%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM216_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 01:04:35 PM UTC 2026
% Result : Theorem 24.04s 4.27s
% Output : CNFRefutation 24.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 692 ( 202 equ)
% Maximal formula atoms : 12 ( 14 avg)
% Number of connectives : 213 ( 49 ~; 132 |; 28 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 479 ( 479 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 45 ( 43 usr; 8 prp; 0-3 aty)
% Number of functors : 85 ( 85 usr; 3 con; 0-3 aty)
% Number of variables : 100 ( 0 sgn 68 !; 32 ?; 100 :)
% 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,
sK40: vOptTerm > vTerm ).
tff(func_def_31,type,
sK41: vTerm > vTerm ).
tff(func_def_32,type,
sK42: ( vTerm * vTerm ) > vTerm ).
tff(func_def_33,type,
sK43: ( vTerm * vTerm ) > vTerm ).
tff(func_def_34,type,
sK44: ( vTerm * vTerm ) > vTerm ).
tff(func_def_35,type,
sK45: ( vTerm * vTerm ) > vTerm ).
tff(func_def_36,type,
sK46: ( vTerm * vTerm ) > vTerm ).
tff(func_def_37,type,
sK47: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_38,type,
sK48: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_39,type,
sK49: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_40,type,
sK50: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_41,type,
sK51: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_42,type,
sK52: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_43,type,
sK53: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_44,type,
sK54: ( vTerm * ( vTerm * vTerm ) ) > vTerm ).
tff(func_def_45,type,
sK55: vTerm > vTerm ).
tff(func_def_46,type,
sK56: vTerm > vTerm ).
tff(func_def_47,type,
sK57: vTerm > vTerm ).
tff(func_def_48,type,
sK58: vTerm > vTerm ).
tff(func_def_49,type,
sK59: vTerm > vTerm ).
tff(func_def_50,type,
sK60: vTerm > vTerm ).
tff(func_def_51,type,
sK61: vTerm > vTerm ).
tff(func_def_52,type,
sK62: vTerm > vTerm ).
tff(func_def_53,type,
sK63: vTerm > vTerm ).
tff(func_def_54,type,
sK64: vTerm > vTerm ).
tff(func_def_55,type,
sK65: vTerm > vTerm ).
tff(func_def_56,type,
sK66: vTerm > vTerm ).
tff(func_def_57,type,
sK67: vTerm > vTerm ).
tff(func_def_58,type,
sK68: vTerm > vTerm ).
tff(func_def_59,type,
sK69: vTerm > vTerm ).
tff(func_def_60,type,
sK70: vTerm > vTerm ).
tff(func_def_61,type,
sK71: vTerm > vTerm ).
tff(func_def_62,type,
sK72: vTerm > vTerm ).
tff(func_def_63,type,
sK73: vTerm > vTerm ).
tff(func_def_64,type,
sK74: vTerm > vTerm ).
tff(func_def_65,type,
sK75: vTerm > vTerm ).
tff(func_def_66,type,
sK76: vTerm > vOptTerm ).
tff(func_def_67,type,
sK77: vTerm > vTerm ).
tff(func_def_68,type,
sK78: vTerm > vOptTerm ).
tff(func_def_69,type,
sK79: vTerm > vTerm ).
tff(func_def_70,type,
sK80: vTerm > vTerm ).
tff(func_def_71,type,
sK81: vTerm > vTerm ).
tff(func_def_72,type,
sK82: vTerm > vOptTerm ).
tff(func_def_73,type,
sK83: vTerm > vTerm ).
tff(func_def_74,type,
sK84: vTerm > vOptTerm ).
tff(func_def_75,type,
sK85: vTerm > vTerm ).
tff(func_def_76,type,
sK86: vTerm > vOptTerm ).
tff(func_def_77,type,
sK87: vTerm > vTerm ).
tff(func_def_78,type,
sK88: vTerm > vOptTerm ).
tff(func_def_79,type,
sK89: vTerm > vTerm ).
tff(func_def_80,type,
sK90: vTerm > vTerm ).
tff(func_def_81,type,
sK91: vTerm > vOptTerm ).
tff(func_def_82,type,
sK92: vTerm > vTerm ).
tff(func_def_83,type,
sK93: vTerm > vTerm ).
tff(func_def_84,type,
sK94: vTerm > vOptTerm ).
tff(func_def_85,type,
sK95: vTerm > vTerm ).
tff(func_def_86,type,
sK96: vTerm > vTerm ).
tff(func_def_87,type,
sK97: vTerm > vTerm ).
