%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM220_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:04:36 PM UTC 2026
% Result : Theorem 18.43s 5.26s
% Output : CNFRefutation 18.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 120 ( 62 unt; 0 typ; 4 def)
% Number of atoms : 720 ( 178 equ)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 233 ( 92 ~; 105 |; 26 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 459 ( 459 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 59 ( 57 usr; 13 prp; 0-3 aty)
% Number of functors : 86 ( 86 usr; 3 con; 0-3 aty)
% Number of variables : 150 ( 0 sgn 126 !; 24 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
vNat: vTy ).
tff(pred_def_1,type,
visValue: vTerm > $o ).
tff(pred_def_2,type,
visNV: vTerm > $o ).
tff(pred_def_3,type,
visSomeTerm: vOptTerm > $o ).
tff(pred_def_4,type,
vptchecksimple: ( vTy * vTerm ) > $o ).
tff(pred_def_5,type,
sP0: ( vTerm * vTerm ) > $o ).
tff(pred_def_6,type,
sP1: ( vTerm * vTerm ) > $o ).
tff(pred_def_7,type,
sP2: ( vTerm * ( vTerm * vTerm ) ) > $o ).
tff(pred_def_8,type,
sP3: ( vTerm * ( vTerm * vTerm ) ) > $o ).
tff(pred_def_9,type,
sP4: vTerm > $o ).
tff(pred_def_10,type,
sP5: vTerm > $o ).
tff(pred_def_11,type,
sP6: vTerm > $o ).
tff(pred_def_12,type,
sP7: vTerm > $o ).
tff(pred_def_13,type,
sP8: vTerm > $o ).
tff(pred_def_14,type,
sP9: vTerm > $o ).
tff(pred_def_15,type,
sP10: vTerm > $o ).
tff(pred_def_16,type,
sP11: vTerm > $o ).
tff(pred_def_17,type,
sP12: vTerm > $o ).
tff(pred_def_18,type,
sP13: vTerm > $o ).
tff(pred_def_19,type,
sP14: vTerm > $o ).
tff(pred_def_20,type,
sP15: vTerm > $o ).
tff(pred_def_21,type,
sP16: vTerm > $o ).
tff(pred_def_22,type,
sP17: vTerm > $o ).
tff(pred_def_23,type,
sP18: vTerm > $o ).
tff(pred_def_24,type,
sP19: vTerm > $o ).
tff(pred_def_25,type,
sP20: vTerm > $o ).
tff(pred_def_26,type,
sP21: vTerm > $o ).
tff(pred_def_27,type,
sP22: vTerm > $o ).
tff(pred_def_28,type,
sP23: vTerm > $o ).
tff(pred_def_29,type,
sP24: vTerm > $o ).
tff(func_def_30,type,
sK39: vTerm > vTerm ).
tff(func_def_31,type,
sK40: vOptTerm > vTerm ).
tff(func_def_32,type,
sK41: vTerm > vTerm ).
tff(func_def_33,type,
sK42: ( vTerm * vTerm ) > vTerm ).
tff(func_def_34,type,
sK43: ( vTerm * vTerm ) > vTerm ).
tff(func_def_35,type,
sK44: ( vTerm * vTerm ) > vTerm ).
tff(func_def_36,type,
sK45: ( vTerm * vTerm ) > vTerm ).
tff(func_def_37,type,
sK46: ( vTerm * vTerm ) > vTerm ).
tff(func_def_38,type,
sK47: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_39,type,
sK48: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_40,type,
sK49: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_41,type,
sK50: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_42,type,
sK51: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_43,type,
sK52: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_44,type,
sK53: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_45,type,
sK54: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_46,type,
sK55: vTerm > vTerm ).
tff(func_def_47,type,
sK56: vTerm > vTerm ).
tff(func_def_48,type,
sK57: vTerm > vTerm ).
tff(func_def_49,type,
sK58: vTerm > vTerm ).
tff(func_def_50,type,
sK59: vTerm > vTerm ).
tff(func_def_51,type,
sK60: vTerm > vTerm ).
tff(func_def_52,type,
sK61: vTerm > vTerm ).
tff(func_def_53,type,
sK62: vTerm > vTerm ).
tff(func_def_54,type,
sK63: vTerm > vTerm ).
tff(func_def_55,type,
sK64: vTerm > vTerm ).
