133894700608004list_f(cOMBC_387500496980327184f_bool(cOMBB_6027208925197716341list_f(ord_le2653721700351411443list_f,cOMBC_2422794320193074410list_f(image_4621308865571145409list_f,top_to1815313666553408473list_f)),collec2591973510557893426list_f(produc7818086228371305747f_bool(R4)))))
          & aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,produc3535155421234910955list_f),Z3) = A7
          & comp_P3270879886602560258list_f(produc7287154213363835177list_f,Z3) = B6 ) ) )).

% fun.in_rel
fof(fact_1006_type__copy__map__cong0,axiom,(
    ! [M,G,X,N,H,F] :
      ( aa_Pro2582230449628027978list_f(M,aa_Pro7428252341792638716list_f(G,X)) = aa_Pro777963009888889592list_f(N,aa_Pro2582230449628027978list_f(H,X))
     => aa_Pro5002280679056845916_a_b_c(comp_P1644921750638218854list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),M),G),X) = aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(F,N)),H),X) ) )).

% type_copy_map_cong0
fof(fact_1007_type__copy__map__cong0,axiom,(
    ! [M,G,X,N,H,F] :
      ( aa_Pro777963009888889592list_f(M,aa_Pro2582230449628027978list_f(G,X)) = aa_Pro2582230449628027978list_f(N,aa_Pro7428252341792638716list_f(H,X))
     => aa_Pro5002280679056845916_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(F,M)),G),X) = aa_Pro5002280679056845916_a_b_c(comp_P1644921750638218854list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),N),H),X) ) )).

% type_copy_map_cong0
fof(fact_1008_DiffI,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4))
     => ( ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5))
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),minus_1356011639430497352at_nat(A4,B5))) ) ) )).

% DiffI
fof(fact_1009_DiffI,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4))
     => ( ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),minus_8321449233255521966at_nat(A4,B5))) ) ) )).

% DiffI
fof(fact_1010_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,Xz),relcomp_nat_nat_nat(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( Xz = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Z2)
           => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y3)),R))
             => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y3),Z2)),S)) ) ) ) )).

% relcompE
fof(fact_1011_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,Xz),relcom7295539661566034944at_nat(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( Xz = aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),Z2)
           => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),Y3)),R))
             => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,Y3),Z2)),S)) ) ) ) )).

% relcompE
fof(fact_1012_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,Xz),relcom7882051849408532656nteger(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( ( gg_Pro3873016545244360254nteger(Y3)
              & gg_Pro3873016545244360254nteger(Z2) )
           => ( Xz = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Z2)
             => ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Y3)),R))
               => ~ member335077259223437328nteger(produc4911887526399440471nteger(Y3,Z2),S) ) ) ) ) )).

% relcompE
fof(fact_1013_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,Xz),relcom5456725021198286719nt_int(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( Xz = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Z2)
           => ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Y3)),R))
             => ~ member8566619992076573584nt_int(produc3646306378393792727nt_int(Y3,Z2),S) ) ) ) )).

% relcompE
fof(fact_1014_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,Xz),relcom3708334122937384570nteger(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( gg_Pro3873016545244360254nteger(Z2)
           => ( Xz = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Z2)
             => ( member3700727801235295592e_term(aa_fun7771121184386139346e_term(aa_fun4065348690927510012e_term(produc4524505180950781815e_term,X3),Y3),R)
               => ~ pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,Y3),Z2)),S)) ) ) ) ) )).

% relcompE
fof(fact_1015_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,Xz),relcom3746783289035943599atural(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( Xz = aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Z2)
           => ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),Y3)),R))
             => ~ member3756964795865971088atural(aa_Pro1971126414814181170atural(aa_Pro1220262147015971502atural(produc4480994950612372183atural,Y3),Z2),S) ) ) ) )).

% relcompE
fof(fact_1016_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,Xz),relcom2723316367480567482nteger(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( ( gg_Pro3873016545244360254nteger(Y3)
              & gg_Pro3873016545244360254nteger(Z2) )
           => ( Xz = aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Z2)
             => ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),Y3)),R))
               => ~ member335077259223437328nteger(produc4911887526399440471nteger(Y3,Z2),S) ) ) ) ) )).

% relcompE
fof(fact_1017_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,Xz),relcom7395765569376975787nt_int(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( Xz = aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Z2)
           => ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),Y3)),R))
             => ~ member8566619992076573584nt_int(produc3646306378393792727nt_int(Y3,Z2),S) ) ) ) )).

% relcompE
fof(fact_1018_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,Xz),relcom7629639294386507898nt_int(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( Xz = aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),Z2)
           => ( member7160087484201369222e_term(aa_fun5006721999989859937e_term(aa_fun4495630950452421628e_term(produc6842831835191658517e_term,X3),Y3),R)
             => ~ pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,Y3),Z2)),S)) ) ) ) )).

% relcompE
fof(fact_1019_relcompE,axiom,(
    ! [Xz,R,S] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,Xz),relcom3224131320492029168nteger(R,S)))
     => ~ ! [X3,Y3,Z2] :
            ( gg_Pro3873016545244360254nteger(Z2)
           => ( Xz = aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),Z2)
             => ( member4377545065863478642e_term(produc1747193454407091329e_term(X3,Y3),R)
               => ~ pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,Y3),Z2)),S)) ) ) ) ) )).

% relcompE
fof(fact_1020_DiffE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),minus_1356011639430497352at_nat(A4,B5)))
     => ~ ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),A4))
         => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,C2),B5)) ) ) )).

% DiffE
fof(fact_1021_DiffE,axiom,(
    ! [C2,A4,B5] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),minus_8321449233255521966at_nat(A4,B5)))
     => ~ ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),A4))
         => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,C2),B5)) ) ) )).

% DiffE
fof(fact_1022_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R))
     => ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),C2)),S))
       => pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),C2)),relcomp_nat_nat_nat(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1023_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),R))
     => ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,B),C2)),S))
       => pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),C2)),relcom7295539661566034944at_nat(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1024_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)),R))
     => ( member335077259223437328nteger(produc4911887526399440471nteger(B,C2),S)
       => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),C2)),relcom7882051849408532656nteger(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1025_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)),R))
     => ( member8566619992076573584nt_int(produc3646306378393792727nt_int(B,C2),S)
       => pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),C2)),relcom5456725021198286719nt_int(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1026_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( member3700727801235295592e_term(aa_fun7771121184386139346e_term(aa_fun4065348690927510012e_term(produc4524505180950781815e_term,A),B),R)
     => ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,B),C2)),S))
       => pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),C2)),relcom3708334122937384570nteger(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1027_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( member7160087484201369222e_term(aa_fun5006721999989859937e_term(aa_fun4495630950452421628e_term(produc6842831835191658517e_term,A),B),R)
     => ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,B),C2)),S))
       => pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),C2)),relcom7629639294386507898nt_int(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1028_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)),R))
     => ( member3756964795865971088atural(aa_Pro1971126414814181170atural(aa_Pro1220262147015971502atural(produc4480994950612372183atural,B),C2),S)
       => pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),C2)),relcom3746783289035943599atural(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1029_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)),R))
     => ( member335077259223437328nteger(produc4911887526399440471nteger(B,C2),S)
       => pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),C2)),relcom2723316367480567482nteger(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1030_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)),R))
     => ( member8566619992076573584nt_int(produc3646306378393792727nt_int(B,C2),S)
       => pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),C2)),relcom7395765569376975787nt_int(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1031_relcomp_OrelcompI,axiom,(
    ! [A,B,R,C2,S] :
      ( member8039183878132087922e_term(produc9061498825293938305e_term(A,B),R)
     => ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,B),C2)),S))
       => pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),C2)),relcom2959821256397535984nteger(R,S))) ) ) )).

% relcomp.relcompI
fof(fact_1032_case__swap,axiom,(
    ! [F6,P4] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,cOMBC_4647895173212359598atural(F6)),aa_Pro4262726347734369532atural(produc5279793246624815241atural,P4)) = aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F6),P4) )).

% case_swap
fof(fact_1033_list_Oset_I1_J,axiom,(
    set_typerep(nil_typerep) = bot_bot_set_typerep )).

% list.set(1)
fof(fact_1034_case__prod__map__prod,axiom,(
    ! [H3,F6,G4,X8] : aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,H3),aa_Pro4262726347734369532atural(produc8950045413935083162atural(F6,G4),X8)) = aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,cOMBC_8986509634241427706atural(cOMBB_130406997377790362atural(cOMBB_8143632497815461569atural,cOMBB_3303863054882352626atural(H3,F6)),G4)),X8) )).

% case_prod_map_prod
fof(fact_1035_prod_Ocase__distrib,axiom,(
    ! [H3,F6,Prod3] : aa_Pro6170093065824087676atural(H3,aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F6),Prod3)) = aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,cOMBB_1026476112683758798atural(cOMBB_6041837087792280206atural(H3),F6)),Prod3) )).

% prod.case_distrib
fof(fact_1036_inj__on__convol__ident,axiom,(
    ! [F6,X9] : inj_on5021857848461062467nteger(cOMBS_6788261484442488790nteger(produc4282985567423050387nteger,F6),X9) )).

% inj_on_convol_ident
fof(fact_1037_inj__on__convol__ident,axiom,(
    ! [F6,X9] : inj_on6605715038195167769atural(cOMBS_2215763095718458372atural(produc2566709293081654762atural,F6),X9) )).

% inj_on_convol_ident
fof(fact_1038_inj__on__convol__ident,axiom,(
    ! [F6,X9] : inj_on6745027588872712131nteger(cOMBS_7501632289793839554nteger(produc7384524951051686153nteger,F6),X9) )).

