%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM216_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 : Tue Sep 29 09:39:48 AM UTC 2026
% Result : Theorem 3.46s 1.17s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 169 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 182 ( 40 ~; 110 |; 28 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-3 aty)
% Number of functors : 114 ( 114 usr; 8 con; 0-3 aty)
% Number of variables : 89 ( 57 !; 32 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
vTerm: $tType ).
tff(type_def_6,type,
vOptTerm: $tType ).
tff(type_def_7,type,
vTy: $tType ).
tff(func_def_0,type,
vNat: vTy ).
tff(func_def_1,type,
vSucc: vTerm > vTerm ).
tff(func_def_2,type,
vPred: vTerm > vTerm ).
tff(func_def_3,type,
vsomeTerm: vTerm > vOptTerm ).
tff(func_def_4,type,
vZero: vTerm ).
tff(func_def_5,type,
vIszero: vTerm > vTerm ).
tff(func_def_6,type,
vTrue: vTerm ).
tff(func_def_7,type,
vFalse: vTerm ).
tff(func_def_8,type,
vnoTerm: vOptTerm ).
tff(func_def_9,type,
vPlus: ( vTerm * vTerm ) > vTerm ).
tff(func_def_10,type,
vB: vTy ).
tff(func_def_11,type,
vIfelse: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_12,type,
vreduce: vTerm > vOptTerm ).
tff(func_def_13,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_14,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_15,type,
sK25: vTerm > vTerm ).
tff(func_def_16,type,
sK26: vTerm > vTerm ).
tff(func_def_17,type,
sK27: vTerm > vTerm ).
tff(func_def_18,type,
sK28: vTerm > vTerm ).
tff(func_def_19,type,
sK29: vTerm > vTerm ).
tff(func_def_20,type,
sK30: vTerm > vTerm ).
tff(func_def_21,type,
sK31: vTerm > vTerm ).
tff(func_def_22,type,
sK32: vTerm > vTerm ).
tff(func_def_23,type,
sK33: vOptTerm > vTerm ).
tff(func_def_24,type,
sK34: vTerm > vTerm ).
tff(func_def_25,type,
sK35: vTerm > vTerm ).
tff(func_def_26,type,
sK36: vTerm > vTerm ).
tff(func_def_27,type,
sK37: vTerm > vTerm ).
tff(func_def_28,type,
sK38: vTerm > vTerm ).
tff(func_def_29,type,
sK39: vTerm > vTerm ).
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(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: ( vTerm * vTy ) > $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(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] :
( ( ! [X1: vTerm,X2: vTerm] : ( X0 != vIfelse(vTrue,X1,X2) )
& ! [X1: vTerm,X2: vTerm] : ( X0 != vIfelse(vFalse,X1,X2) )
& ! [X3: vTerm,X1: vTerm,X2: vTerm] : ( X0 != vIfelse(X3,X1,X2) )
& ! [X3: vTerm] : ( X0 != vSucc(X3) )
& ( X0 != vPred(vZero) )
& ! [X4: vTerm] : ( X0 != vPred(vSucc(X4)) )
& ! [X3: vTerm] : ( X0 != vPred(X3) )
& ( X0 != vIszero(vZero) )
& ! [X4: vTerm] : ( X0 != vIszero(vSucc(X4)) )
& ! [X3: vTerm] : ( X0 != vIszero(X3) )
& ! [X3: vTerm,X1: vTerm] : ( X0 != vPlus(X3,X1) ) )
=> ( vreduce(X0) = vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-23') ).
tff(f105,conjecture,
! [X0: vTy,X1: vTerm] :
( ( vptchecksimple(vFalse,X0)
& ( vreduce(vFalse) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-False') ).
tff(f106,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( vptchecksimple(vFalse,X0)
& ( vreduce(vFalse) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f105]) ).
tff(f108,plain,
! [X0: vTerm] :
( ( ! [X1: vTerm,X2: vTerm] : ( X0 != vIfelse(vTrue,X1,X2) )
& ! [X3: vTerm,X4: vTerm] : ( vIfelse(vFalse,X3,X4) != X0 )
& ! [X5: vTerm,X6: vTerm,X7: vTerm] : ( vIfelse(X5,X6,X7) != X0 )
& ! [X8: vTerm] : ( vSucc(X8) != X0 )
& ( X0 != vPred(vZero) )
& ! [X9: vTerm] : ( vPred(vSucc(X9)) != X0 )
& ! [X10: vTerm] : ( vPred(X10) != X0 )
& ( X0 != vIszero(vZero) )
& ! [X11: vTerm] : ( vIszero(vSucc(X11)) != X0 )
& ! [X12: vTerm] : ( vIszero(X12) != X0 )
& ! [X13: vTerm,X14: vTerm] : ( vPlus(X13,X14) != X0 ) )
=> ( vreduce(X0) = vnoTerm ) ),
inference(rectify,[],[f82]) ).