tff(func_def_56,type,
sK65: vTerm > vTerm ).
tff(func_def_57,type,
sK66: vTerm > vTerm ).
tff(func_def_58,type,
sK67: vTerm > vTerm ).
tff(func_def_59,type,
sK68: vTerm > vTerm ).
tff(func_def_60,type,
sK69: vTerm > vTerm ).
tff(func_def_61,type,
sK70: vTerm > vTerm ).
tff(func_def_62,type,
sK71: vTerm > vTerm ).
tff(func_def_63,type,
sK72: vTerm > vTerm ).
tff(func_def_64,type,
sK73: vTerm > vTerm ).
tff(func_def_65,type,
sK74: vTerm > vTerm ).
tff(func_def_66,type,
sK75: vTerm > vTerm ).
tff(func_def_67,type,
sK76: vTerm > vOptTerm ).
tff(func_def_68,type,
sK77: vTerm > vTerm ).
tff(func_def_69,type,
sK78: vTerm > vOptTerm ).
tff(func_def_70,type,
sK79: vTerm > vTerm ).
tff(func_def_71,type,
sK80: vTerm > vTerm ).
tff(func_def_72,type,
sK81: vTerm > vTerm ).
tff(func_def_73,type,
sK82: vTerm > vOptTerm ).
tff(func_def_74,type,
sK83: vTerm > vTerm ).
tff(func_def_75,type,
sK84: vTerm > vOptTerm ).
tff(func_def_76,type,
sK85: vTerm > vTerm ).
tff(func_def_77,type,
sK86: vTerm > vOptTerm ).
tff(func_def_78,type,
sK87: vTerm > vTerm ).
tff(func_def_79,type,
sK88: vTerm > vOptTerm ).
tff(func_def_80,type,
sK89: vTerm > vTerm ).
tff(func_def_81,type,
sK90: vTerm > vTerm ).
tff(func_def_82,type,
sK91: vTerm > vOptTerm ).
tff(func_def_83,type,
sK92: vTerm > vTerm ).
tff(func_def_84,type,
sK93: vTerm > vTerm ).
tff(func_def_85,type,
sK94: vTerm > vOptTerm ).
tff(func_def_86,type,
sK95: vTerm > vTerm ).
tff(func_def_87,type,
sK96: vTerm > vTerm ).
tff(func_def_88,type,
sK97: vTerm > vTerm ).
tff(func_def_89,type,
sK98: vTerm > vOptTerm ).
tff(func_def_90,type,
sK99: vTerm > vTerm ).
tff(func_def_91,type,
sK100: vTerm > vTerm ).
tff(func_def_92,type,
sK101: vTerm > vTerm ).
tff(func_def_93,type,
sK102: vTerm > vOptTerm ).
tff(func_def_94,type,
sK103: vTerm > vTerm ).
tff(func_def_95,type,
sK104: vTerm > vOptTerm ).
tff(func_def_96,type,
sK105: vTerm > vTerm ).
tff(func_def_97,type,
sK106: vTerm > vOptTerm ).
tff(func_def_98,type,
sK107: vTerm > vTerm ).
tff(func_def_99,type,
sK108: vTerm > vOptTerm ).
tff(func_def_100,type,
sK109: vTerm > vTerm ).
tff(func_def_101,type,
sK110: vTerm > vOptTerm ).
tff(func_def_102,type,
sK111: vTerm > vTerm ).
tff(func_def_103,type,
sK112: vTerm > vTerm ).
tff(func_def_104,type,
sK113: vTerm > vOptTerm ).
tff(func_def_105,type,
sK114: vTerm > vTerm ).
tff(func_def_106,type,
sK115: vTerm > vTerm ).
tff(func_def_107,type,
sK116: vTerm > vOptTerm ).
tff(func_def_108,type,
sK117: vTerm > vTerm ).
tff(func_def_109,type,
sK118: vTerm > vTerm ).
tff(func_def_110,type,
sK119: vTerm > vTerm ).
tff(func_def_111,type,
sK120: vTerm > vTerm ).
tff(func_def_112,type,
sK121: vTerm > vTerm ).
tff(func_def_113,type,
sK122: vTy ).
tff(func_def_114,type,
sK123: vTerm ).