% inj_on_convol_ident
fof(fact_1039_inj__on__convol__ident,axiom,(
    ! [F6,X9] : inj_on3859921853975086881nt_int(cOMBS_1321081462047153692nt_int(produc1560874099174258678nt_int,F6),X9) )).

% inj_on_convol_ident
fof(fact_1040_inj__on__convol__ident,axiom,(
    ! [F6,X9] : inj_on7316603330526774305nt_int(cOMBS_6357492497858634356nt_int(produc4852315488734385442nt_int,F6),X9) )).

% inj_on_convol_ident
fof(fact_1041_inf_Ocobounded1,axiom,(
    ! [A,B] : pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(inf_inf_nat,A),B)),A)) )).

% inf.cobounded1
fof(fact_1042_Compr__image__eq,axiom,(
    ! [F6,A5,P3] : collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),image_5168914502847457605at_nat(F6,A5))),P3)) = image_5168914502847457605at_nat(F6,collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),A5)),cOMBB_150397177082651397at_nat(P3,F6)))) )).

% Compr_image_eq
fof(fact_1043_Compr__image__eq,axiom,(
    ! [F6,A5,P3] : collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),image_6706873702294942047at_nat(F6,A5))),P3)) = image_6706873702294942047at_nat(F6,collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),A5)),cOMBB_3190877037383586923at_nat(P3,F6)))) )).

% Compr_image_eq
fof(fact_1044_Compr__image__eq,axiom,(
    ! [F6,A5,P3] : collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),image_1119892238107900587at_nat(F6,A5))),P3)) = image_1119892238107900587at_nat(F6,collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),A5)),cOMBB_5528459013814913387at_nat(P3,F6)))) )).

% Compr_image_eq
fof(fact_1045_Compr__image__eq,axiom,(
    ! [F6,A5,P3] : collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),image_6321802852832981957at_nat(F6,A5))),P3)) = image_6321802852832981957at_nat(F6,collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),A5)),cOMBB_74244353674774993at_nat(P3,F6)))) )).

% Compr_image_eq
fof(fact_1046_interrupt__action_Oset__intros_I2_J,axiom,(
    ! [X2] : pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X2),interr3917558629499790676at_nat(interr6945818126708391058at_nat(X2)))) )).

% interrupt_action.set_intros(2)
fof(fact_1047_interrupt__action_Oset__intros_I2_J,axiom,(
    ! [X2] : pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X2),interr4604075546494911546at_nat(interr7700225897186592376at_nat(X2)))) )).

% interrupt_action.set_intros(2)
fof(fact_1048_interrupt__action_Oset__intros_I3_J,axiom,(
    ! [X32] : pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X32),interr3917558629499790676at_nat(interr4077302776001012533at_nat(X32)))) )).

% interrupt_action.set_intros(3)
fof(fact_1049_interrupt__action_Oset__intros_I3_J,axiom,(
    ! [X32] : pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X32),interr4604075546494911546at_nat(interr1275353696496618651at_nat(X32)))) )).

% interrupt_action.set_intros(3)
fof(fact_1050_transfer__start,axiom,(
    ! [P] :
      ( pp(P)
     => ~ pp(aa_bool_bool(aa_boo8970175072276269406l_bool(rel_bool_bool(fequal_bool),P),fFalse)) ) )).

% transfer_start
fof(fact_1051_add_Oright__neutral,axiom,(
    ! [A] : aa_Cod4272041906116450446atural(plus_p4538020629002901425atural(A),zero_z2226904508553997617atural) = A )).

% add.right_neutral
fof(fact_1052_add_Oright__neutral,axiom,(
    ! [A] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),zero_zero_nat) = A )).

% add.right_neutral
fof(fact_1053_add_Oright__neutral,axiom,(
    ! [A] :
      ( gg_literal(A)
     => plus_plus_literal(A,zero_zero_literal) = A ) )).

% add.right_neutral
fof(fact_1054_subset__CollectI,axiom,(
    ! [B7,A5,Q3,P3] :
      ( pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(B7),A5))
     => ( ! [X3] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),B7))
           => ( pp(aa_Pro2232559814647311250t_bool(Q3,X3))
             => pp(aa_Pro2232559814647311250t_bool(P3,X3)) ) )
       => pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),B7)),Q3))),collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),A5)),P3)))) ) ) )).

% subset_CollectI
fof(fact_1055_subset__CollectI,axiom,(
    ! [B7,A5,Q3,P3] :
      ( pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(B7),A5))
     => ( ! [X3] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),B7))
           => ( pp(aa_Pro6098352494050694700t_bool(Q3,X3))
             => pp(aa_Pro6098352494050694700t_bool(P3,X3)) ) )
       => pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),B7)),Q3))),collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),A5)),P3)))) ) ) )).

% subset_CollectI
fof(fact_1056_subset__Collect__iff,axiom,(
    ! [B7,A5,P3] :
      ( pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(B7),A5))
     => ( pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(B7),collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),A5)),P3))))
      <=> ! [X5] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X5),B7))
           => pp(aa_Pro2232559814647311250t_bool(P3,X5)) ) ) ) )).

% subset_Collect_iff
fof(fact_1057_subset__Collect__iff,axiom,(
    ! [B7,A5,P3] :
      ( pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(B7),A5))
     => ( pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(B7),collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),A5)),P3))))
      <=> ! [X5] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X5),B7))
           => pp(aa_Pro6098352494050694700t_bool(P3,X5)) ) ) ) )).

% subset_Collect_iff
fof(fact_1058_prop__restrict,axiom,(
    ! [X8,Z4,X9,P3] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X8),Z4))
     => ( pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(Z4),collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),X9)),P3))))
       => pp(aa_Pro2232559814647311250t_bool(P3,X8)) ) ) )).

% prop_restrict
fof(fact_1059_prop__restrict,axiom,(
    ! [X8,Z4,X9,P3] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X8),Z4))
     => ( pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(Z4),collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),X9)),P3))))
       => pp(aa_Pro6098352494050694700t_bool(P3,X8)) ) ) )).

% prop_restrict
fof(fact_1060_Collect__restrict,axiom,(
    ! [X9,P3] : pp(aa_set3135850010578026034t_bool(ord_le3146513528884898305at_nat(collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fconj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),X9)),P3))),X9)) )).

% Collect_restrict
fof(fact_1061_Collect__restrict,axiom,(
    ! [X9,P3] : pp(aa_set1680211184867041100t_bool(ord_le3000389064537975527at_nat(collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fconj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),X9)),P3))),X9)) )).

% Collect_restrict
fof(fact_1062_split__seed__def,axiom,(
    ! [S5] : aa_Pro1971126414814181170atural(split_seed,S5) = aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,cOMBC_8548339932275315702atural(cOMBB_6558986659707910040atural(cOMBC_6936323340639911621atural,cOMBB_1326504860456885980atural(cOMBB_8113829899795609350atural(produc8282080750456430313atural),cOMBC_3501613152056342390atural(cOMBB_96704837724660068atural(cOMBB_489448995879531957atural,cOMBB_4849420086525620964atural(cOMBB_944832782022194677atural,cOMBB_6558986659707910040atural(cOMBC_6936323340639911621atural,cOMBB_624496947066355268atural(cOMBB_3012511739362972014atural(produc4480994950612372183atural),cOMBB_6959547025548011708atural(produc3574140220909816553atural,inc_shift(numera5444537566228673987atural(bit0(bit1(bit0(bit1(bit0(bit1(bit0(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(one))))))))))))))))))))))))))))))))))))),cOMBB_6959547025548011708atural(cOMBC_1248919038785528696atural(produc3574140220909816553atural),inc_shift(numera5444537566228673987atural(bit0(bit1(bit1(bit0(bit0(bit0(bit0(bit0(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(bit1(one)))))))))))))))))))))))))))))))))))),aa_Pro3673693039631929973atural(produc6591912806276919810atural,next(S5)))),S5) )).

% split_seed_def
fof(fact_1063_sup__set__def,axiom,(
    ! [A5,B7] : sup_su6327502436637775413at_nat(A5,B7) = collec3392354462482085612at_nat(sup_su5674415786711694021t_bool(aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),A5),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),B7))) )).

% sup_set_def
fof(fact_1064_sup__set__def,axiom,(
    ! [A5,B7] : sup_su718114333110466843at_nat(A5,B7) = collec7088162979684241874at_nat(sup_su3901408610078580575t_bool(aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),A5),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),B7))) )).

% sup_set_def
fof(fact_1065_Un__def,axiom,(
    ! [A5,B7] : sup_su6327502436637775413at_nat(A5,B7) = collec3392354462482085612at_nat(cOMBS_7530496056240154442l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(fdisj),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),A5)),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),B7))) )).

% Un_def
fof(fact_1066_Un__def,axiom,(
    ! [A5,B7] : sup_su718114333110466843at_nat(A5,B7) = collec7088162979684241874at_nat(cOMBS_2815829179688385072l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(fdisj),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),A5)),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),B7))) )).

% Un_def
fof(fact_1067_sup__Un__eq,axiom,(
    ! [R4,S4,X4] :
      ( pp(aa_Pro2232559814647311250t_bool(sup_su5674415786711694021t_bool(aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),R4),aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(member8440522571783428010at_nat),S4)),X4))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X4),sup_su6327502436637775413at_nat(R4,S4))) ) )).