tff(f164,plain,
! [X0: vTerm] :
( ( vreduce(X0) = vnoTerm )
| ? [X1: vTerm,X2: vTerm] : ( vIfelse(vTrue,X1,X2) = X0 )
| ? [X3: vTerm,X4: vTerm] : ( vIfelse(vFalse,X3,X4) = X0 )
| ? [X5: vTerm,X6: vTerm,X7: vTerm] : ( vIfelse(X5,X6,X7) = X0 )
| ? [X8: vTerm] : ( vSucc(X8) = X0 )
| ( vPred(vZero) = X0 )
| ? [X9: vTerm] : ( vPred(vSucc(X9)) = X0 )
| ? [X10: vTerm] : ( vPred(X10) = X0 )
| ( vIszero(vZero) = X0 )
| ? [X11: vTerm] : ( vIszero(vSucc(X11)) = X0 )
| ? [X12: vTerm] : ( vIszero(X12) = X0 )
| ? [X13: vTerm,X14: vTerm] : ( vPlus(X13,X14) = X0 ) ),
inference(ennf_transformation,[],[f108]) ).
tff(f165,plain,
! [X0: vTerm] :
( ( vreduce(X0) = vnoTerm )
| ? [X1: vTerm,X2: vTerm] : ( vIfelse(vTrue,X1,X2) = X0 )
| ? [X3: vTerm,X4: vTerm] : ( vIfelse(vFalse,X3,X4) = X0 )
| ? [X5: vTerm,X6: vTerm,X7: vTerm] : ( vIfelse(X5,X6,X7) = X0 )
| ? [X8: vTerm] : ( vSucc(X8) = X0 )
| ( vPred(vZero) = X0 )
| ? [X9: vTerm] : ( vPred(vSucc(X9)) = X0 )
| ? [X10: vTerm] : ( vPred(X10) = X0 )
| ( vIszero(vZero) = X0 )
| ? [X11: vTerm] : ( vIszero(vSucc(X11)) = X0 )
| ? [X12: vTerm] : ( vIszero(X12) = X0 )
| ? [X13: vTerm,X14: vTerm] : ( vPlus(X13,X14) = X0 ) ),
inference(flattening,[],[f164]) ).
tff(f186,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& vptchecksimple(vFalse,X0)
& ( vreduce(vFalse) = vsomeTerm(X1) ) ),
inference(ennf_transformation,[],[f106]) ).
tff(f187,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& vptchecksimple(vFalse,X0)
& ( vreduce(vFalse) = vsomeTerm(X1) ) ),
inference(flattening,[],[f186]) ).
tff(f247,plain,
! [X0: vTerm] :
( ( vreduce(X0) = vnoTerm )
| ( vIfelse(vTrue,sK59(X0),sK60(X0)) = X0 )
| ( vIfelse(vFalse,sK61(X0),sK62(X0)) = X0 )
| ( vIfelse(sK63(X0),sK64(X0),sK65(X0)) = X0 )
| ( vSucc(sK66(X0)) = X0 )
| ( vPred(vZero) = X0 )
| ( vPred(vSucc(sK67(X0))) = X0 )
| ( vPred(sK68(X0)) = X0 )
| ( vIszero(vZero) = X0 )
| ( vIszero(vSucc(sK69(X0))) = X0 )
| ( vIszero(sK70(X0)) = X0 )
| ( vPlus(sK71(X0),sK72(X0)) = X0 ) ),
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,
( ~ vptchecksimple(sK123,sK122)
& vptchecksimple(vFalse,sK122)
& ( vreduce(vFalse) = vsomeTerm(sK123) ) ),
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] :
( ( vIfelse(sK63(X0),sK64(X0),sK65(X0)) = X0 )
| ( vIfelse(vTrue,sK59(X0),sK60(X0)) = X0 )
| ( vIfelse(vFalse,sK61(X0),sK62(X0)) = X0 )
| ( vnoTerm = vreduce(X0) )
| ( vSucc(sK66(X0)) = X0 )
| ( vPred(vZero) = X0 )
| ( vPred(vSucc(sK67(X0))) = X0 )
| ( vPred(sK68(X0)) = X0 )
| ( vIszero(vZero) = X0 )
| ( vIszero(vSucc(sK69(X0))) = X0 )
| ( vIszero(sK70(X0)) = X0 )
| ( vPlus(sK71(X0),sK72(X0)) = X0 ) ),
inference(cnf_transformation,[],[f247]) ).
