%------------------------------------------------------------------------------
% File     : SWX202-1 : TPTP v9.3.0. Released v9.3.0.
% Domain   : Software Verification
% Problem  : Faulty property about permutations
% Version  : Especial.
% English  :

% Refs     : [CST26] Claessen et al. (2026), Email to Geoff Sutcliffe
% Source   : [CST26]
% Names    : MergeSort_prop_permutation_wrong2.p [CST26]

% Status   : Unsatisfiable
% Rating   : 0.72 v9.3.0
% Syntax   : Number of clauses     :   36 (  36 unt;   0 nHn;   7 RR)
%            Number of literals    :   36 (  36 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   22 (  22 usr;   4 con; 0-5 aty)
%            Number of variables   :   63 (  17 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
    aux(Z,X2,X3,pair2(Ys1,Zs)) = pair2(cons(X2,Ys1),Zs) ).

cnf(axiom_001,axiom,
    aux2(Z,Xs,Y2,Ys,btrue) = cons(Z,merge(Xs,cons(Y2,Ys))) ).

cnf(axiom_002,axiom,
    aux2(Z,Xs,Y2,Ys,bfalse) = cons(Y2,merge(cons(Z,Xs),Ys)) ).

cnf(axiom_003,axiom,
    aux3(Y,X2,X3,pair2(Ys1,Zs)) = merge(msort(Ys1),msort(Zs)) ).

cnf(axiom_004,axiom,
    aux4(X,Z,Xs,btrue) = s(count(X,Xs)) ).

cnf(axiom_005,axiom,
    aux4(X,Z,Xs,bfalse) = count(X,Xs) ).

cnf(axiom_006,axiom,
    splitAtNat(z,Y) = pair2(nil,Y) ).

cnf(axiom_007,axiom,
    splitAtNat(s(Z),nil) = pair2(nil,nil) ).

cnf(axiom_008,axiom,
    splitAtNat(s(Z),cons(X2,X3)) = aux(Z,X2,X3,splitAtNat(Z,X3)) ).

cnf(axiom_009,axiom,
    leqNat(z,Y) = btrue ).

cnf(axiom_010,axiom,
    leqNat(s(Z),z) = bfalse ).

cnf(axiom_011,axiom,
    leqNat(s(Z),s(M)) = leqNat(Z,M) ).

cnf(axiom_012,axiom,
    merge(nil,Y) = Y ).

cnf(axiom_013,axiom,
    merge(cons(Z,Xs),nil) = cons(Z,Xs) ).

cnf(axiom_014,axiom,
    merge(cons(Z,Xs),cons(Y2,Ys)) = aux2(Z,Xs,Y2,Ys,leqNat(Z,Y2)) ).

cnf(axiom_015,axiom,
    lengthNat(nil) = z ).

cnf(axiom_016,axiom,
    lengthNat(cons(Y,Xs)) = s(lengthNat(Xs)) ).

cnf(axiom_017,axiom,
    impl(btrue,Q) = Q ).

cnf(axiom_018,axiom,
    impl(bfalse,Q) = btrue ).

cnf(axiom_019,axiom,
    div2(z) = z ).

cnf(axiom_020,axiom,
    div2(s(z)) = z ).

cnf(axiom_021,axiom,
    div2(s(s(N))) = s(div2(N)) ).

cnf(axiom_022,axiom,
    msort(nil) = nil ).

cnf(axiom_023,axiom,
    msort(cons(Y,nil)) = cons(Y,nil) ).

cnf(axiom_024,axiom,
    msort(cons(Y,cons(X2,X3))) = aux3(Y,X2,X3,splitAtNat(div2(lengthNat(cons(Y,cons(X2,X3)))),cons(Y,cons(X2,X3)))) ).

cnf(axiom_025,axiom,
    count(X,nil) = z ).

cnf(axiom_026,axiom,
    count(X,cons(Z,Xs)) = aux4(X,Z,Xs,eq(Z,X)) ).

cnf(axiom_027,axiom,
    prop_msort_permutation_wrong2(X,Y) = impl(eq2(leqNat(count(Y,X),s(s(s(s(s(z)))))),bfalse),eq(count(s(Y),X),count(Y,msort(X)))) ).

cnf(axiom_028,axiom,
    eq2(bfalse,btrue) = bfalse ).

cnf(axiom_029,axiom,
    eq2(btrue,bfalse) = bfalse ).

cnf(axiom_030,axiom,
    eq(s(X),s(Y)) = eq(X,Y) ).

cnf(axiom_031,axiom,
    eq(z,s(X)) = bfalse ).

cnf(axiom_032,axiom,
    eq(s(X),z) = bfalse ).

cnf(axiom_033,axiom,
    eq(X,X) = btrue ).

cnf(axiom_034,axiom,
    eq2(X,X) = btrue ).

cnf(goal,negated_conjecture,
    eq2(prop_msort_permutation_wrong2(X,Y),bfalse) != btrue ).

%------------------------------------------------------------------------------