% sup_Un_eq
fof(fact_1068_sup__Un__eq,axiom,(
    ! [R4,S4,X4] :
      ( pp(aa_Pro6098352494050694700t_bool(sup_su3901408610078580575t_bool(aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),R4),aa_set6997699984206591038t_bool(cOMBC_9012026442144072464t_bool(member8206827879206165904at_nat),S4)),X4))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X4),sup_su718114333110466843at_nat(R4,S4))) ) )).

% sup_Un_eq
fof(fact_1069_conditional__action_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( gg_con1658195355420310406nteger(B6)
     => ( pp(aa_con5738070099517397040r_bool(aa_con1623875276633070770r_bool(condit6184561423513516559nteger(R4),A7),B6))
      <=> ? [Z3] :
            ( member6180653861673990470nteger(Z3,collec8013588583170467972nteger(cOMBC_1412576520028865000r_bool(cOMBB_6453866196482202699nteger(ord_le5347933966117430903nteger,condit7952600011703662612nteger),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,R4)))))
            & aa_con6081442682657178282e_term(condit2633228709571318698e_term(produc3971164842776949671nteger),Z3) = A7
            & aa_con6461004814926059446nteger(condit9202156164625486240nteger(produc7330894765516781285nteger),Z3) = B6 ) ) ) )).

% conditional_action.in_rel
fof(fact_1070_conditional__action_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( pp(aa_con8041701148131775130l_bool(aa_con6156384551402013211l_bool(condit8136067717219687782atural(R4),A7),B6))
    <=> ? [Z3] :
          ( member6163144751841541661atural(Z3,collec6097989394234547547atural(cOMBC_4777985434584799034l_bool(cOMBB_69603593386543220atural(ord_le8467756462758155086atural,condit6721827335151951979atural),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,R4)))))
          & aa_con1092570966786250880e_term(condit530872168517844736e_term(produc1168782837711296254atural),Z3) = A7
          & aa_con2292861600631905205atural(condit110732285524013727atural(produc3992340709582277180atural),Z3) = B6 ) ) )).

% conditional_action.in_rel
fof(fact_1071_conditional__action_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( gg_con1658195355420310406nteger(B6)
     => ( pp(aa_con5738070099517397040r_bool(aa_con3033407470087011260r_bool(condit3730511338334943365nteger(R4),A7),B6))
      <=> ? [Z3] :
            ( member1032970377862898876nteger(Z3,collec967815020255904762nteger(cOMBC_8733656865795830012r_bool(cOMBB_1842404469168437973nteger(ord_le3337582088779512301nteger,condit7686862880692381322nteger),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,R4)))))
            & aa_con3298917038284919594e_term(condit3166682508218680618e_term(produc5986598495681327645nteger),Z3) = A7
            & aa_con4378243020094724544nteger(condit3587349607997788074nteger(produc8810156367552308571nteger),Z3) = B6 ) ) ) )).

% conditional_action.in_rel
fof(fact_1072_conditional__action_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( pp(aa_con3870485526895031954t_bool(aa_con6423989922710986511t_bool(condit2775462794712788850nt_int(R4),A7),B6))
    <=> ? [Z3] :
          ( member2650117077833728553nt_int(Z3,collec5845839669341505895nt_int(cOMBC_6803298798058583842t_bool(cOMBB_418042858550060136nt_int(ord_le5172437211506631514nt_int,condit2367099723822225015nt_int),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,R4)))))
          & aa_con5194767075275078024e_term(condit8347815893170957832e_term(produc6655012789309278474nt_int),Z3) = A7
          & aa_con8618817592691734705nt_int(condit7137826502243047323nt_int(produc7622839952223151176nt_int),Z3) = B6 ) ) )).

% conditional_action.in_rel
fof(fact_1073_conditional__action_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( pp(aa_con3870485526895031954t_bool(aa_con1991058238916365539t_bool(condit3271435385184627870nt_int(R4),A7),B6))
    <=> ? [Z3] :
          ( member5130677871921602901nt_int(Z3,collec8282763664059201683nt_int(cOMBC_6809366433643302090t_bool(cOMBB_7614080557269926204nt_int(ord_le172202941055982214nt_int,condit7400265531455562659nt_int),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,R4)))))
          & aa_con605714200004147848e_term(condit6729456979053129992e_term(produc2507970727455213110nt_int),Z3) = A7
          & aa_con6366738833360172165nt_int(condit3930740424007402351nt_int(produc726383008135262580nt_int),Z3) = B6 ) ) )).

% conditional_action.in_rel
fof(fact_1074_conditional__action_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( pp(aa_con8041701148131775130l_bool(aa_con6328194478143685077l_bool(condit1127689873879419692atural(R4),A7),B6))
    <=> ? [Z3] :
          ( member5077444122367321059atural(Z3,collec3264392531641636129atural(cOMBC_6514811739612929710l_bool(cOMBB_1840833620497539502atural(ord_le2202040463148982292atural,condit6773436539961436209atural),collec1991479681304692691atural(produc5868410056131333498l_bool(R4)))))
          & aa_con4661744543005849856atural(condit7067702762122744960atural(produc497848011034438852atural),Z3) = A7
          & aa_con6173485833423625583atural(condit4604360551831230809atural(produc6591912806276919810atural),Z3) = B6 ) ) )).

% conditional_action.in_rel
fof(fact_1075_conditional__action_Oin__rel,axiom,(
    ! [R4,A7,B6] :
      ( gg_con5341393946966126678action(A7)
     => ( pp(aa_con7178005104978336878f_bool(aa_con6037231209153826126f_bool(condit1543564991105445733list_f(R4),A7),B6))
      <=> ? [Z3] :
            ( member3716888906625679770list_f(Z3,collec7820802666344048348list_f(cOMBC_3324183268558603608f_bool(cOMBB_5499718888831777787list_f(ord_le3852096572277380649list_f,condit6827580605863688246list_f),collec2941370454899091988list_f(produc4709439930048449441f_bool(R4)))))
            & aa_con2705967329354826990action(condit7155426171764300860action(produc3089225533250117581list_f),Z3) = A7
            & aa_con6974328736262822752list_f(condit4069896782405135150list_f(produc8710481132536983823list_f),Z3) = B6 ) ) ) )).

% conditional_action.in_rel
fof(fact_1076_sup__Un__eq2,axiom,(
    ! [R4,S4,X4,Xa2] :
      ( pp(aa_nat_bool(aa_nat_fun_nat_bool(sup_su8404041055355318397t_bool(cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),R4),cOMBC_6245729688356921590t_bool(cOMBB_6870708132184939840ol_nat(cOMBC_6089182126854364013t_bool,cOMBB_7227252839205164092ol_nat(cOMBB_8823940721079071078ol_nat(member8440522571783428010at_nat),product_Pair_nat_nat)),S4)),X4),Xa2))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Xa2)),sup_su6327502436637775413at_nat(R4,S4))) ) )).

% sup_Un_eq2
fof(fact_1077_sup__Un__eq2,axiom,(
    ! [R4,S4,X4,Xa2] :
      ( pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(sup_su8812873402214772865t_bool(cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),R4),cOMBC_8707992278803734470t_bool(cOMBB_4054337248528292751at_nat(cOMBC_4555905863570137130t_bool,cOMBB_805735269680691817at_nat(cOMBB_185029674437798763at_nat(member8206827879206165904at_nat),produc6161850002892822231at_nat)),S4)),X4),Xa2))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X4),Xa2)),sup_su718114333110466843at_nat(R4,S4))) ) )).

% sup_Un_eq2
fof(fact_1078_sup__Un__eq2,axiom,(
    ! [R4,S4,X4,Xa2] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5646951941296221740r_bool(sup_su5661509286765721239r_bool(cOMBC_1701604444625769262r_bool(cOMBB_2051620022066736427e_term(cOMBC_1849943191596060938r_bool,cOMBB_2794114419360077275e_term(cOMBB_7221559756505762377nteger(member4581088367259704696nteger),produc4282985567423050387nteger)),R4),cOMBC_1701604444625769262r_bool(cOMBB_2051620022066736427e_term(cOMBC_1849943191596060938r_bool,cOMBB_2794114419360077275e_term(cOMBB_7221559756505762377nteger(member4581088367259704696nteger),produc4282985567423050387nteger)),S4)),X4),Xa2))
    <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X4),Xa2)),sup_su2921085720131085635nteger(R4,S4))) ) )).

% sup_Un_eq2
fof(fact_1079_sup__Un__eq2,axiom,(
    ! [R4,S4,X4,Xa2] :
      ( pp(aa_Pro8754844875067278050l_bool(aa_fun2237767473747863189l_bool(sup_su8095728789641411072l_bool(cOMBC_8519344746081138158l_bool(cOMBB_2417629582155303358e_term(cOMBC_1922632389518567517l_bool,cOMBB_7937736296159719194e_term(cOMBB_6132650689756367373atural(member5458643631506449871atural),produc2566709293081654762atural)),R4),cOMBC_8519344746081138158l_bool(cOMBB_2417629582155303358e_term(cOMBC_1922632389518567517l_bool,cOMBB_7937736296159719194e_term(cOMBB_6132650689756367373atural(member5458643631506449871atural),produc2566709293081654762atural)),S4)),X4),Xa2))
    <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X4),Xa2)),sup_su1748669630276497946atural(R4,S4))) ) )).