tff(f570,plain,
vreduce(vFalse) = vsomeTerm(sK123),
inference(cnf_transformation,[],[f310]) ).
tff(f582,plain,
vnoTerm != vreduce(vFalse),
inference(superposition,[],[f350,f570]) ).
tff(f1062,plain,
! [X0: vTerm] :
( ( vFalse != X0 )
| ( vIfelse(vTrue,sK59(X0),sK60(X0)) = X0 )
| ( vIfelse(vFalse,sK61(X0),sK62(X0)) = X0 )
| ( vnoTerm = vreduce(X0) )
| ( vSucc(sK66(X0)) = X0 )
| ( vPred(vZero) = X0 )
| ( vPred(vSucc(sK67(X0))) = X0 )
| ( vPred(sK68(X0)) = X0 )
| ( vIszero(vZero) = X0 )
| ( vIszero(vSucc(sK69(X0))) = X0 )
| ( vIszero(sK70(X0)) = X0 )
| ( vPlus(sK71(X0),sK72(X0)) = X0 ) ),
inference(superposition,[],[f327,f429]) ).
tff(f3166,plain,
( ( vFalse = vIfelse(vTrue,sK59(vFalse),sK60(vFalse)) )
| ( vFalse = vIfelse(vFalse,sK61(vFalse),sK62(vFalse)) )
| ( vnoTerm = vreduce(vFalse) )
| ( vFalse = vSucc(sK66(vFalse)) )
| ( vFalse = vPred(vZero) )
| ( vFalse = vPred(vSucc(sK67(vFalse))) )
| ( vFalse = vPred(sK68(vFalse)) )
| ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(equality_resolution,[],[f1062]) ).
tff(f3167,plain,
( ( vFalse = vIfelse(vTrue,sK59(vFalse),sK60(vFalse)) )
| ( vnoTerm = vreduce(vFalse) )
| ( vFalse = vSucc(sK66(vFalse)) )
| ( vFalse = vPred(vZero) )
| ( vFalse = vPred(vSucc(sK67(vFalse))) )
| ( vFalse = vPred(sK68(vFalse)) )
| ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3166,f327]) ).
tff(f3168,plain,
( ( vnoTerm = vreduce(vFalse) )
| ( vFalse = vSucc(sK66(vFalse)) )
| ( vFalse = vPred(vZero) )
| ( vFalse = vPred(vSucc(sK67(vFalse))) )
| ( vFalse = vPred(sK68(vFalse)) )
| ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3167,f327]) ).
tff(f3169,plain,
( ( vFalse = vSucc(sK66(vFalse)) )
| ( vFalse = vPred(vZero) )
| ( vFalse = vPred(vSucc(sK67(vFalse))) )
| ( vFalse = vPred(sK68(vFalse)) )
| ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3168,f582]) ).
tff(f3170,plain,
( ( vFalse = vPred(vZero) )
| ( vFalse = vPred(vSucc(sK67(vFalse))) )
| ( vFalse = vPred(sK68(vFalse)) )
| ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3169,f329]) ).
tff(f3171,plain,
( ( vFalse = vPred(vSucc(sK67(vFalse))) )
| ( vFalse = vPred(sK68(vFalse)) )
| ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3170,f330]) ).
tff(f3172,plain,
( ( vFalse = vPred(sK68(vFalse)) )
| ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3171,f330]) ).
tff(f3173,plain,
( ( vFalse = vIszero(vZero) )
| ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3172,f330]) ).
tff(f3174,plain,
( ( vFalse = vIszero(vSucc(sK69(vFalse))) )
| ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3173,f331]) ).
tff(f3175,plain,
( ( vFalse = vIszero(sK70(vFalse)) )
| ( vFalse = vPlus(sK71(vFalse),sK72(vFalse)) ) ),
inference(forward_subsumption_resolution,[],[f3174,f331]) ).
tff(f3176,plain,
vFalse = vPlus(sK71(vFalse),sK72(vFalse)),
inference(forward_subsumption_resolution,[],[f3175,f331]) ).
tff(f3177,plain,
$false,
inference(forward_subsumption_resolution,[],[f3176,f332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM216_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n017.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 21:57:22 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.46/1.16 % (4079694)Detected formulas, will run a generic FOF schedule.