tff(f1,axiom,
! [X0: vTerm] :
( ? [X1: vTerm,X2: vTerm] : ( X0 = vPlus(X1,X2) )
| ? [X1: vTerm] : ( X0 = vIszero(X1) )
| ? [X1: vTerm] : ( X0 = vPred(X1) )
| ? [X1: vTerm] : ( X0 = vSucc(X1) )
| ( X0 = vZero )
| ? [X1: vTerm,X2: vTerm,X3: vTerm] : ( X0 = vIfelse(X1,X2,X3) )
| ( X0 = vFalse )
| ( X0 = vTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-Term') ).
tff(f5,axiom,
! [X0: vTerm,X1: vTerm] :
( ( vIszero(X0) = vIszero(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-Iszero') ).
tff(f12,axiom,
! [X0: vTerm] : ( vTrue != vIszero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-True-Iszero') ).
tff(f18,axiom,
! [X0: vTerm] : ( vFalse != vIszero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-False-Iszero') ).
tff(f23,axiom,
! [X0: vTerm,X1: vTerm,X2: vTerm,X3: vTerm] : ( vIfelse(X0,X1,X2) != vIszero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Ifelse-Iszero') ).
tff(f27,axiom,
! [X0: vTerm] : ( vZero != vIszero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Zero-Iszero') ).
tff(f30,axiom,
! [X0: vTerm,X1: vTerm] : ( vSucc(X0) != vIszero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Succ-Iszero') ).
tff(f32,axiom,
! [X0: vTerm,X1: vTerm] : ( vPred(X0) != vIszero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Pred-Iszero') ).
tff(f34,axiom,
! [X0: vTerm,X1: vTerm,X2: vTerm] : ( vIszero(X0) != vPlus(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Iszero-Plus') ).
tff(f36,axiom,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X0) = vsomeTerm(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someTerm') ).
tff(f40,axiom,
! [X0: vTerm] : ( vgetTerm(vsomeTerm(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getTerm-0') ).
tff(f53,axiom,
! [X0: vOptTerm] :
( visSomeTerm(X0)
=> ? [X1: vTerm] : ( X0 = vsomeTerm(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeTerm-true-INV') ).
tff(f75,axiom,
! [X0: vTerm] :
( ( visSomeTerm(vreduce(X0))
& ! [X1: vTerm] : ( X0 != vSucc(X1) )
& ( X0 != vZero ) )
=> ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-16') ).
tff(f98,axiom,
! [X0: vTerm] :
( vptchecksimple(X0,vNat)
=> vptchecksimple(vIszero(X0),vB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tiszero') ).
tff(f99,axiom,
! [X0: vTerm] :
( vptchecksimple(vIszero(X0),vB)
=> vptchecksimple(X0,vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tiszero_inv1') ).
tff(f100,axiom,
! [X0: vTerm,X1: vTy] :
( vptchecksimple(vIszero(X0),X1)
=> ( X1 = vB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tiszero_inv2') ).
tff(f105,axiom,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vt1) = vsomeTerm(X1) )
& vptchecksimple(vt1,X0) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-IH0') ).
tff(f106,conjecture,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vIszero(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vIszero(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-t1-isSomeTerm-True') ).
tff(f107,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vIszero(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vIszero(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f108,plain,
! [X0: vTerm] :
( ? [X7: vTerm,X8: vTerm] : ( vPlus(X7,X8) = X0 )
| ? [X6: vTerm] : ( vIszero(X6) = X0 )
| ? [X5: vTerm] : ( vPred(X5) = X0 )
| ? [X4: vTerm] : ( vSucc(X4) = X0 )
| ( X0 = vZero )
| ? [X1: vTerm,X2: vTerm,X3: vTerm] : ( X0 = vIfelse(X1,X2,X3) )
| ( X0 = vFalse )
| ( X0 = vTrue ) ),
inference(rectify,[],[f1]) ).
tff(f113,plain,
! [X0: vTerm,X1: vTerm] :
( ( vIszero(X1) != vIszero(X0) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f5]) ).
tff(f115,plain,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(X0) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f127,plain,
! [X0: vOptTerm] :
( ~ visSomeTerm(X0)
| ? [X1: vTerm] : ( X0 = vsomeTerm(X1) ) ),
inference(ennf_transformation,[],[f53]) ).
tff(f151,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ? [X1: vTerm] : ( vSucc(X1) = X0 )
| ( vZero = X0 )
| ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) ) ),
inference(ennf_transformation,[],[f75]) ).
