TPTP Problem File: SWX142_1.p
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%------------------------------------------------------------------------------
% File : SWX142_1 : TPTP v9.3.0. Released v9.3.0.
% Domain : Software Verification
% Problem : Neural network verification problem B_020
% Version : Especial.
% English :
% Refs : [PT12] Pulina & Tacchella (2012), Challenging SMT Solvers to
% : [GPP23] Guidotti et al. (2023), Leveraging Satisfiability Modu
% : [Pul25] Pulina (2025), Email to Geoff Sutcliffe
% Source : [Pul25]
% Names : B_020_cvc.smt2 [Pul25]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 36 ( 21 unt; 13 typ; 1 def)
% Number of atoms : 31 ( 5 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 9 ( 1 ~; 5 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 63 ( 4 avg)
% Number arithmetic : 57738 ( 26 atm;39083 fun;18627 num; 2 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 939 ( 13 usr; 935 con; 0-2 aty)
% Number of variables : 2 ( 2 !; 0 ?; 2 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
%------------------------------------------------------------------------------
%---Declarations:
tff('X_7',type,
'X_7': $real ).
tff('X_8',type,
'X_8': $real ).
tff('X_3',type,
'X_3': $real ).
tff('Y_0',type,
'Y_0': $real ).
tff('Y_2',type,
'Y_2': $real ).
tff('X_0',type,
'X_0': $real ).
tff('X_4',type,
'X_4': $real ).
tff(max,type,
max: ( $real * $real ) > $real ).
tff('X_1',type,
'X_1': $real ).
tff('Y_1',type,
'Y_1': $real ).
tff('X_2',type,
'X_2': $real ).
tff('X_6',type,
'X_6': $real ).
tff('X_5',type,
'X_5': $real ).
%---Assertions:
%---((-1.0 * X_0) ≤ -0.146896813422542)
tff(formula_1,axiom,
$lesseq($product($uminus(1.0),'X_0'),$uminus(0.146896813422542)) ).
%---((1.0 * X_0) ≤ 0.166896813422542)
tff(formula_2,axiom,
$lesseq($product(1.0,'X_0'),0.166896813422542) ).
%---((-1.0 * X_1) ≤ -0.047416492942258)
tff(formula_3,axiom,
$lesseq($product($uminus(1.0),'X_1'),$uminus(0.047416492942258)) ).
%---((1.0 * X_1) ≤ 0.067416492942258)
tff(formula_4,axiom,
$lesseq($product(1.0,'X_1'),0.067416492942258) ).
%---((-1.0 * X_2) ≤ -0.0)
tff(formula_5,axiom,
$lesseq($product($uminus(1.0),'X_2'),$uminus(0.0)) ).
%---((1.0 * X_2) ≤ 0.014079381401531001)
tff(formula_6,axiom,
$lesseq($product(1.0,'X_2'),0.014079381401531001) ).
%---((-1.0 * X_3) ≤ -0.488784248037036)
tff(formula_7,axiom,
$lesseq($product($uminus(1.0),'X_3'),$uminus(0.488784248037036)) ).
%---((1.0 * X_3) ≤ 0.508784248037036)
tff(formula_8,axiom,
$lesseq($product(1.0,'X_3'),0.508784248037036) ).
%---((-1.0 * X_4) ≤ -0.336103843238191)
tff(formula_9,axiom,
$lesseq($product($uminus(1.0),'X_4'),$uminus(0.336103843238191)) ).
%---((1.0 * X_4) ≤ 0.356103843238191)
tff(formula_10,axiom,
$lesseq($product(1.0,'X_4'),0.356103843238191) ).
%---((-1.0 * X_5) ≤ -0.033908722363159)
tff(formula_11,axiom,
$lesseq($product($uminus(1.0),'X_5'),$uminus(0.033908722363159)) ).
%---((1.0 * X_5) ≤ 0.053908722363159)
tff(formula_12,axiom,
$lesseq($product(1.0,'X_5'),0.053908722363159) ).
%---((-1.0 * X_6) ≤ -0.989829251495207)
tff(formula_13,axiom,
$lesseq($product($uminus(1.0),'X_6'),$uminus(0.989829251495207)) ).
%---((1.0 * X_6) ≤ 1.0)
tff(formula_14,axiom,
$lesseq($product(1.0,'X_6'),1.0) ).