tff(func_def_88,type,
sK98: vTerm > vOptTerm ).
tff(func_def_89,type,
sK99: vTerm > vTerm ).
tff(func_def_90,type,
sK100: vTerm > vTerm ).
tff(func_def_91,type,
sK101: vTerm > vTerm ).
tff(func_def_92,type,
sK102: vTerm > vOptTerm ).
tff(func_def_93,type,
sK103: vTerm > vTerm ).
tff(func_def_94,type,
sK104: vTerm > vOptTerm ).
tff(func_def_95,type,
sK105: vTerm > vTerm ).
tff(func_def_96,type,
sK106: vTerm > vOptTerm ).
tff(func_def_97,type,
sK107: vTerm > vTerm ).
tff(func_def_98,type,
sK108: vTerm > vOptTerm ).
tff(func_def_99,type,
sK109: vTerm > vTerm ).
tff(func_def_100,type,
sK110: vTerm > vOptTerm ).
tff(func_def_101,type,
sK111: vTerm > vTerm ).
tff(func_def_102,type,
sK112: vTerm > vTerm ).
tff(func_def_103,type,
sK113: vTerm > vOptTerm ).
tff(func_def_104,type,
sK114: vTerm > vTerm ).
tff(func_def_105,type,
sK115: vTerm > vTerm ).
tff(func_def_106,type,
sK116: vTerm > vOptTerm ).
tff(func_def_107,type,
sK117: vTerm > vTerm ).
tff(func_def_108,type,
sK118: vTerm > vTerm ).
tff(func_def_109,type,
sK119: vTerm > vTerm ).
tff(func_def_110,type,
sK120: vTerm > vTerm ).
tff(func_def_111,type,
sK121: vTerm > vTerm ).
tff(func_def_112,type,
sK122: vTy ).
tff(func_def_113,type,
sK123: vTerm ).
tff(f14,axiom,
! [X0: vTerm,X1: vTerm,X2: vTerm] : ( vFalse != vIfelse(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-False-Ifelse') ).
tff(f16,axiom,
! [X0: vTerm] : ( vFalse != vSucc(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-False-Succ') ).
tff(f17,axiom,
! [X0: vTerm] : ( vFalse != vPred(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-False-Pred') ).
tff(f18,axiom,
! [X0: vTerm] : ( vFalse != vIszero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-False-Iszero') ).
tff(f19,axiom,
! [X0: vTerm,X1: vTerm] : ( vFalse != vPlus(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-False-Plus') ).
tff(f37,axiom,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noTerm-someTerm') ).
tff(f82,axiom,
! [X0: vTerm] :
( ( ! [X3: vTerm,X1: vTerm] : ( X0 != vPlus(X3,X1) )
& ! [X3: vTerm] : ( X0 != vIszero(X3) )
& ! [X4: vTerm] : ( X0 != vIszero(vSucc(X4)) )
& ( X0 != vIszero(vZero) )
& ! [X3: vTerm] : ( X0 != vPred(X3) )
& ! [X4: vTerm] : ( X0 != vPred(vSucc(X4)) )
& ( X0 != vPred(vZero) )
& ! [X3: vTerm] : ( X0 != vSucc(X3) )
& ! [X3: vTerm,X1: vTerm,X2: vTerm] : ( X0 != vIfelse(X3,X1,X2) )
& ! [X1: vTerm,X2: vTerm] : ( X0 != vIfelse(vFalse,X1,X2) )
& ! [X1: vTerm,X2: vTerm] : ( X0 != vIfelse(vTrue,X1,X2) ) )
=> ( vreduce(X0) = vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-23') ).
tff(f105,conjecture,
! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vFalse) = vsomeTerm(X1) )
& vptchecksimple(vFalse,X0) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-False') ).
tff(f106,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( ( vreduce(vFalse) = vsomeTerm(X1) )
& vptchecksimple(vFalse,X0) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f105]) ).
tff(f108,plain,
! [X0: vTerm] :
( ( ! [X13: vTerm,X14: vTerm] : ( vPlus(X13,X14) != X0 )
& ! [X12: vTerm] : ( vIszero(X12) != X0 )
& ! [X11: vTerm] : ( vIszero(vSucc(X11)) != X0 )
& ( X0 != vIszero(vZero) )
& ! [X10: vTerm] : ( vPred(X10) != X0 )
& ! [X9: vTerm] : ( vPred(vSucc(X9)) != X0 )
& ( X0 != vPred(vZero) )
& ! [X8: vTerm] : ( vSucc(X8) != X0 )
& ! [X5: vTerm,X6: vTerm,X7: vTerm] : ( vIfelse(X5,X6,X7) != X0 )
& ! [X3: vTerm,X4: vTerm] : ( vIfelse(vFalse,X3,X4) != X0 )
& ! [X1: vTerm,X2: vTerm] : ( X0 != vIfelse(vTrue,X1,X2) ) )
=> ( vreduce(X0) = vnoTerm ) ),
inference(rectify,[],[f82]) ).