tff(f152,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ? [X1: vTerm] : ( vSucc(X1) = X0 )
| ( vZero = X0 )
| ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) ) ),
inference(flattening,[],[f151]) ).
tff(f179,plain,
! [X0: vTerm] :
( ~ vptchecksimple(X0,vNat)
| vptchecksimple(vIszero(X0),vB) ),
inference(ennf_transformation,[],[f98]) ).
tff(f180,plain,
! [X0: vTerm] :
( ~ vptchecksimple(vIszero(X0),vB)
| vptchecksimple(X0,vNat) ),
inference(ennf_transformation,[],[f99]) ).
tff(f181,plain,
! [X0: vTerm,X1: vTy] :
( ~ vptchecksimple(vIszero(X0),X1)
| ( X1 = vB ) ),
inference(ennf_transformation,[],[f100]) ).
tff(f187,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vt1) )
| ~ vptchecksimple(vt1,X0)
| vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f105]) ).
tff(f188,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vt1) )
| ~ vptchecksimple(vt1,X0)
| vptchecksimple(X1,X0) ),
inference(flattening,[],[f187]) ).
tff(f189,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vIszero(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vIszero(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1))
& ~ vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f107]) ).
tff(f190,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vIszero(vt1)) = vsomeTerm(X1) )
& vptchecksimple(vIszero(vt1),X0)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1))
& ~ vptchecksimple(X1,X0) ),
inference(flattening,[],[f189]) ).
tff(f220,plain,
! [X0: vTerm] :
( ( vPlus(sK31(X0),sK32(X0)) = X0 )
| ( vIszero(sK30(X0)) = X0 )
| ( vPred(sK29(X0)) = X0 )
| ( vSucc(sK28(X0)) = X0 )
| ( X0 = vZero )
| ( vIfelse(sK25(X0),sK26(X0),sK27(X0)) = X0 )
| ( X0 = vFalse )
| ( X0 = vTrue ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32]),skolemize(X1,sK25(X0)),skolemize(X2,sK26(X0)),skolemize(X3,sK27(X0)),skolemize(X4,sK28(X0)),skolemize(X5,sK29(X0)),skolemize(X6,sK30(X0)),skolemize(X7,sK31(X0)),skolemize(X8,sK32(X0))],[f108]) ).
tff(f229,plain,
! [X0: vOptTerm] :
( ~ visSomeTerm(X0)
| ( vsomeTerm(sK40(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X1,sK40(X0))],[f127]) ).
tff(f248,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ( vSucc(sK57(X0)) = X0 )
| ( vZero = X0 )
| ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(X1,sK57(X0))],[f152]) ).
tff(f313,plain,
( ( vreduce(vIszero(vt1)) = vsomeTerm(sK123) )
& vptchecksimple(vIszero(vt1),sK122)
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1))
& ~ vptchecksimple(sK123,sK122) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123]),skolemize(X0,sK122),skolemize(X1,sK123)],[f190]) ).
tff(f314,plain,
! [X0: vTerm] :
( ( vPlus(sK31(X0),sK32(X0)) = X0 )
| ( vIszero(sK30(X0)) = X0 )
| ( vPred(sK29(X0)) = X0 )
| ( vSucc(sK28(X0)) = X0 )
| ( vZero = X0 )
| ( vIfelse(sK25(X0),sK26(X0),sK27(X0)) = X0 )
| ( vFalse = X0 )
| ( vTrue = X0 ) ),
inference(cnf_transformation,[],[f220]) ).
tff(f320,plain,
! [X0: vTerm,X1: vTerm] :
( ( vIszero(X1) != vIszero(X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f113]) ).
tff(f328,plain,
! [X0: vTerm] : ( vTrue != vIszero(X0) ),
inference(cnf_transformation,[],[f12]) ).
tff(f334,plain,
! [X0: vTerm] : ( vFalse != vIszero(X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f339,plain,
! [X2: vTerm,X3: vTerm,X0: vTerm,X1: vTerm] : ( vIfelse(X0,X1,X2) != vIszero(X3) ),
inference(cnf_transformation,[],[f23]) ).
tff(f343,plain,
! [X0: vTerm] : ( vZero != vIszero(X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f346,plain,
! [X0: vTerm,X1: vTerm] : ( vIszero(X1) != vSucc(X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f348,plain,
! [X0: vTerm,X1: vTerm] : ( vIszero(X1) != vPred(X0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f350,plain,
! [X2: vTerm,X0: vTerm,X1: vTerm] : ( vPlus(X1,X2) != vIszero(X0) ),
inference(cnf_transformation,[],[f34]) ).