%---((-1.0 * X_7) ≤ -0.48304324987277797)
tff(formula_15,axiom,
$lesseq($product($uminus(1.0),'X_7'),$uminus(0.48304324987277797)) ).
%---((1.0 * X_7) ≤ 0.5030432498727779)
tff(formula_16,axiom,
$lesseq($product(1.0,'X_7'),0.5030432498727779) ).
%---((-1.0 * X_8) ≤ -0.029862760896398)
tff(formula_17,axiom,
$lesseq($product($uminus(1.0),'X_8'),$uminus(0.029862760896398)) ).
%---((1.0 * X_8) ≤ 0.049862760896398)
tff(formula_18,axiom,
$lesseq($product(1.0,'X_8'),0.049862760896398) ).
%---(((1.0 * Y_0) ≤ -0.10295232286467162) ∨ ((-1.0 * Y_0) ≤ -0.09704767713532839) ∨ ((1.0 * Y_1) ≤ -0.09422071184312367) ∨ ((-1.0 * Y_1) ≤ -0.10577928815687634) ∨ ((1.0 * Y_2) ≤ 0.3902529870039524) ∨ ((-1.0 * Y_2) ≤ -0.5902529870039523))
tff(formula_19,axiom,
( $lesseq($product(1.0,'Y_0'),$uminus(0.10295232286467162))
| $lesseq($product($uminus(1.0),'Y_0'),$uminus(0.09704767713532839))
| $lesseq($product(1.0,'Y_1'),$uminus(0.09422071184312367))
| $lesseq($product($uminus(1.0),'Y_1'),$uminus(0.10577928815687634))
| $lesseq($product(1.0,'Y_2'),0.3902529870039524)
| $lesseq($product($uminus(1.0),'Y_2'),$uminus(0.5902529870039523)) ) ).
%---(Y_0 = ((max(((max(((X_0 * -0.188433724538083963) + (X_1 * 0.103022167358878647) + (X_2 * -0.104693638809655681) + (X_3 * 0.309720640581067019) + (X_4 * 0.257993427896927308) + (X_5 * 0.212919095317761931) + (X_6 * 0.075035756248121588) + (X_7 * 0.039561105419513909) + (X_8 * 0.099539522788427481) + 0.329324286445503434), 0.0) * -0.012160649769794446) + (max(((X_0 * -0.104623901109950623) + (X_1 * 0.143692248661314359) + (X_2 * 0.327623223911859884) + (X_3 * 0.197611764396378564) + (X_4 * -0.332446144974987645) + (X_5 * -0.277862474695495631) + (X_6 * -0.127721451519498264) + (X_7 * 0.046461247850873022) + (X_8 * 0.017326420329680958) + -0.245269471351741514), 0.0) * 0.17293366469817964) + (max(((X_0 * 0.128794037286135088) + (X_1 * 0.212920902496007647) + (X_2 * -0.046153824320720849) + (X_3 * -0.236732218421845581) + (X_4 * -0.026536177529491944) + (X_5 * 0.317305856264620656) + (X_6 * 0.21300994391257938) + (X_7 * 0.319183691390222013) + (X_8 * 0.069141341839752457) + 0.190401030814638161), 0.0) * -0.071214532820450385) + (max(((X_0 * -0.316610196720403358) + (X_1 * 0.057029663744318115) + (X_2 * -0.139622802384412964) + (X_3 * 0.042960687738296921) + (X_4 * 0.167117545647415155) + (X_5 * 0.053385405427321231) + (X_6 * -0.041036295625047903) + (X_7 * -0.001907541697383053) + (X_8 * 0.05461110577583228) + -0.153924324683693881), 0.0) * -0.162417298004118776) + (max(((X_0 * -0.141770009424840637) + (X_1 * 0.208958455433687018) + (X_2 * -0.060724729133568023) + (X_3 * 0.173473834704309382) + (X_4 * 0.013241396301108654) + (X_5 * -0.142356466165991735) + (X_6 * -0.288063902346686329) + (X_7 * 0.091241317779715558) + (X_8 * -0.021016212611143503) + -0.235756875288909207), 0.0) * -0.123726240996494097) + (max(((X_0 * 0.126241566445341791) + (X_1 * 0.125665342154246129) + (X_2 * -0.017891082219947618) + (X_3 * 0.072749563456526334) + (X_4 * -0.265213920600111841) + (X_5 * 0.303482785006484568) + (X_6 * -0.320582064366762065) + (X_7 * -0.321778126072234216) + (X_8 * -0.219231693764024099) + 