% sup_Un_eq2
fof(fact_1080_sup__Un__eq2,axiom,(
    ! [R4,S4,X4,Xa2] :
      ( pp(aa_Pro5843519176478241656r_bool(aa_fun5449300841655810358r_bool(sup_su2691584770669240737r_bool(cOMBC_2430318800797357742r_bool(cOMBB_680426673656512949e_term(cOMBC_1164745642197396244r_bool,cOMBB_5316222305875338853e_term(cOMBB_3072517373778436405nteger(member6423679177046879214nteger),produc7384524951051686153nteger)),R4),cOMBC_2430318800797357742r_bool(cOMBB_680426673656512949e_term(cOMBC_1164745642197396244r_bool,cOMBB_5316222305875338853e_term(cOMBB_3072517373778436405nteger(member6423679177046879214nteger),produc7384524951051686153nteger)),S4)),X4),Xa2))
    <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X4),Xa2)),sup_su5841867293152630969nteger(R4,S4))) ) )).

% sup_Un_eq2
fof(fact_1081_sup__Un__eq2,axiom,(
    ! [R4,S4,X4,Xa2] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun5300525129335604105t_bool(sup_su8737265340369414900t_bool(cOMBC_4650738552150274286t_bool(cOMBB_9203412279331060138e_term(cOMBC_3685975587475309385t_bool,cOMBB_2463357054279533846e_term(cOMBB_1737989579323207725nt_int(member690604328116145115nt_int),produc1560874099174258678nt_int)),R4),cOMBC_4650738552150274286t_bool(cOMBB_9203412279331060138e_term(cOMBC_3685975587475309385t_bool,cOMBB_2463357054279533846e_term(cOMBB_1737989579323207725nt_int(member690604328116145115nt_int),produc1560874099174258678nt_int)),S4)),X4),Xa2))
    <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X4),Xa2)),sup_su3143671203043873318nt_int(R4,S4))) ) )).

% sup_Un_eq2
fof(fact_1082_sup__Un__eq2,axiom,(
    ! [R4,S4,X4,Xa2] :
      ( pp(aa_Pro4501881432599481050t_bool(aa_fun4446166836006121821t_bool(sup_su8464148172981958856t_bool(cOMBC_1018679855623880686t_bool(cOMBB_944033637513888382e_term(cOMBC_2995058810049920797t_bool,cOMBB_7430342728797892074e_term(cOMBB_952788161300084357nt_int(member500491123954006279nt_int),produc4852315488734385442nt_int)),R4),cOMBC_1018679855623880686t_bool(cOMBB_944033637513888382e_term(cOMBC_2995058810049920797t_bool,cOMBB_7430342728797892074e_term(cOMBB_952788161300084357nt_int(member500491123954006279nt_int),produc4852315488734385442nt_int)),S4)),X4),Xa2))
    <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X4),Xa2)),sup_su1426507467619248466nt_int(R4,S4))) ) )).

% sup_Un_eq2
fof(fact_1083_ImageE,axiom,(
    ! [B,R,A4] :
      ( member_nat(B,image_nat_nat(R,A4))
     => ~ ! [X3] :
            ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),B)),R))
           => ~ member_nat(X3,A4) ) ) )).

% ImageE
fof(fact_1084_ImageE,axiom,(
    ! [B,R,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_4802155899172601389at_nat(R,A4)))
     => ~ ! [X3] :
            ( member3919319858682911658at_nat(produc1860397064299428849at_nat(X3,B),R)
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4)) ) ) )).

% ImageE
fof(fact_1085_ImageE,axiom,(
    ! [B,R,A4] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_2484338115069272851at_nat(R,A4)))
     => ~ ! [X3] :
            ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,X3),B)),R))
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4)) ) ) )).

% ImageE
fof(fact_1086_ImageE,axiom,(
    ! [B,R,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_8438546471840335737at_nat(R,A4)))
     => ~ ! [X3] :
            ( member6033505038158179318at_nat(produc5496787636967163197at_nat(X3,B),R)
           => ~ pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,X3),A4)) ) ) )).

% ImageE
fof(fact_1087_ImageE,axiom,(
    ! [B,R,A4] :
      ( pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,B),image_2092125385209402259at_nat(R,A4)))
     => ~ ! [X3] :
            ( member8062223511168850704at_nat(produc4662710985925991255at_nat(X3,B),R)
           => ~ pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,X3),A4)) ) ) )).

% ImageE
fof(fact_1088_ImageE,axiom,(
    ! [B,R,A4] :
      ( member157494554546826820nteger(B,image_1218129382900921687nteger(R,A4))
     => ~ ! [X3] :
            ( pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,X3),B)),R))
           => ~ member4312719604404396038e_term(X3,A4) ) ) )).

% ImageE
fof(fact_1089_ImageE,axiom,(
    ! [B,R,A4] :
      ( member8280416476884352090atural(B,image_615082366656534702atural(R,A4))
     => ~ ! [X3] :
            ( pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,X3),B)),R))
           => ~ member3406593020217859077e_term(X3,A4) ) ) )).

% ImageE
fof(fact_1090_ImageE,axiom,(
    ! [B,R,A4] :
      ( member157494554546826820nteger(B,image_5432898024626566093nteger(R,A4))
     => ~ ! [X3] :
            ( pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,X3),B)),R))
           => ~ member4565687819040644368e_term(X3,A4) ) ) )).

% ImageE
fof(fact_1091_ImageE,axiom,(
    ! [B,R,A4] :
      ( member5262025264175285858nt_int(B,image_5659330387682446010nt_int(R,A4))
     => ~ ! [X3] :
            ( pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,X3),B)),R))
           => ~ member2948136515907314945e_term(X3,A4) ) ) )).

% ImageE
fof(fact_1092_ImageE,axiom,(
    ! [B,R,A4] :
      ( member5262025264175285858nt_int(B,image_5290376555693934566nt_int(R,A4))
     => ~ ! [X3] :
            ( pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,X3),B)),R))
           => ~ member7723273712176309973e_term(X3,A4) ) ) )).

% ImageE
fof(fact_1093_conditional__action_Orel__compp__Grp,axiom,(
    ! [R4] : condit6184561423513516559nteger(R4) = relcom99973385474455940nteger(conver309101513159102947e_term(bNF_Gr337280025065919164e_term(collec8013588583170467972nteger(cOMBC_1412576520028865000r_bool(cOMBB_6453866196482202699nteger(ord_le5347933966117430903nteger,condit7952600011703662612nteger),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,R4)))),condit2633228709571318698e_term(produc3971164842776949671nteger))),bNF_Gr8116150563447489316nteger(collec8013588583170467972nteger(cOMBC_1412576520028865000r_bool(cOMBB_6453866196482202699nteger(ord_le5347933966117430903nteger,condit7952600011703662612nteger),collec7922087001056311734nteger(aa_fun3323788978832462054r_bool(produc401098500374025047r_bool,R4)))),condit9202156164625486240nteger(produc7330894765516781285nteger))) )).

% conditional_action.rel_compp_Grp
fof(fact_1094_conditional__action_Orel__compp__Grp,axiom,(
    ! [R4] : condit8136067717219687782atural(R4) = relcom256228386380075716atural(conver7098552031471122361e_term(bNF_Gr7710201126091049106e_term(collec6097989394234547547atural(cOMBC_4777985434584799034l_bool(cOMBB_69603593386543220atural(ord_le8467756462758155086atural,condit6721827335151951979atural),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,R4)))),condit530872168517844736e_term(produc1168782837711296254atural))),bNF_Gr7469776983787714339atural(collec6097989394234547547atural(cOMBC_4777985434584799034l_bool(cOMBB_69603593386543220atural(ord_le8467756462758155086atural,condit6721827335151951979atural),collec6367547018462048781atural(aa_fun6400397208912365478l_bool(produc8343529308684018112l_bool,R4)))),condit110732285524013727atural(produc3992340709582277180atural))) )).

% conditional_action.rel_compp_Grp
fof(fact_1095_conditional__action_Orel__compp__Grp,axiom,(
    ! [R4] : condit3730511338334943365nteger(R4) = relcom1621412717945473540nteger(conver81526066115015267e_term(bNF_Gr693175160734942012e_term(collec967815020255904762nteger(cOMBC_8733656865795830012r_bool(cOMBB_1842404469168437973nteger(ord_le3337582088779512301nteger,condit7686862880692381322nteger),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,R4)))),condit3166682508218680618e_term(produc5986598495681327645nteger))),bNF_Gr331786366395757870nteger(collec967815020255904762nteger(cOMBC_8733656865795830012r_bool(cOMBB_1842404469168437973nteger(ord_le3337582088779512301nteger,condit7686862880692381322nteger),collec7332582564002478124nteger(aa_fun4743479584365168742r_bool(produc1236900166980094561r_bool,R4)))),condit3587349607997788074nteger(produc8810156367552308571nteger))) )).

% conditional_action.rel_compp_Grp
fof(fact_1096_conditional__action_Orel__compp__Grp,axiom,(
    ! [R4] : condit2775462794712788850nt_int(R4) = relcom3405438673302639556nt_int(conver3480862838003837121e_term(bNF_Gr621134324465781146e_term(collec5845839669341505895nt_int(cOMBC_6803298798058583842t_bool(cOMBB_418042858550060136nt_int(ord_le5172437211506631514nt_int,condit2367099723822225015nt_int),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,R4)))),condit8347815893170957832e_term(produc6655012789309278474nt_int))),bNF_Gr5978729743880596511nt_int(collec5845839669341505895nt_int(cOMBC_6803298798058583842t_bool(cOMBB_418042858550060136nt_int(ord_le5172437211506631514nt_int,condit2367099723822225015nt_int),collec3203402231325458457nt_int(aa_fun7074524131408103078t_bool(produc625993674133193396t_bool,R4)))),condit7137826502243047323nt_int(produc7622839952223151176nt_int))) )).