tff(f352,plain,
! [X0: vTerm,X1: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(X0) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f115]) ).
tff(f356,plain,
! [X0: vTerm] : ( vgetTerm(vsomeTerm(X0)) = X0 ),
inference(cnf_transformation,[],[f40]) ).
tff(f383,plain,
! [X0: vOptTerm] :
( ~ visSomeTerm(X0)
| ( vsomeTerm(sK40(X0)) = X0 ) ),
inference(cnf_transformation,[],[f229]) ).
tff(f425,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ( vSucc(sK57(X0)) = X0 )
| ( vZero = X0 )
| ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) ) ),
inference(cnf_transformation,[],[f248]) ).
tff(f566,plain,
! [X0: vTerm] :
( ~ vptchecksimple(X0,vNat)
| vptchecksimple(vIszero(X0),vB) ),
inference(cnf_transformation,[],[f179]) ).
tff(f567,plain,
! [X0: vTerm] :
( ~ vptchecksimple(vIszero(X0),vB)
| vptchecksimple(X0,vNat) ),
inference(cnf_transformation,[],[f180]) ).
tff(f568,plain,
! [X0: vTerm,X1: vTy] :
( ~ vptchecksimple(vIszero(X0),X1)
| ( vB = X1 ) ),
inference(cnf_transformation,[],[f181]) ).
tff(f573,plain,
! [X0: vTy,X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vt1) )
| ~ vptchecksimple(vt1,X0)
| vptchecksimple(X1,X0) ),
inference(cnf_transformation,[],[f188]) ).
tff(f574,plain,
vreduce(vIszero(vt1)) = vsomeTerm(sK123),
inference(cnf_transformation,[],[f313]) ).
tff(f575,plain,
vptchecksimple(vIszero(vt1),sK122),
inference(cnf_transformation,[],[f313]) ).
tff(f576,plain,
! [X2: vTerm] : ( vSucc(X2) != vt1 ),
inference(cnf_transformation,[],[f313]) ).
tff(f577,plain,
vZero != vt1,
inference(cnf_transformation,[],[f313]) ).
tff(f578,plain,
visSomeTerm(vreduce(vt1)),
inference(cnf_transformation,[],[f313]) ).
tff(f579,plain,
~ vptchecksimple(sK123,sK122),
inference(cnf_transformation,[],[f313]) ).
tcf(c_49,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = vFalse )
| ( X0_vTerm = vTrue )
| ( X0_vTerm = vZero )
| ( vIszero(sK30(X0_vTerm)) = X0_vTerm )
| ( vPred(sK29(X0_vTerm)) = X0_vTerm )
| ( vSucc(sK28(X0_vTerm)) = X0_vTerm )
| ( vPlus(sK31(X0_vTerm),sK32(X0_vTerm)) = X0_vTerm )
| ( vIfelse(sK25(X0_vTerm),sK26(X0_vTerm),sK27(X0_vTerm)) = X0_vTerm ) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_55,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( ( X0_vTerm = X1_vTerm )
| ( vIszero(X0_vTerm) != vIszero(X1_vTerm) ) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_63,plain,
! [X0_vTerm: vTerm] : vIszero(X0_vTerm) != vTrue,
inference(cnf_transformation,[],[f328]) ).
tcf(c_69,plain,
! [X0_vTerm: vTerm] : vIszero(X0_vTerm) != vFalse,
inference(cnf_transformation,[],[f334]) ).
tcf(c_74,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm,X2_vTerm: vTerm,X3_vTerm: vTerm] : vIfelse(X0_vTerm,X1_vTerm,X2_vTerm) != vIszero(X3_vTerm),
inference(cnf_transformation,[],[f339]) ).
tcf(c_78,plain,
! [X0_vTerm: vTerm] : vIszero(X0_vTerm) != vZero,
inference(cnf_transformation,[],[f343]) ).
tcf(c_81,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] : vSucc(X0_vTerm) != vIszero(X1_vTerm),
inference(cnf_transformation,[],[f346]) ).
tcf(c_83,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] : vPred(X0_vTerm) != vIszero(X1_vTerm),
inference(cnf_transformation,[],[f348]) ).