tff(f164,plain,
! [X0: vTerm] :
( ? [X13: vTerm,X14: vTerm] : ( vPlus(X13,X14) = X0 )
| ? [X12: vTerm] : ( vIszero(X12) = X0 )
| ? [X11: vTerm] : ( vIszero(vSucc(X11)) = X0 )
| ( vIszero(vZero) = X0 )
| ? [X10: vTerm] : ( vPred(X10) = X0 )
| ? [X9: vTerm] : ( vPred(vSucc(X9)) = X0 )
| ( vPred(vZero) = X0 )
| ? [X8: vTerm] : ( vSucc(X8) = X0 )
| ? [X5: vTerm,X6: vTerm,X7: vTerm] : ( vIfelse(X5,X6,X7) = X0 )
| ? [X3: vTerm,X4: vTerm] : ( vIfelse(vFalse,X3,X4) = X0 )
| ? [X1: vTerm,X2: vTerm] : ( vIfelse(vTrue,X1,X2) = X0 )
| ( vreduce(X0) = vnoTerm ) ),
inference(ennf_transformation,[],[f108]) ).
tff(f165,plain,
! [X0: vTerm] :
( ? [X13: vTerm,X14: vTerm] : ( vPlus(X13,X14) = X0 )
| ? [X12: vTerm] : ( vIszero(X12) = X0 )
| ? [X11: vTerm] : ( vIszero(vSucc(X11)) = X0 )
| ( vIszero(vZero) = X0 )
| ? [X10: vTerm] : ( vPred(X10) = X0 )
| ? [X9: vTerm] : ( vPred(vSucc(X9)) = X0 )
| ( vPred(vZero) = X0 )
| ? [X8: vTerm] : ( vSucc(X8) = X0 )
| ? [X5: vTerm,X6: vTerm,X7: vTerm] : ( vIfelse(X5,X6,X7) = X0 )
| ? [X3: vTerm,X4: vTerm] : ( vIfelse(vFalse,X3,X4) = X0 )
| ? [X1: vTerm,X2: vTerm] : ( vIfelse(vTrue,X1,X2) = X0 )
| ( vreduce(X0) = vnoTerm ) ),
inference(flattening,[],[f164]) ).
tff(f186,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vFalse) = vsomeTerm(X1) )
& vptchecksimple(vFalse,X0)
& ~ vptchecksimple(X1,X0) ),
inference(ennf_transformation,[],[f106]) ).
tff(f187,plain,
? [X0: vTy,X1: vTerm] :
( ( vreduce(vFalse) = vsomeTerm(X1) )
& vptchecksimple(vFalse,X0)
& ~ vptchecksimple(X1,X0) ),
inference(flattening,[],[f186]) ).
tff(f247,plain,
! [X0: vTerm] :
( ( vPlus(sK71(X0),sK72(X0)) = X0 )
| ( vIszero(sK70(X0)) = X0 )
| ( vIszero(vSucc(sK69(X0))) = X0 )
| ( vIszero(vZero) = X0 )
| ( vPred(sK68(X0)) = X0 )
| ( vPred(vSucc(sK67(X0))) = X0 )
| ( vPred(vZero) = X0 )
| ( vSucc(sK66(X0)) = X0 )
| ( vIfelse(sK63(X0),sK64(X0),sK65(X0)) = X0 )
| ( vIfelse(vFalse,sK61(X0),sK62(X0)) = X0 )
| ( vIfelse(vTrue,sK59(X0),sK60(X0)) = X0 )
| ( vreduce(X0) = vnoTerm ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62,sK63,sK64,sK65,sK66,sK67,sK68,sK69,sK70,sK71,sK72]),skolemize(X1,sK59(X0)),skolemize(X2,sK60(X0)),skolemize(X3,sK61(X0)),skolemize(X4,sK62(X0)),skolemize(X5,sK63(X0)),skolemize(X6,sK64(X0)),skolemize(X7,sK65(X0)),skolemize(X8,sK66(X0)),skolemize(X9,sK67(X0)),skolemize(X10,sK68(X0)),skolemize(X11,sK69(X0)),skolemize(X12,sK70(X0)),skolemize(X13,sK71(X0)),skolemize(X14,sK72(X0))],[f165]) ).