% conditional_action.rel_compp_Grp
fof(fact_1097_conditional__action_Orel__compp__Grp,axiom,(
    ! [R4] : condit3271435385184627870nt_int(R4) = relcom3847978374845482180nt_int(conver5636284800009640385e_term(bNF_Gr8199425639716154010e_term(collec8282763664059201683nt_int(cOMBC_6809366433643302090t_bool(cOMBB_7614080557269926204nt_int(ord_le172202941055982214nt_int,condit7400265531455562659nt_int),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,R4)))),condit6729456979053129992e_term(produc2507970727455213110nt_int))),bNF_Gr3797495339062392819nt_int(collec8282763664059201683nt_int(cOMBC_6809366433643302090t_bool(cOMBB_7614080557269926204nt_int(ord_le172202941055982214nt_int,condit7400265531455562659nt_int),collec8164060689515068741nt_int(aa_fun7956820646887163302t_bool(produc6627716702706253960t_bool,R4)))),condit3930740424007402351nt_int(produc726383008135262580nt_int))) )).

% conditional_action.rel_compp_Grp
fof(fact_1098_conditional__action_Orel__compp__Grp,axiom,(
    ! [R4] : condit1127689873879419692atural(R4) = relcom7477549861947874628atural(conver9184724556494050873atural(bNF_Gr659660228831487250atural(collec3264392531641636129atural(cOMBC_6514811739612929710l_bool(cOMBB_1840833620497539502atural(ord_le2202040463148982292atural,condit6773436539961436209atural),collec1991479681304692691atural(produc5868410056131333498l_bool(R4)))),condit7067702762122744960atural(produc497848011034438852atural))),bNF_Gr7139796620294019805atural(collec3264392531641636129atural(cOMBC_6514811739612929710l_bool(cOMBB_1840833620497539502atural(ord_le2202040463148982292atural,condit6773436539961436209atural),collec1991479681304692691atural(produc5868410056131333498l_bool(R4)))),condit4604360551831230809atural(produc6591912806276919810atural))) )).

% conditional_action.rel_compp_Grp
fof(fact_1099_conditional__action_Orel__compp__Grp,axiom,(
    ! [R4] : condit1543564991105445733list_f(R4) = relcom7515417596351238834list_f(conver7720072225776492021action(bNF_Gr6437747679974042972action(collec7820802666344048348list_f(cOMBC_3324183268558603608f_bool(cOMBB_5499718888831777787list_f(ord_le3852096572277380649list_f,condit6827580605863688246list_f),collec2941370454899091988list_f(produc4709439930048449441f_bool(R4)))),condit7155426171764300860action(produc3089225533250117581list_f))),bNF_Gr9208479453086946510list_f(collec7820802666344048348list_f(cOMBC_3324183268558603608f_bool(cOMBB_5499718888831777787list_f(ord_le3852096572277380649list_f,condit6827580605863688246list_f),collec2941370454899091988list_f(produc4709439930048449441f_bool(R4)))),condit4069896782405135150list_f(produc8710481132536983823list_f))) )).

% conditional_action.rel_compp_Grp
fof(fact_1100_Image__singleton__iff,axiom,(
    ! [B,R,A] :
      ( member_nat(B,image_nat_nat(R,insert_nat(A,bot_bot_set_nat)))
    <=> pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R)) ) )).

% Image_singleton_iff
fof(fact_1101_Image__singleton__iff,axiom,(
    ! [B,R,A] :
      ( pp(aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(member8440522571783428010at_nat,B),image_2484338115069272851at_nat(R,insert8211810215607154385at_nat(A,bot_bo2099793752762293965at_nat))))
    <=> pp(aa_set1680211184867041100t_bool(aa_Pro6744037673880449662t_bool(member8206827879206165904at_nat,aa_Pro314188276017538018at_nat(aa_Pro5145766267327615662at_nat(produc6161850002892822231at_nat,A),B)),R)) ) )).

% Image_singleton_iff
fof(fact_1102_Image__singleton__iff,axiom,(
    ! [B,R,A] :
      ( member157494554546826820nteger(B,image_1218129382900921687nteger(R,insert190971643640263327e_term(A,bot_bo7261247930815417913e_term)))
    <=> pp(aa_set3464050655127758210r_bool(aa_Pro2389691766940459706r_bool(member4581088367259704696nteger,aa_Pro6252757739892038976nteger(aa_fun3790775640809306146nteger(produc4282985567423050387nteger,A),B)),R)) ) )).

% Image_singleton_iff
fof(fact_1103_Image__singleton__iff,axiom,(
    ! [B,R,A] :
      ( member8280416476884352090atural(B,image_615082366656534702atural(R,insert5978560002646234782e_term(A,bot_bo9191057816668355256e_term)))
    <=> pp(aa_set4207312397001245291l_bool(aa_Pro8078843286258240140l_bool(member5458643631506449871atural,aa_Pro4163967833709371565atural(aa_fun5152780764703512272atural(produc2566709293081654762atural,A),B)),R)) ) )).

% Image_singleton_iff
fof(fact_1104_Image__singleton__iff,axiom,(
    ! [B,R,A] :
      ( member157494554546826820nteger(B,image_5432898024626566093nteger(R,insert7137654801469020073e_term(A,bot_bo7010734887469065795e_term)))
    <=> pp(aa_set1981577615330639756r_bool(aa_Pro8002950007301694158r_bool(member6423679177046879214nteger,aa_Pro490869892464487350nteger(aa_fun4101202993852558094nteger(produc7384524951051686153nteger,A),B)),R)) ) )).

% Image_singleton_iff
fof(fact_1105_Image__singleton__iff,axiom,(
    ! [B,R,A] :
      ( member5262025264175285858nt_int(B,image_5659330387682446010nt_int(R,insert2106057668996072346e_term(A,bot_bo5496473946294314420e_term)))
    <=> pp(aa_set462754579954174303t_bool(aa_Pro2723816575955516532t_bool(member690604328116145115nt_int,aa_Pro3513184699142849729nt_int(aa_fun1388719692539776744nt_int(produc1560874099174258678nt_int,A),B)),R)) ) )).

% Image_singleton_iff
fof(fact_1106_Image__singleton__iff,axiom,(
    ! [B,R,A] :
      ( member5262025264175285858nt_int(B,image_5290376555693934566nt_int(R,insert5784700836022525294e_term(A,bot_bo8374228283394309512e_term)))
    <=> pp(aa_set6451871791712458035t_bool(aa_Pro2057418844460291100t_bool(member500491123954006279nt_int,aa_Pro835648289009615341nt_int(aa_fun7940596247606734144nt_int(produc4852315488734385442nt_int,A),B)),R)) ) )).

% Image_singleton_iff
fof(fact_1107_exE__realizer,axiom,(
    ! [P,P2,Q,F] :
      ( pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(P,produc8662200840462671639atural(P2)),produc1773691148792264405atural(P2)))
     => ( ! [X3,Y3] :
            ( pp(aa_Code_natural_bool(aa_Cod6910080592713026658l_bool(P,Y3),X3))
           => pp(aa_Pro8832322792688638508l_bool(Q,aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(F,X3),Y3))) )
       => pp(aa_Pro8832322792688638508l_bool(Q,aa_Pro1971126414814181170atural(aa_fun4394021921911188166atural(produc8282080750456430313atural,F),P2))) ) ) )).

% exE_realizer
fof(fact_1108_type__copy__map__comp0,axiom,(
    ! [Rep,Abs,M,M1,M2,F,G] :
      ( type_d8388589096064860894list_f(Rep,Abs,top_to1815313666553408473list_f)
     => ( M = comp_P4267156721827287172list_f(M1,M2)
       => comp_P1644921750638218854list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),M),G) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P7466797539550205536list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),M1),Rep)),comp_P4267156721827287172list_f(comp_P4267156721827287172list_f(Abs,M2),G)) ) ) )).

% type_copy_map_comp0
fof(fact_1109_type__copy__map__comp0,axiom,(
    ! [Rep,Abs,M,M1,M2,F,G] :
      ( type_d8650893153313958540list_f(Rep,Abs,top_to1815313666553408473list_f)
     => ( M = comp_P5708296701725499586list_f(M1,M2)
       => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(F,M)),G) = comp_l8432902307485339590list_f(comp_P2924191066912980934_a_b_c(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),M1),Rep),aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P7466797539550205536list_f(Abs,M2)),G)) ) ) )).

% type_copy_map_comp0
fof(fact_1110_type__copy__map__comp0,axiom,(
    ! [Rep,Abs,M,M1,M2,F,G] :
      ( type_d8388589096064860894list_f(Rep,Abs,top_to1815313666553408473list_f)
     => ( M = comp_P5708296701725499586list_f(M1,M2)
       => aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(F,M)),G) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P7466797539550205536list_f(aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,F),M1),Rep)),comp_P2673361230361438154list_f(comp_P5708296701725499586list_f(Abs,M2),G)) ) ) )).

% type_copy_map_comp0
fof(fact_1111_type__copy__map__comp0,axiom,(
    ! [Rep,Abs,M,M1,M2,F,G] :
      ( type_d4693429255118607336list_f(Rep,Abs,top_to3090985321854968643list_f)
     => ( M = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,M1),M2)
       => comp_P1644921750638218854list_f(comp_l8432902307485339590list_f(F,M),G) = aa_fun2596409532572620736_a_b_c(aa_fun7869170901863626566_a_b_c(comp_P4767578765025054880list_f,comp_P5271726855292207526list_f(comp_l6492537726383095040list_f(F,M1),Rep)),comp_P4267156721827287172list_f(comp_P2673361230361438154list_f(Abs,M2),G)) ) ) )).