0.317695546325278688), 0.0) * 0.074475196014797324) + (max(((X_0 * -0.067848207977760311) + (X_1 * -0.158045653396074487) + (X_2 * 0.03276743263395071) + (X_3 * 0.196422307270102736) + (X_4 * -0.033255321429539242) + (X_5 * 0.291080493340092061) + (X_6 * -0.286866015234330418) + (X_7 * 0.173838480010427732) + (X_8 * -0.289926191999641703) + -0.323441489818827255), 0.0) * 0.09755876612054129) + (max(((X_0 * 0.169301083438651523) + (X_1 * -0.203839906621080591) + (X_2 * 0.260241031859075489) + (X_3 * 0.316663869872302717) + (X_4 * 0.130063056507396579) + (X_5 * -0.24066489494523316) + (X_6 * -0.204845443917873127) + (X_7 * 0.12204462482210432) + (X_8 * 0.029252644235688463) + 0.036173174702086808), 0.0) * 0.087393266263367103) + (max(((X_0 * -0.326838360900566949) + (X_1 * 0.024933317451856674) + (X_2 * -0.095887139052035331) + (X_3 * 0.247319376667468116) + (X_4 * 0.00538547760035768) + (X_5 * 0.145564974172020134) + (X_6 * 0.025241179982156803) + (X_7 * -0.258320304625232589) + (X_8 * 0.113844696297660197) + 0.239284821909524881), 0.0) * 0.123175488323484544) + (max(((X_0 * -0.117824276135852335) + (X_1 * 0.077830177819542434) + (X_2 * 0.212228614859507558) + (X_3 * -0.095644266956262713) + (X_4 * -0.182092400824106854) + (X_5 * 0.04963583754550932) + (X_6 * -0.130098385711244463) + (X_7 * 0.128922379150422428) + (X_8 * -0.031995788242713596) + 0.001084831445445245), 0.0) * -0.069605953819360827) + (max(((X_0 * 0.097176319701710978) + (X_1 * -0.137796030282233861) + (X_2 * 0.02244207292102196) + (X_3 * -0.070322405795672616) + (X_4 * 0.197494124549168315) + (X_5 * -0.133265820243278155) + (X_6 * 0.156212564087235828) + (X_7 * -0.254265221510615813) + (X_8 * -0.237227927809398192) + 0.001707369126384473), 0.0) * 0.113855133189112862) + (max(((X_0 * -0.09487292330708344) + (X_1 * -0.02208674940254518) + (X_2 * 0.327195273201664028) + (X_3 * 0.321053557625457675) + (X_4 * 0.317596490166048129) + (X_5 * -0.039524407183250065) + (X_6 * -0.205433417851655697) + (X_7 * 0.097114813671868749) + (X_8 * -0.145112446709140086) + -0.179274636994634307), 0.0) * 0.039113988816581707) + (max(((X_0 * 0.071573922525926592) + (X_1 * 0.261373544885844467) + (X_2 * 0.04870073330811947) + (X_3 * 0.088125460700731573) + (X_4 * -0.079192340579830989) + (X_5 * -0.03367409272130556) + (X_6 * -0.166609477689913993) + (X_7 * -0.173750309258181052) + (X_8 * 0.297126374598982446) + -0.134970569538265972), 0.0) * 0.04746734096842456) + (max(((X_0 * -0.171751249593010968) + (X_1 * 0.140249888919204591) + (X_2 * 0.271292873287671099) + (X_3 * 0.183100677851479599) + (X_4 * -0.186044839013877722) + (X_5 * 0.260300663623905304) + (X_6 * 0.011017659803550017) + (X_7 * 0.08113175344752066) + (X_8 * -0.007062743939395821) + 0.304207924172989308), 0.0) * 0.100616852055628342) + (max(((X_0 * 0.130290038633072369) + (X_1 * -0.064777354559160949) + (X_2 * 0.178937838625517209) + (X_3 * 0.115856045632829752) + (X_4 * 0.175638405483927229) + (X_5 * 0.134538101654033904) + (X_6 * -0.239609023759233708) + (X_7 * -0.004600142903664617) + (X_8 * 0.261996590616496883) + -0.053509751558061147), 0.0) * 0.171854016357236933) + (max(((X_0 * -0.259327937900441508) + (X_1 * -0.252988523161737311) + (X_2 * -0.123540357607632961) + (X_3 * 0.264564511822031945) + (X_4 * 0.221226381915638315) + (X_5 * -0.124624218075112925) + (X_6 * 0.25715611958505008) + (X_7 * 0.298302309890288109) + (X_8 * -0.257677360251386323) + -0.169619955504439368), 0.0) * 0.167415117527008911) + (max(((X_0 * 0.052438217514146956) + (X_1 * 0.124143806173621696) + (X_2 * -0.261635387189453117) + (X_3 * 0.310567729335157139) + (X_4 * -0.135699847839970911) + (X_5 * 0.168690097662674343) + (X_6 * 0.324149505088900447) + (X_7 * 0.294380044860495016) + (X_8 * -0.271504299526465431) + 0.022619763863971076), 0.0) * 0.106756589842227662) + (max(((X_0 * 0.176081097744298087) + (X_1 * -0.016400470110426779) + (X_2 * 0.119388083796354405) + (X_3 * 0.056636519206662239) + (X_4 * 0.320532725913826144) + (X_5 * -0.316046822774617875) + (X_6 * 0.175834351847994175) + (X_7 * -0.044203003060605484) + (X_8 * 0.255647276162268289) + 0.330638860727302364), 0.0) * -0.027295359360182764) + (max(((X_0 * 0.028192489229337259) + (X_1 * -0.265672769125509523) + (X_2 * -0.2534036898881592) + (X_3 * -0.055548356101149166) + (X_4 * -0.266664835837502556) + (X_5 * 0.110214646666958016) + (X_6 * 0.108665544125445213) + (X_7 * 0.076859428792906581) + (X_8 * 0.248124870100853656) + 0.17376015699894104), 0.0) * 0.011978611036772085) + (max(((X_0 * 0.248288711546185425) + (X_1 * -0.280287698142216324) + (X_2 * -0.32285162118185512) + (X_3 * -0.240644190376185341) + (X_4 * 0.169413224137504759) + (X_5 * 0.030173409808405882) + (X_6 * 0.235651387214530439) + (X_7 * -0.234556494959096362) + (X_8 * -0.001807369434441986) + 0.270524896894616507), 0.0) * -0.051304641556174396) + (max(((X_0 * 0.257128817458894876) + (X_1 * -0.304100484562850659) + (X_2 * -0.064488609944596542) + (X_3 * 0.114091509935290381) + (X_4 * 0.237193303318258109) + (X_5 * -0.15836058298622091) + (X_6 * 0.18008588413813803) + (X_7 * -0.126301090703339419) + (X_8 * 0.049626746239051167) + -0.212067504848319072), 0.0) * -0.107606611329466292) + (max(((X_0 * 0.163811079638648993) + (X_1 * 0.127362048978825637) + (X_2 * -0.06678834904390557) + (X_3 * 0.310252355456933471) + (X_4 * 0.220323706731622104) + (X_5 * -0.277047634546621735) + (X_6 * 0.139790115565273876) + (X_7 * -0.286637782408986574) + (X_8 * 0.061093232624281402) + -0.240957792590464376), 0.0) * -0.071861520719229258) + (max(((X_0 * -0.151901551634323229) + (X_1 * 0.283979253385162111) + (X_2 * 0.182510023526476883) + (X_3 * -0.008917689841919485) + (X_4 * -0.149951898369714842) + (X_5 * -0.095906210773906958) + (X_6 * -0.14505265431341785) + (X_7 * -0.029789919429530742) + (X_8 * 0.124047374947088784) + 0.059083224783199773), 0.0) * 0.048056123120160665) + (max(((X_0 * -0.009148436553245765) + (X_1 * -0.219415259150958608) + (X_2 * 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%---∀ x:Real y:Real (max(x, y) = (if (x < y) y else x))
tff(formula_23,definition,
! [X: $real,Y: $real] :
( ( $less(X,Y)
=> ( max(X,Y) = Y ) )
& ( ~ $less(X,Y)
=> ( max(X,Y) = X ) ) ) ).
%------------------------------------------------------------------------------