tff(f310,plain,
( ( vreduce(vFalse) = vsomeTerm(sK123) )
& vptchecksimple(vFalse,sK122)
& ~ vptchecksimple(sK123,sK122) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123]),skolemize(X0,sK122),skolemize(X1,sK123)],[f187]) ).
tff(f327,plain,
! [X2: vTerm,X0: vTerm,X1: vTerm] : ( vFalse != vIfelse(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tff(f329,plain,
! [X0: vTerm] : ( vFalse != vSucc(X0) ),
inference(cnf_transformation,[],[f16]) ).
tff(f330,plain,
! [X0: vTerm] : ( vFalse != vPred(X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f331,plain,
! [X0: vTerm] : ( vFalse != vIszero(X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f332,plain,
! [X0: vTerm,X1: vTerm] : ( vFalse != vPlus(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tff(f350,plain,
! [X0: vTerm] : ( vnoTerm != vsomeTerm(X0) ),
inference(cnf_transformation,[],[f37]) ).
tff(f429,plain,
! [X0: vTerm] :
( ( vPlus(sK71(X0),sK72(X0)) = X0 )
| ( vIszero(sK70(X0)) = X0 )
| ( vIszero(vSucc(sK69(X0))) = X0 )
| ( vIszero(vZero) = X0 )
| ( vPred(sK68(X0)) = X0 )
| ( vPred(vSucc(sK67(X0))) = X0 )
| ( vPred(vZero) = X0 )
| ( vSucc(sK66(X0)) = X0 )
| ( vIfelse(sK63(X0),sK64(X0),sK65(X0)) = X0 )
| ( vIfelse(vFalse,sK61(X0),sK62(X0)) = X0 )
| ( vIfelse(vTrue,sK59(X0),sK60(X0)) = X0 )
| ( vnoTerm = vreduce(X0) ) ),
inference(cnf_transformation,[],[f247]) ).
tff(f570,plain,
vreduce(vFalse) = vsomeTerm(sK123),
inference(cnf_transformation,[],[f310]) ).
tcf(c_65,negated_conjecture,
! [X0_vTerm: vTerm,X1_vTerm: vTerm,X2_vTerm: vTerm] : vIfelse(X0_vTerm,X1_vTerm,X2_vTerm) != vFalse,
inference(cnf_transformation,[],[f327]) ).
tcf(c_67,negated_conjecture,
! [X0_vTerm: vTerm] : vSucc(X0_vTerm) != vFalse,
inference(cnf_transformation,[],[f329]) ).
tcf(c_68,negated_conjecture,
! [X0_vTerm: vTerm] : vPred(X0_vTerm) != vFalse,
inference(cnf_transformation,[],[f330]) ).
tcf(c_69,negated_conjecture,
! [X0_vTerm: vTerm] : vIszero(X0_vTerm) != vFalse,
inference(cnf_transformation,[],[f331]) ).
tcf(c_70,negated_conjecture,
! [X0_vTerm: vTerm,X1_vTerm: vTerm] : vPlus(X0_vTerm,X1_vTerm) != vFalse,
inference(cnf_transformation,[],[f332]) ).
tcf(c_88,negated_conjecture,
! [X0_vTerm: vTerm] : vsomeTerm(X0_vTerm) != vnoTerm,
inference(cnf_transformation,[],[f350]) ).
tcf(c_167,plain,
! [X0_vTerm: vTerm] :
( ( vIszero(vZero) = X0_vTerm )
| ( vPred(vZero) = X0_vTerm )
| ( vreduce(X0_vTerm) = vnoTerm )
| ( vIszero(sK70(X0_vTerm)) = X0_vTerm )
| ( vPred(sK68(X0_vTerm)) = X0_vTerm )
| ( vSucc(sK66(X0_vTerm)) = X0_vTerm )
| ( vIszero(vSucc(sK69(X0_vTerm))) = X0_vTerm )
| ( vPred(vSucc(sK67(X0_vTerm))) = X0_vTerm )
| ( vPlus(sK71(X0_vTerm),sK72(X0_vTerm)) = X0_vTerm )
| ( vIfelse(vFalse,sK61(X0_vTerm),sK62(X0_vTerm)) = X0_vTerm )
| ( vIfelse(vTrue,sK59(X0_vTerm),sK60(X0_vTerm)) = X0_vTerm )
| ( vIfelse(sK63(X0_vTerm),sK64(X0_vTerm),sK65(X0_vTerm)) = X0_vTerm ) ),
inference(cnf_transformation,[],[f429]) ).