% type_copy_map_comp0
fof(fact_1112_add__Suc__right,axiom,(
    ! [M3,N2] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M3),aa_nat_nat(suc,N2)) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M3),N2)) )).

% add_Suc_right
fof(fact_1113_nat__induct,axiom,(
    ! [P,N2] :
      ( pp(aa_nat_bool(P,zero_zero_nat))
     => ( ! [N3] :
            ( pp(aa_nat_bool(P,N3))
           => pp(aa_nat_bool(P,aa_nat_nat(suc,N3))) )
       => pp(aa_nat_bool(P,N2)) ) ) )).

% nat_induct
fof(fact_1114_nat_Oinject,axiom,(
    ! [X2,Y2] :
      ( aa_nat_nat(suc,X2) = aa_nat_nat(suc,Y2)
    <=> X2 = Y2 ) )).

% nat.inject

% Helper facts (452)
fof(help_fNot_2_1_U,axiom,(
    ! [P] :
      ( pp(P)
      | pp(aa_bool_bool(fNot,P)) ) )).

fof(help_fNot_1_1_U,axiom,(
    ! [P] :
      ( ~ pp(aa_bool_bool(fNot,P))
      | ~ pp(P) ) )).

fof(help_fTrue_1_1_U,axiom,(
    pp(fTrue) )).

fof(help_fconj_3_1_U,axiom,(
    ! [P,Q] :
      ( ~ pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fconj,P),Q))
      | pp(Q) ) )).

fof(help_fconj_2_1_U,axiom,(
    ! [P,Q] :
      ( ~ pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fconj,P),Q))
      | pp(P) ) )).

fof(help_fconj_1_1_U,axiom,(
    ! [P,Q] :
      ( ~ pp(P)
      | ~ pp(Q)
      | pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fconj,P),Q)) ) )).

fof(help_fdisj_3_1_U,axiom,(
    ! [P,Q] :
      ( ~ pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fdisj,P),Q))
      | pp(P)
      | pp(Q) ) )).

fof(help_fdisj_2_1_U,axiom,(
    ! [Q,P] :
      ( ~ pp(Q)
      | pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fdisj,P),Q)) ) )).

fof(help_fdisj_1_1_U,axiom,(
    ! [P,Q] :
      ( ~ pp(P)
      | pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fdisj,P),Q)) ) )).

fof(help_fFalse_1_1_U,axiom,(
    ~ pp(fFalse) )).

fof(help_fequal_2_1_fequal_001t__Nat__Onat_T,axiom,(
    ! [X,Y] :
      ( X != Y
      | pp(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,X),Y)) ) )).

fof(help_fequal_1_1_fequal_001t__Nat__Onat_T,axiom,(
    ! [X,Y] :
      ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,X),Y))
      | X = Y ) )).

fof(help_fequal_2_1_fequal_001t__HOL__Obool_T,axiom,(
    ! [X,Y] :
      ( X != Y
      | pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fequal_bool,X),Y)) ) )).

fof(help_fequal_1_1_fequal_001t__HOL__Obool_T,axiom,(
    ! [X,Y] :
      ( ( gg_bool(X)
        & gg_bool(Y) )
     => ( ~ pp(aa_bool_bool(aa_boo8970175072276269406l_bool(fequal_bool,X),Y))
        | X = Y ) ) )).

fof(help_COMBK_1_1_COMBK_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q] : aa_nat_set_nat(cOMBK_set_nat_nat(P),Q) = P )).

fof(help_If_3_1_If_001t__Predicate__Opred_It__Product____Type__Ounit_J_T,axiom,(
    ! [P] :
      ( gg_bool(P)
     => ( P = fTrue
        | P = fFalse ) ) )).

fof(help_If_2_1_If_001t__Predicate__Opred_It__Product____Type__Ounit_J_T,axiom,(
    ! [X,Y] : aa_pre3989069114404521604t_unit(aa_pre1931757783800482596t_unit(aa_boo5334558160969881534t_unit(if_pred_Product_unit,fFalse),X),Y) = Y )).

fof(help_If_1_1_If_001t__Predicate__Opred_It__Product____Type__Ounit_J_T,axiom,(
    ! [X,Y] : aa_pre3989069114404521604t_unit(aa_pre1931757783800482596t_unit(aa_boo5334558160969881534t_unit(if_pred_Product_unit,fTrue),X),Y) = X )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__HOL__Obool_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat_bool(aa_fun3878383735219268284t_bool(aa_fun6180650586719570436t_bool(cOMBB_bool_bool_nat,P),Q),R2) = aa_bool_bool(P,aa_nat_bool(Q,R2)) )).

fof(help_fequal_2_1_fequal_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,(
    ! [X,Y] :
      ( X != Y
      | pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(fequal9188845342289841878at_nat,X),Y)) ) )).

fof(help_fequal_1_1_fequal_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,(
    ! [X,Y] :
      ( ~ pp(aa_Pro2232559814647311250t_bool(aa_Pro595088089689268830t_bool(fequal9188845342289841878at_nat,X),Y))
      | X = Y ) )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat_fun_bool_bool(aa_fun2989677294862114484l_bool(cOMBB_4201503070600411334ol_nat(P),Q),R2) = aa_boo8970175072276269406l_bool(P,aa_nat_bool(Q,R2)) )).

fof(help_fequal_2_1_fequal_001t__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_T,axiom,(
    ! [X,Y] :
      ( X != Y
      | pp(aa_lis2459260365661518090c_bool(aa_lis7273232353230549214c_bool(fequal170887312758788190_a_b_c,X),Y)) ) )).

fof(help_fequal_1_1_fequal_001t__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_T,axiom,(
    ! [X,Y] :
      ( ~ pp(aa_lis2459260365661518090c_bool(aa_lis7273232353230549214c_bool(fequal170887312758788190_a_b_c,X),Y))
      | X = Y ) )).

fof(help_COMBI_1_1_COMBI_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_U,axiom,(
    ! [P] : aa_Pro4262726347734369532atural(cOMBI_5557065343485138948atural,P) = P )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__HOL__Obool_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro2232559814647311250t_bool(aa_fun830836278467416944t_bool(aa_fun2412459903328548336t_bool(cOMBB_3950327738894754075at_nat,P),Q),R2) = aa_bool_bool(P,aa_Pro2232559814647311250t_bool(Q,R2)) )).

fof(help_COMBS_1_1_COMBS_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__HOL__Obool_001t__HOL__Obool_U,axiom,(
    ! [P,Q,R2] : aa_Pro2232559814647311250t_bool(cOMBS_7530496056240154442l_bool(P,Q),R2) = aa_bool_bool(aa_Pro209297932965175752l_bool(P,R2),aa_Pro2232559814647311250t_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_nat_fun_nat_bool(aa_fun8271680885375493061t_bool(aa_fun2322726656987972634t_bool(cOMBC_1981652900330269559t_bool,P),Q),R2) = aa_fun3878383735219268284t_bool(aa_nat834873606189959505t_bool(P,R2),Q) )).

fof(help_COMBS_1_1_COMBS_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_nat_fun_nat_bool(aa_fun3051233943552222972t_bool(aa_fun4650549077784175441t_bool(cOMBS_9184950873606742919t_bool,P),Q),R2) = aa_fun3878383735219268284t_bool(aa_nat834873606189959505t_bool(P,R2),aa_nat_fun_nat_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__HOL__Obool_U,axiom,(
    ! [P,Q,R2] : aa_nat_bool(aa_set8326603473350452667t_bool(aa_fun1731190876918621446t_bool(cOMBC_6089182126854364013t_bool,P),Q),R2) = aa_set3135850010578026034t_bool(aa_nat1303072629729950279t_bool(P,R2),Q) )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro209297932965175752l_bool(aa_fun5074320335491881728l_bool(cOMBB_1143792199142760587at_nat(P),Q),R2) = aa_boo8970175072276269406l_bool(P,aa_Pro2232559814647311250t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat8637530788439456283t_bool(aa_fun204589911651413381t_bool(aa_fun1018874135808871318t_bool(cOMBB_1789210886255972223ol_nat,P),Q),R2) = aa_fun8271680885375493061t_bool(P,aa_nat_fun_nat_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_001t__fun_It__Nat__Onat_Mt__fun_It__HOL__Obool_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat3163428491658862046l_bool(cOMBB_7721905284830110236ol_nat(P,Q),R2) = aa_fun2989677294862114484l_bool(P,aa_nat_fun_nat_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8506890182770087144t_unit(aa_fun750287645178195360t_unit(cOMBB_5909589190342145515at_nat(P),Q),R2) = aa_boo4159737051336811902t_unit(P,aa_Pro2232559814647311250t_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_nat_fun_nat_bool(cOMBC_6245729688356921590t_bool(P,Q),R2) = aa_set8326603473350452667t_bool(aa_nat1720457667890852176t_bool(P,R2),Q) )).

fof(help_COMBK_1_1_COMBK_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q] : aa_Pro2745879313366468188at_nat(cOMBK_4933461867592223342at_nat(P),Q) = P )).

fof(help_COMBB_1_1_COMBB_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__HOL__Obool_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro2232559814647311250t_bool(cOMBB_150397177082651397at_nat(P,Q),R2) = aa_Pro2232559814647311250t_bool(P,aa_Pro262675715343573244at_nat(Q,R2)) )).