tcf(c_85,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm,X2_vTerm: vTerm] : vPlus(X0_vTerm,X1_vTerm) != vIszero(X2_vTerm),
inference(cnf_transformation,[],[f350]) ).
tcf(c_87,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( ( X0_vTerm = X1_vTerm )
| ( vsomeTerm(X0_vTerm) != vsomeTerm(X1_vTerm) ) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_91,plain,
! [X0_vTerm: vTerm] : vgetTerm(vsomeTerm(X0_vTerm)) = X0_vTerm,
inference(cnf_transformation,[],[f356]) ).
tcf(c_118,plain,
! [X0_vOptTerm: vOptTerm] :
( ( vsomeTerm(sK40(X0_vOptTerm)) = X0_vOptTerm )
| ~ visSomeTerm(X0_vOptTerm) ),
inference(cnf_transformation,[],[f383]) ).
tcf(c_160,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = vZero )
| ( vSucc(sK57(X0_vTerm)) = X0_vTerm )
| ( vsomeTerm(vIszero(vgetTerm(vreduce(X0_vTerm)))) = vreduce(vIszero(X0_vTerm)) )
| ~ visSomeTerm(vreduce(X0_vTerm)) ),
inference(cnf_transformation,[],[f425]) ).
tcf(c_301,plain,
! [X0_vTerm: vTerm] :
( vptchecksimple(vIszero(X0_vTerm),vB)
| ~ vptchecksimple(X0_vTerm,vNat) ),
inference(cnf_transformation,[],[f566]) ).
tcf(c_302,plain,
! [X0_vTerm: vTerm] :
( vptchecksimple(X0_vTerm,vNat)
| ~ vptchecksimple(vIszero(X0_vTerm),vB) ),
inference(cnf_transformation,[],[f567]) ).
tcf(c_303,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( ( X0_vTy = vB )
| ~ vptchecksimple(vIszero(X0_vTerm),X0_vTy) ),
inference(cnf_transformation,[],[f568]) ).
tcf(c_308,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vt1,X0_vTy)
| ( vsomeTerm(X0_vTerm) != vreduce(vt1) ) ),
inference(cnf_transformation,[],[f573]) ).
tcf(c_309,negated_conjecture,
~ vptchecksimple(sK123,sK122),
inference(cnf_transformation,[],[f579]) ).
tcf(c_310,negated_conjecture,
visSomeTerm(vreduce(vt1)),
inference(cnf_transformation,[],[f578]) ).
tcf(c_311,negated_conjecture,
vZero != vt1,
inference(cnf_transformation,[],[f577]) ).
tcf(c_312,negated_conjecture,
! [X0_vTerm: vTerm] : vSucc(X0_vTerm) != vt1,
inference(cnf_transformation,[],[f576]) ).
tcf(c_313,negated_conjecture,
vptchecksimple(vIszero(vt1),sK122),
inference(cnf_transformation,[],[f575]) ).
tcf(c_314,negated_conjecture,
vreduce(vIszero(vt1)) = vsomeTerm(sK123),
inference(cnf_transformation,[],[f574]) ).
tcf(c_50942,definition,
iPr_def_10 = vIszero(vt1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_50943,definition,
iPr_def_11 = vreduce(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_50944,definition,
iPr_def_12 = vsomeTerm(sK123),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_50945,definition,
iPr_def_13 = vreduce(vt1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_50946,negated_conjecture,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_314,c_50944,c_50942,c_50943]) ).
tcf(c_50947,negated_conjecture,
vptchecksimple(iPr_def_10,sK122),
inference(demodulation,[status(thm)],[c_313]) ).
tcf(c_50948,negated_conjecture,
! [X0_vTerm: vTerm] : vSucc(X0_vTerm) != vt1,
inference(demodulation,[status(thm)],[c_312]) ).
tcf(c_50949,negated_conjecture,
vZero != vt1,
inference(demodulation,[status(thm)],[c_311]) ).
tcf(c_50950,negated_conjecture,
visSomeTerm(iPr_def_13),
inference(demodulation,[status(thm)],[c_310,c_50945]) ).
tcf(c_50951,negated_conjecture,
~ vptchecksimple(sK123,sK122),
inference(demodulation,[status(thm)],[c_309]) ).
tcf(c_53571,plain,
vsomeTerm(sK123) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_50944,c_50946]) ).