tcf(c_310,negated_conjecture,
vsomeTerm(sK123) = vreduce(vFalse),
inference(cnf_transformation,[],[f570]) ).
tcf(c_316,plain,
vIszero(vZero) != vFalse,
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_317,plain,
vPred(vZero) != vFalse,
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1033,plain,
vreduce(vFalse) != vnoTerm,
inference(superposition,[status(thm)],[c_310,c_88]) ).
tcf(c_18107,plain,
! [X0_vTerm: vTerm] :
( ( vIszero(vZero) = X0_vTerm )
| ( vPred(vZero) = X0_vTerm )
| ( vreduce(X0_vTerm) = vnoTerm )
| ( vIszero(sK70(X0_vTerm)) = X0_vTerm )
| ( vPred(sK68(X0_vTerm)) = X0_vTerm )
| ( vSucc(sK66(X0_vTerm)) = X0_vTerm )
| ( vIszero(vSucc(sK69(X0_vTerm))) = X0_vTerm )
| ( vPred(vSucc(sK67(X0_vTerm))) = X0_vTerm )
| ( vPlus(sK71(X0_vTerm),sK72(X0_vTerm)) = X0_vTerm )
| ( vIfelse(vFalse,sK61(X0_vTerm),sK62(X0_vTerm)) = X0_vTerm )
| ( vIfelse(vTrue,sK59(X0_vTerm),sK60(X0_vTerm)) = X0_vTerm )
| ( X0_vTerm != vFalse ) ),
inference(superposition,[status(thm)],[c_167,c_65]) ).
tcf(c_19143,plain,
( ( vreduce(vFalse) = vnoTerm )
| ( vIszero(vZero) = vFalse )
| ( vPred(vZero) = vFalse )
| ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vIszero(vSucc(sK69(vFalse))) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse )
| ( vPlus(sK71(vFalse),sK72(vFalse)) = vFalse )
| ( vIfelse(vFalse,sK61(vFalse),sK62(vFalse)) = vFalse )
| ( vIfelse(vTrue,sK59(vFalse),sK60(vFalse)) = vFalse ) ),
inference(equality_resolution,[status(thm)],[c_18107]) ).
tcf(c_28289,plain,
! [X0_vTerm: vTerm] :
( ( vIszero(vZero) = X0_vTerm )
| ( vPred(vZero) = X0_vTerm )
| ( vreduce(X0_vTerm) = vnoTerm )
| ( vIszero(sK70(X0_vTerm)) = X0_vTerm )
| ( vPred(sK68(X0_vTerm)) = X0_vTerm )
| ( vSucc(sK66(X0_vTerm)) = X0_vTerm )
| ( vIszero(vSucc(sK69(X0_vTerm))) = X0_vTerm )
| ( vPred(vSucc(sK67(X0_vTerm))) = X0_vTerm )
| ( vPlus(sK71(X0_vTerm),sK72(X0_vTerm)) = X0_vTerm )
| ( vIfelse(vFalse,sK61(X0_vTerm),sK62(X0_vTerm)) = X0_vTerm )
| ( vIfelse(vTrue,sK59(X0_vTerm),sK60(X0_vTerm)) = X0_vTerm )
| ( X0_vTerm != vFalse ) ),
inference(superposition,[status(thm)],[c_167,c_65]) ).
tcf(c_28457,plain,
( ( vreduce(vFalse) = vnoTerm )
| ( vIszero(vZero) = vFalse )
| ( vPred(vZero) = vFalse )
| ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vIszero(vSucc(sK69(vFalse))) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse )
| ( vPlus(sK71(vFalse),sK72(vFalse)) = vFalse )
| ( vIfelse(vFalse,sK61(vFalse),sK62(vFalse)) = vFalse )
| ( vIfelse(vTrue,sK59(vFalse),sK60(vFalse)) = vFalse ) ),
inference(equality_resolution,[status(thm)],[c_28289]) ).
tcf(c_30911,plain,
( ( vIfelse(vTrue,sK59(vFalse),sK60(vFalse)) = vFalse )
| ( vIfelse(vFalse,sK61(vFalse),sK62(vFalse)) = vFalse )
| ( vPlus(sK71(vFalse),sK72(vFalse)) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse )
| ( vIszero(vSucc(sK69(vFalse))) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vIszero(sK70(vFalse)) = vFalse ) ),
inference(global_subsumption_just,[status(thm)],[c_28457,c_316,c_317,c_1033,c_19143]) ).