fof(help_COMBI_1_1_COMBI_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_U,axiom,(
    ! [P] : aa_fun78455448157554618e_term(cOMBI_2333703903009992107e_term,P) = P )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro6053131305333494555t_bool(aa_fun189373014291222662t_bool(aa_fun7664782273987169786t_bool(cOMBC_1646952264703196058t_bool,P),Q),R2) = aa_fun3878383735219268284t_bool(aa_Pro746613062265399688t_bool(P,R2),Q) )).

fof(help_COMBS_1_1_COMBS_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro6053131305333494555t_bool(aa_fun5443727378596093570t_bool(aa_fun6229411332278246492t_bool(cOMBS_1476421882506702730t_bool,P),Q),R2) = aa_fun3878383735219268284t_bool(aa_Pro746613062265399688t_bool(P,R2),aa_Pro6053131305333494555t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat8637530788439456283t_bool(aa_fun3506238582381801276t_bool(aa_fun889501055239289092t_bool(cOMBB_7554325574139592886ol_nat,P),Q),R2) = aa_fun3051233943552222972t_bool(P,aa_nat8637530788439456283t_bool(Q,R2)) )).

fof(help_fequal_2_1_fequal_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,(
    ! [X,Y] :
      ( X != Y
      | pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(fequal3254904519494148796at_nat,X),Y)) ) )).

fof(help_fequal_1_1_fequal_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,(
    ! [X,Y] :
      ( ~ pp(aa_Pro6098352494050694700t_bool(aa_Pro3036501517321368926t_bool(fequal3254904519494148796at_nat,X),Y))
      | X = Y ) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__fun_It__fun_It__Nat__Onat_Mt__HOL__Obool_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat834873606189959505t_bool(aa_fun1592868304168936478t_bool(cOMBB_2778472989460164414ol_nat(P),Q),R2) = aa_fun6180650586719570436t_bool(P,aa_nat_fun_bool_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__HOL__Obool_U,axiom,(
    ! [P,Q,R2] : aa_Pro2232559814647311250t_bool(aa_set5223363028666124222t_bool(cOMBC_4213388754263852048t_bool(P),Q),R2) = aa_set3135850010578026034t_bool(aa_Pro5021235949175849214t_bool(P,R2),Q) )).

fof(help_COMBC_1_1_COMBC_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_U,axiom,(
    ! [P,Q,R2] : aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(cOMBC_1248919038785528696atural(P),Q),R2) = aa_Cod5614077553384211403atural(aa_Cod3891347372088052988atural(P,R2),Q) )).

fof(help_COMBI_1_1_COMBI_001t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_U,axiom,(
    ! [P] : aa_fun1274623470434842396e_term(cOMBI_114885526001389276e_term,P) = P )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8506890182770087144t_unit(aa_pre208042025896535190t_unit(aa_fun1657288031602172754t_unit(cOMBC_1552180646880195170t_unit,P),Q),R2) = aa_pre3989069114404521604t_unit(aa_Pro6751710116387044744t_unit(P,R2),Q) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat6473910981375751856t_bool(aa_fun1933221252834185820t_bool(aa_fun8791520983537993042t_bool(cOMBB_3629999415770602094ol_nat,P),Q),R2) = aa_fun189373014291222662t_bool(P,aa_nat_fun_nat_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat4401263874371387303t_bool(aa_fun48933764387891548t_bool(cOMBB_6165210988431530350ol_nat(P),Q),R2) = aa_fun2126031879273811846t_bool(P,aa_nat8637530788439456283t_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_J_U,axiom,(
    ! [P,Q,R2] : aa_nat6217843819516004004t_bool(cOMBC_6336148525615794240t_bool(P,Q),R2) = aa_fun204589911651413381t_bool(aa_nat4154366228397672218t_bool(P,R2),Q) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8506890182770087144t_unit(aa_Pro1289996471523352882t_unit(aa_fun7850576842391497904t_unit(cOMBC_4661858004074810762t_unit,P),Q),R2) = aa_Pro8506890182770087144t_unit(aa_Pro1289996471523352882t_unit(P,R2),Q) )).

fof(help_COMBB_1_1_COMBB_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__HOL__Obool_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat1303072629729950279t_bool(aa_fun2243412928714297300t_bool(cOMBB_8823940721079071078ol_nat(P),Q),R2) = aa_Pro5021235949175849214t_bool(P,aa_nat7603221163087113075at_nat(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__HOL__Obool_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro6098352494050694700t_bool(aa_fun3665199231186260388t_bool(aa_fun387114033786370596t_bool(cOMBB_2433561337776822657at_nat,P),Q),R2) = aa_bool_bool(P,aa_Pro6098352494050694700t_bool(Q,R2)) )).

fof(help_COMBS_1_1_COMBS_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__HOL__Obool_001t__HOL__Obool_U,axiom,(
    ! [P,Q,R2] : aa_Pro6098352494050694700t_bool(cOMBS_2815829179688385072l_bool(P,Q),R2) = aa_bool_bool(aa_Pro3835118249596729774l_bool(P,R2),aa_Pro6098352494050694700t_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_nat4401263874371387303t_bool(aa_fun6469607317360106941t_bool(aa_fun4648349037183602870t_bool(cOMBC_5836600391518924715t_bool,P),Q),R2) = aa_fun830836278467416944t_bool(aa_nat8680207125483269565t_bool(P,R2),Q) )).

fof(help_COMBS_1_1_COMBS_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_nat4401263874371387303t_bool(aa_fun5049402356129940746t_bool(aa_fun4518904131321711619t_bool(cOMBS_6457767331776253883t_bool,P),Q),R2) = aa_fun830836278467416944t_bool(aa_nat8680207125483269565t_bool(P,R2),aa_nat4401263874371387303t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__fun_It__fun_It__Nat__Onat_Mt__HOL__Obool_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro746613062265399688t_bool(aa_fun6939514116782475324t_bool(cOMBB_571549606332118035at_nat(P),Q),R2) = aa_fun6180650586719570436t_bool(P,aa_Pro209297932965175752l_bool(Q,R2)) )).

fof(help_COMBS_1_1_COMBS_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_J_U,axiom,(
    ! [P,Q,R2] : aa_nat6217843819516004004t_bool(cOMBS_7975979422065336327t_bool(P,Q),R2) = aa_fun3506238582381801276t_bool(aa_nat6407440567134823633t_bool(P,R2),aa_nat6217843819516004004t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__Code____Numeral__Onatural_001t__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_U,axiom,(
    ! [P,Q,R2] : aa_Cod3891347372088052988atural(cOMBB_6959547025548011708atural(P,Q),R2) = aa_Cod3891347372088052988atural(P,aa_Cod4272041906116450446atural(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__fun_It__HOL__Obool_Mt__HOL__Obool_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__fun_It__Nat__Onat_Mt__HOL__Obool_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat1946370342503694750t_bool(cOMBB_7887238097748047192ol_nat(P,Q),R2) = aa_fun1592868304168936478t_bool(P,aa_nat3163428491658862046l_bool(Q,R2)) )).

fof(help_COMBK_1_1_COMBK_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_U,axiom,(
    ! [P,Q] : aa_Pro3947048415938404539e_term(aa_fun944592746569834766e_term(cOMBK_1145910323346499051nt_int,P),Q) = P )).

fof(help_COMBB_1_1_COMBB_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__fun_It__Product____Type__Ounit_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro4556594967771855678t_unit(aa_fun2159987164234823744t_unit(cOMBB_852830008901541831at_nat(P),Q),R2) = aa_pre8602123596742896802t_unit(P,aa_Pro8506890182770087144t_unit(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Product____Type__Ounit_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8506890182770087144t_unit(aa_fun4298207804742365940t_unit(aa_fun999544733659075342t_unit(cOMBB_115759876198316351at_nat,P),Q),R2) = aa_fun146729347719784746t_unit(P,aa_Pro4556594967771855678t_unit(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Ounit_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8506890182770087144t_unit(aa_fun5818004955337293424t_unit(aa_fun773889731798638256t_unit(cOMBC_1545691546122322636t_unit,P),Q),R2) = aa_fun146729347719784746t_unit(aa_Pro784238087273524980t_unit(P,R2),Q) )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro3835118249596729774l_bool(aa_fun1881461277634404812l_bool(cOMBB_6335558003536670961at_nat(P),Q),R2) = aa_boo8970175072276269406l_bool(P,aa_Pro6098352494050694700t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat4909001760120733684t_bool(cOMBB_2831812752480454468ol_nat(P,Q),R2) = aa_fun48933764387891548t_bool(P,aa_nat6217843819516004004t_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8907290612264431874at_nat(aa_lis7918485433062139092at_nat(cOMBC_5135100225479720282at_nat(P),Q),R2) = aa_lis7799128381380053116at_nat(aa_Pro8296961830729446856at_nat(P,R2),Q) )).

fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro1271188383344610766t_unit(aa_fun7890836787989247596t_unit(cOMBB_4063035190317856337at_nat(P),Q),R2) = aa_boo4159737051336811902t_unit(P,aa_Pro6098352494050694700t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__HOL__Obool_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro6098352494050694700t_bool(cOMBB_3190877037383586923at_nat(P,Q),R2) = aa_Pro2232559814647311250t_bool(P,aa_Pro5901169740204579478at_nat(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__HOL__Obool_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro2232559814647311250t_bool(cOMBB_5528459013814913387at_nat(P,Q),R2) = aa_Pro6098352494050694700t_bool(P,aa_Pro314188276017538018at_nat(Q,R2)) )).