tcf(c_53665,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = vt1 )
| ( vIszero(X0_vTerm) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_50942,c_55]) ).
tcf(c_53971,plain,
( vptchecksimple(vt1,vNat)
| ~ vptchecksimple(iPr_def_10,vB) ),
inference(superposition,[status(thm)],[c_50942,c_302]) ).
tcf(c_54035,plain,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] :
( ( X1_vTerm = vFalse )
| ( X1_vTerm = vTrue )
| ( X1_vTerm = vZero )
| ( vIszero(sK30(X1_vTerm)) = X1_vTerm )
| ( vPred(sK29(X1_vTerm)) = X1_vTerm )
| ( vSucc(sK28(X1_vTerm)) = X1_vTerm )
| ( vPlus(sK31(X1_vTerm),sK32(X1_vTerm)) = X1_vTerm )
| ( vIszero(X0_vTerm) != X1_vTerm ) ),
inference(superposition,[status(thm)],[c_49,c_74]) ).
tcf(c_54059,plain,
vsomeTerm(sK40(iPr_def_13)) = iPr_def_13,
inference(superposition,[status(thm)],[c_50950,c_118]) ).
tcf(c_54088,plain,
vgetTerm(iPr_def_13) = sK40(iPr_def_13),
inference(superposition,[status(thm)],[c_54059,c_91]) ).
tcf(c_54091,plain,
vsomeTerm(vgetTerm(iPr_def_13)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_54059,c_54088]) ).
tcf(c_54275,plain,
! [X0_vTy: vTy] :
( ( X0_vTy = vB )
| ~ vptchecksimple(iPr_def_10,X0_vTy) ),
inference(superposition,[status(thm)],[c_50942,c_303]) ).
tcf(c_54283,plain,
vB = sK122,
inference(superposition,[status(thm)],[c_50947,c_54275]) ).
tcf(c_54291,plain,
~ vptchecksimple(sK123,vB),
inference(demodulation,[status(thm)],[c_50951,c_54283]) ).
tcf(c_54292,plain,
vptchecksimple(iPr_def_10,vB),
inference(demodulation,[status(thm)],[c_50947,c_54283]) ).
tcf(c_54293,plain,
vptchecksimple(vt1,vNat),
inference(backward_subsumption_resolution,[status(thm)],[c_53971,c_54292]) ).
tcf(c_54320,plain,
! [X0_vTerm: vTerm] :
( ( vIszero(X0_vTerm) = vFalse )
| ( vIszero(X0_vTerm) = vTrue )
| ( vIszero(X0_vTerm) = vZero )
| ( vIszero(sK30(vIszero(X0_vTerm))) = vIszero(X0_vTerm) )
| ( vPred(sK29(vIszero(X0_vTerm))) = vIszero(X0_vTerm) )
| ( vSucc(sK28(vIszero(X0_vTerm))) = vIszero(X0_vTerm) )
| ( vPlus(sK31(vIszero(X0_vTerm)),sK32(vIszero(X0_vTerm))) = vIszero(X0_vTerm) ) ),
inference(equality_resolution,[status(thm)],[c_54035]) ).
tcf(c_54329,plain,
! [X0_vTerm: vTerm] : vIszero(sK30(vIszero(X0_vTerm))) = vIszero(X0_vTerm),
inference(forward_subsumption_resolution,[status(thm)],[c_54320,c_69,c_63,c_78,c_83,c_81,c_85]) ).
tcf(c_54369,plain,
vIszero(sK30(iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_50942,c_54329]) ).
tcf(c_54405,plain,
sK30(iPr_def_10) = vt1,
inference(superposition,[status(thm)],[c_54369,c_53665]) ).
tcf(c_54413,plain,
vIszero(vt1) = iPr_def_10,
inference(demodulation,[status(thm)],[c_54369,c_54405]) ).
tcf(c_54713,plain,
! [X0_vTerm: vTerm] :
( ( X0_vTerm = sK123 )
| ( vsomeTerm(X0_vTerm) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_53571,c_87]) ).
tcf(c_56499,plain,
! [X0_vTerm: vTerm,X0_vTy: vTy] :
( vptchecksimple(X0_vTerm,X0_vTy)
| ~ vptchecksimple(vt1,X0_vTy)
| ( vsomeTerm(X0_vTerm) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_308,c_50945]) ).