tcf(c_30912,plain,
( ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vIszero(vSucc(sK69(vFalse))) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse )
| ( vPlus(sK71(vFalse),sK72(vFalse)) = vFalse )
| ( vIfelse(vFalse,sK61(vFalse),sK62(vFalse)) = vFalse )
| ( vIfelse(vTrue,sK59(vFalse),sK60(vFalse)) = vFalse ) ),
inference(renaming,[status(thm)],[c_30911]) ).
tcf(c_30925,plain,
( ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vIszero(vSucc(sK69(vFalse))) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse )
| ( vPlus(sK71(vFalse),sK72(vFalse)) = vFalse )
| ( vIfelse(vFalse,sK61(vFalse),sK62(vFalse)) = vFalse ) ),
inference(superposition,[status(thm)],[c_30912,c_65]) ).
tcf(c_30945,plain,
( ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vIszero(vSucc(sK69(vFalse))) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse )
| ( vPlus(sK71(vFalse),sK72(vFalse)) = vFalse ) ),
inference(superposition,[status(thm)],[c_30925,c_65]) ).
tcf(c_30967,plain,
( ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vIszero(vSucc(sK69(vFalse))) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse ) ),
inference(superposition,[status(thm)],[c_30945,c_70]) ).
tcf(c_31118,plain,
( ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse )
| ( vPred(vSucc(sK67(vFalse))) = vFalse ) ),
inference(superposition,[status(thm)],[c_30967,c_69]) ).
tcf(c_31142,plain,
( ( vIszero(sK70(vFalse)) = vFalse )
| ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse ) ),
inference(superposition,[status(thm)],[c_31118,c_68]) ).
tcf(c_31166,plain,
( ( vPred(sK68(vFalse)) = vFalse )
| ( vSucc(sK66(vFalse)) = vFalse ) ),
inference(superposition,[status(thm)],[c_31142,c_69]) ).
tcf(c_31187,plain,
vSucc(sK66(vFalse)) = vFalse,
inference(superposition,[status(thm)],[c_31166,c_68]) ).
tcf(c_31229,plain,
$false,
inference(superposition,[status(thm)],[c_31187,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM216_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 08:00:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 24.04/4.27 % SZS status Started for theBenchmark.p
% 24.04/4.27 % SZS status Theorem for theBenchmark.p
% 24.04/4.27
% 24.04/4.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 24.04/4.27
% 24.04/4.27 % ------ iProver source info
% 24.04/4.27
% 24.04/4.27 % git: date: 2026-07-19 20:42:38 +0200
% 24.04/4.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 24.04/4.27 % git: non_committed_changes: false
% 24.04/4.27
% 24.04/4.27 % ------ Parsing...
% 24.04/4.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 24.04/4.27
% 24.04/4.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e %
% 24.04/4.27
% 24.04/4.27 % ------ Preprocessing...%
% 24.04/4.27
% 24.04/4.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.04/4.27 % ------ Proving...
% 24.04/4.27 % ------ Problem Properties
% 24.04/4.27
% 24.04/4.27 %
% 24.04/4.27 % clauses 262
% 24.04/4.27 % conjectures 75
% 24.04/4.27 % EPR 21
% 24.04/4.27 % Horn 212
% 24.04/4.27 % unary 48
% 24.04/4.27 % binary 164
% 24.04/4.27 % lits 727
% 24.04/4.27 % lits eq 281
% 24.04/4.27 % fd_pure 1
% 24.04/4.27 % fd_pseudo 0
% 24.04/4.27 % fd_cond 19
% 24.04/4.27 % fd_pseudo_cond 9
% 24.04/4.27 % AC symbols 0
% 24.04/4.27
% 24.04/4.27 % ------ Input Options Time Limit: Unbounded
% 24.04/4.27
% 24.04/4.27
% 24.04/4.27 % ------
% 24.04/4.27 % Current options:
% 24.04/4.27 % ------
% 24.04/4.27
% 24.04/4.27
% 24.04/4.27 %
% 24.04/4.27
% 24.04/4.27 % ------ Proving...
% 24.04/4.27 %
% 24.04/4.27
% 24.04/4.27 % SZS status Theorem for theBenchmark.p
% 24.04/4.27
% 24.04/4.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.04/4.27
% 24.04/4.27
%------------------------------------------------------------------------------