fof(help_COMBK_1_1_COMBK_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_U,axiom,(
    ! [P,Q] : aa_Cod1269109650860651881atural(cOMBK_3223473554123672507atural(P),Q) = P )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat84984821910774420t_bool(cOMBB_7227252839205164092ol_nat(P,Q),R2) = aa_fun2243412928714297300t_bool(P,aa_nat8803788312118491388at_nat(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__fun_It__Predicate__Opred_It__Product____Type__Ounit_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro6751710116387044744t_unit(aa_pre6155415440720408630t_unit(aa_fun4576160418549306194t_unit(cOMBC_2112645637916996866t_unit,P),Q),R2) = aa_pre1931757783800482596t_unit(aa_Pro1195099120564181800t_unit(P,R2),Q) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro595088089689268830t_bool(aa_fun6334770939707717654t_bool(aa_fun2468199098371297510t_bool(cOMBC_3379778804465295182t_bool,P),Q),R2) = aa_fun830836278467416944t_bool(aa_Pro5529731459010903924t_bool(P,R2),Q) )).

fof(help_COMBS_1_1_COMBS_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro595088089689268830t_bool(aa_fun7646573545999865340t_bool(aa_fun5759540267560836618t_bool(cOMBS_5963004598402476862t_bool,P),Q),R2) = aa_fun830836278467416944t_bool(aa_Pro5529731459010903924t_bool(P,R2),aa_Pro595088089689268830t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8506890182770087144t_unit(aa_fun1391145070468373888t_unit(aa_fun8845813833396145318t_unit(cOMBB_6816641055676022475at_nat,P),Q),R2) = aa_fun3990267935303614238t_unit(P,aa_Pro1289996471523352882t_unit(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro1289996471523352882t_unit(aa_pre3988284201554867738t_unit(aa_fun8620934445070975814t_unit(cOMBC_1831313084446023480t_unit,P),Q),R2) = aa_pre208042025896535190t_unit(aa_Pro4493927905640485544t_unit(P,R2),Q) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro8506890182770087144t_unit(aa_fun7389658442252459900t_unit(aa_fun1900588733094304816t_unit(cOMBC_5613538993853102528t_unit,P),Q),R2) = aa_fun3990267935303614238t_unit(aa_Pro1683622670112538216t_unit(P,R2),Q) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat6473910981375751856t_bool(aa_fun1051380719783103260t_bool(aa_fun8097148653287952090t_bool(cOMBB_2123595567760207548ol_nat,P),Q),R2) = aa_fun5443727378596093570t_bool(P,aa_nat6473910981375751856t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat8680207125483269565t_bool(aa_fun3191157362054829962t_bool(cOMBB_4813502403176724906ol_nat(P),Q),R2) = aa_fun2412459903328548336t_bool(P,aa_nat_fun_bool_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_U,axiom,(
    ! [P,Q,R2] : aa_lis1888721035181932644t_bool(cOMBB_4314901741678400945at_nat(P,Q),R2) = aa_set5223363028666124222t_bool(P,aa_lis156294325248309974at_nat(Q,R2)) )).

fof(help_COMBI_1_1_COMBI_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_U,axiom,(
    ! [P] : aa_fun6283001615389677586e_term(cOMBI_276860953521691607e_term,P) = P )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__HOL__Obool_U,axiom,(
    ! [P,Q,R2] : aa_Pro2232559814647311250t_bool(aa_set7133975444747598372t_bool(aa_fun5101074560878262024t_bool(cOMBC_4555905863570137130t_bool,P),Q),R2) = aa_set1680211184867041100t_bool(aa_Pro673679001362789016t_bool(P,R2),Q) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__fun_It__fun_It__Nat__Onat_Mt__HOL__Obool_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_J_001t__fun_It__fun_It__Nat__Onat_Mt__HOL__Obool_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_J_001t__Nat__Onat_U,axiom,(
    ! [P,Q,R2] : aa_nat1091549829444833754t_bool(cOMBB_8897308571653880148ol_nat(P,Q),R2) = aa_fun2322726656987972634t_bool(P,aa_nat1946370342503694750t_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__HOL__Obool_J_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_U,axiom,(
    ! [P,Q,R2] : aa_lis1888721035181932644t_bool(cOMBB_4426666140241859373at_nat(P,Q),R2) = aa_fun830836278467416944t_bool(P,aa_lis1888721035181932644t_bool(Q,R2)) )).

fof(help_COMBK_1_1_COMBK_001t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_U,axiom,(
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fof(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__Predicate__Opred_It__Product____Type__Ounit_J_Mt__fun_It__Predicate__Opred_It__Product____Type__Ounit_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
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fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_001t__Predicate__Opred_It__Product____Type__Ounit_J_U,axiom,(
    ! [P,Q,R2] : aa_Pro1271188383344610766t_unit(aa_pre7336892875040048892t_unit(aa_fun2415461962621118546t_unit(cOMBC_889979299708343368t_unit,P),Q),R2) = aa_pre3989069114404521604t_unit(aa_Pro8882091768032951406t_unit(P,R2),Q) )).

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fof(help_COMBB_1_1_COMBB_001t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__HOL__Obool_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__HOL__Obool_J_J_001t__Nat__Onat_U,axiom,(
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    ! [X,Y] :
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    ! [P,Q,R2] : aa_Pro2990399855731684818t_unit(aa_pre6399090365428005818t_unit(aa_fun7899406617516134918t_unit(cOMBC_1152749508414443480t_unit,P),Q),R2) = aa_pre6430407070445525148t_unit(aa_Pro5211009889480899784t_unit(P,R2),Q) )).

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    ! [P,Q,R2] : aa_fun5449300841655810358r_bool(aa_fun4955923304055977320r_bool(cOMBB_2211189884751476963e_term(P),Q),R2) = aa_fun4727240567092119378r_bool(P,aa_fun8328143705649857432r_bool(Q,R2)) )).

fof(help_COMBB_1_1_COMBB_001t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Code____Numeral__Onatural_Mt__HOL__Obool_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_U,axiom,(
    ! [P,Q,R2] : aa_fun2237767473747863189l_bool(aa_fun3547110515371744892l_bool(cOMBB_3730184279310646956e_term(P),Q),R2) = aa_fun8474804861307533862l_bool(P,aa_fun9177371286630637389l_bool(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__HOL__Obool_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__HOL__Obool_J_U,axiom,(
    ! [P,Q,R2] : aa_fun4446166836006121821t_bool(cOMBC_1018679855623880686t_bool(P,Q),R2) = aa_set7689349865687036101t_bool(aa_fun8540507702595137920t_bool(P,R2),Q) )).

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    ! [P,Q,R2] : aa_lis8139133409912471826t_unit(cOMBB_725290839343848585at_nat(P,Q),R2) = aa_fun762978388704573670t_unit(P,aa_lis2506519724559586180t_unit(Q,R2)) )).

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    ! [P,Q,R2] : aa_typ2890955493076408557yperep(aa_fun4397140845006124742yperep(cOMBB_7462520177858535266yperep(P),Q),R2) = aa_fun7667238708423709092yperep(P,aa_typ6459841660691640093yperep(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_U,axiom,(
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    ! [P,Q,R2] : aa_fun12647182544461973nt_int(aa_fun4113236929402169470nt_int(cOMBC_1970634365177666650nt_int(P),Q),R2) = aa_fun4515943541990323139nt_int(aa_fun6202088590179050134nt_int(P,R2),Q) )).

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fof(help_COMBC_1_1_COMBC_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__HOL__Obool_J_U,axiom,(
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fof(help_COMBS_1_1_COMBS_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Ounit_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_J_U,axiom,(
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fof(help_COMBB_1_1_COMBB_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Product____Type__Ounit_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_J_001t__fun_It__fun_It__Product____Type__Ounit_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Predicate__Opred_It__Product____Type__Ounit_J_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_U,axiom,(
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    ! [P,Q,R2] : aa_fun6449790820940968040nteger(aa_fun7400512047292831810nteger(cOMBC_4772695251711667176nteger(P),Q),R2) = aa_fun3548662207239920076nteger(aa_fun6304923853830561828nteger(P,R2),Q) )).

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    ! [P,Q,R2] : aa_fun5948458986716103817atural(aa_fun4476102648722432878atural(cOMBC_4821272514476200682atural(P),Q),R2) = aa_fun5440178235464249219atural(aa_fun3928575249174453030atural(P,R2),Q) )).

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fof(help_COMBB_1_1_COMBB_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_Mt__HOL__Obool_J_001t__fun_It__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_U,axiom,(
    ! [P,Q,R2] : aa_fun2167848890301310464f_bool(cOMBB_6027208925197716341list_f(P,Q),R2) = aa_set891392515867043596f_bool(P,aa_fun977368851958964592list_f(Q,R2)) )).

fof(help_COMBC_1_1_COMBC_001t__fun_It__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__FinFun__Ofinfun_Itf__d_Mt__List__Olist_It__FWState__Olock____action_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__FWState__Onew____thread____action_Itf__a_Mtf__b_Mtf__c_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Oconditional____action_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Owait____set____action_Itf__a_Mtf__e_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__FWState__Ointerrupt____action_Itf__a_J_J_Mt__List__Olist_Itf__f_J_J_J_J_J_J_U,axiom,(
    ! [P,Q,R2] : aa_fun977368851958964592list_f(cOMBC_2422794320193074410list_f(P,Q),R2) = aa_set4815688690586077536list_f(aa_fun3298456610982006034list_f(P,R2),Q) )).

% Conjectures (1)
fof(conj_0,conjecture,(
    aa_Pro5002280679056845916_a_b_c(thr_a_d_a_b_c_e_f,aa_Pro2754906569428029390list_f(produc8331056147679645153list_f(ls),produc8608434180808776663list_f(nts,jswss))) = nts )).