tcf(c_56512,plain,
! [X0_vTy: vTy] :
( vptchecksimple(vgetTerm(iPr_def_13),X0_vTy)
| ~ vptchecksimple(vt1,X0_vTy) ),
inference(superposition,[status(thm)],[c_54091,c_56499]) ).
tcf(c_56544,plain,
( vptchecksimple(vgetTerm(iPr_def_13),vNat)
| ~ vptchecksimple(vt1,vNat) ),
inference(instantiation,[status(thm)],[c_56512]) ).
tcf(c_58858,plain,
( ( vZero = vt1 )
| ( vSucc(sK57(vt1)) = vt1 )
| ( vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))) = vreduce(vIszero(vt1)) )
| ~ visSomeTerm(iPr_def_13) ),
inference(superposition,[status(thm)],[c_50945,c_160]) ).
tcf(c_58866,plain,
( ( vZero = vt1 )
| ( vSucc(sK57(vt1)) = vt1 )
| ( vsomeTerm(vIszero(vgetTerm(iPr_def_13))) = iPr_def_11 )
| ~ visSomeTerm(iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_58858,c_50943,c_50945,c_54413]) ).
tcf(c_58867,plain,
vsomeTerm(vIszero(vgetTerm(iPr_def_13))) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_58866,c_50949,c_50948,c_50950]) ).
tcf(c_59105,plain,
vIszero(vgetTerm(iPr_def_13)) = sK123,
inference(superposition,[status(thm)],[c_58867,c_54713]) ).
tcf(c_59150,plain,
( vptchecksimple(sK123,vB)
| ~ vptchecksimple(vgetTerm(iPr_def_13),vNat) ),
inference(superposition,[status(thm)],[c_59105,c_301]) ).
tcf(c_59156,plain,
~ vptchecksimple(vgetTerm(iPr_def_13),vNat),
inference(forward_subsumption_resolution,[status(thm)],[c_59150,c_54291]) ).
tcf(c_59175,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_59156,c_56544,c_54293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM220_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 08:00:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 18.43/5.26 % SZS status Started for theBenchmark.p
% 18.43/5.26 % SZS status Theorem for theBenchmark.p
% 18.43/5.26
% 18.43/5.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.43/5.26
% 18.43/5.26 % ------ iProver source info
% 18.43/5.26
% 18.43/5.26 % git: date: 2026-07-19 20:42:38 +0200
% 18.43/5.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.43/5.26 % git: non_committed_changes: false
% 18.43/5.26
% 18.43/5.26 % ------ Parsing...
% 18.43/5.26 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 18.43/5.26 %
% 18.43/5.26
% 18.43/5.26 % ------ Preprocessing... sup_sim: 0 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 18.43/5.26
% 18.43/5.26 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 18.43/5.26 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 18.43/5.26 %
% 18.43/5.26
% 18.43/5.26 % ------ Preprocessing...
% 18.43/5.26 % ------ Proving...
% 18.43/5.26 % ------ Problem Properties
% 18.43/5.26
% 18.43/5.26 %
% 18.43/5.26 % clauses 266
% 18.43/5.26 % conjectures 6
% 18.43/5.26 % EPR 24
% 18.43/5.26 % Horn 216
% 18.43/5.26 % unary 55
% 18.43/5.26 % binary 160
% 18.43/5.26 % lits 729
% 18.43/5.26 % lits eq 284
% 18.43/5.26 % fd_pure 1
% 18.43/5.26 % fd_pseudo 0
% 18.43/5.26 % fd_cond 19
% 18.43/5.26 % fd_pseudo_cond 9
% 18.43/5.26 % AC symbols 0
% 18.43/5.26
% 18.43/5.26 % ------ Schedule dynamic 5 is on
% 18.43/5.26
% 18.43/5.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.43/5.26
% 18.43/5.26
% 18.43/5.26 % ------
% 18.43/5.26 % Current options:
% 18.43/5.26 % ------
% 18.43/5.26
% 18.43/5.26
% 18.43/5.26 %
% 18.43/5.26
% 18.43/5.26 % ------ Proving...
% 18.43/5.26 %
% 18.43/5.26
% 18.43/5.26 % SZS status Theorem for theBenchmark.p
% 18.43/5.26
% 18.43/5.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.43/5.26
% 18.43/5.26
%------------------------------------------------------------------------------