% 3.46/1.16 % (4079716)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2729830803:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.16 % (4079718)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1133385885:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.16 % (4079721)dis-21_1_sil=8000:lcm=predicate:random_seed=497082737:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.46/1.16 % (4079715)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=666597136:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.16 % (4079717)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=933986626:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.16 % (4079720)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3112112273:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.16 % (4079718)Refutation not found, incomplete strategy
% 3.46/1.16 % (4079718)------------------------------
% 3.46/1.16 % (4079718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.16 % (4079718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.16 % (4079718)CaDiCaL version: 2.1.3
% 3.46/1.16 % (4079718)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.16 % (4079718)Time elapsed: 0.001 s
% 3.46/1.16 % (4079718)Peak memory usage: 88 MB
% 3.46/1.16 % (4079719)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=895566605:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.16 % (4079720)First to succeed.
% 3.46/1.16 % (4079720)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4079694"
% 3.46/1.16 % (4079721)Instruction limit reached!
% 3.46/1.16 % (4079721)------------------------------
% 3.46/1.16 % (4079721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.16 % (4079721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.16 % (4079721)CaDiCaL version: 2.1.3
% 3.46/1.16 % (4079721)Termination reason: Instruction limit
% 3.46/1.16 % (4079721)Termination phase: Saturation
% 3.46/1.16 % (4079721)Time elapsed: 0.076 s
% 3.46/1.16 % (4079721)Peak memory usage: 90 MB
% 3.46/1.16 % (4079721)Instructions burned: 131 (million)
% 3.46/1.16 % (4079719)Instruction limit reached!
% 3.46/1.16 % (4079719)------------------------------
% 3.46/1.16 % (4079719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.16 % (4079719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.16 % (4079719)CaDiCaL version: 2.1.3
% 3.46/1.16 % (4079719)Termination reason: Instruction limit
% 3.46/1.16 % (4079719)Termination phase: Saturation
% 3.46/1.16 % (4079719)Time elapsed: 0.078 s
% 3.46/1.16 % (4079719)Peak memory usage: 88 MB
% 3.46/1.16 % (4079719)Instructions burned: 119 (million)
% 3.46/1.16 % (4079733)lrs+10_1_sil=8000:sp=occurrence:random_seed=4065261762:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.46/1.17 % (4079744)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3476085892:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.46/1.17 % (4079744)Refutation not found, incomplete strategy
% 3.46/1.17 % (4079744)------------------------------
% 3.46/1.17 % (4079744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.17 % (4079744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.17 % (4079744)CaDiCaL version: 2.1.3
% 3.46/1.17 % (4079744)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.17 % (4079744)Time elapsed: 0.002 s
% 3.46/1.17 % (4079744)Peak memory usage: 89 MB
% 3.46/1.17 % (4079744)Instructions burned: 2 (million)
% 3.46/1.17 % (4079718)------------------------------
% 3.46/1.17 % (4079718)------------------------------
% 3.46/1.17 % (4079720)Refutation found. Thanks to Tanya!
% 3.46/1.17 % SZS status Theorem for theBenchmark
% 3.46/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 3.82/1.26 % (4079720)------------------------------
% 3.82/1.26 % (4079720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.26 % (4079720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.26 % (4079720)CaDiCaL version: 2.1.3
% 3.82/1.26 % (4079720)Termination reason: Refutation
% 3.82/1.26 % (4079720)Time elapsed: 0.069 s
% 3.82/1.26 % (4079720)Peak memory usage: 90 MB
% 3.82/1.26 % (4079720)Instructions burned: 108 (million)
% 3.82/1.26 % (4079720)------------------------------
% 3.82/1.26 % (4079720)------------------------------
% 3.82/1.26 % (4079694)Success in time 0.457 s
% 3.82/1.26 % Vampire exiting
%------------------------------------------------------------------------------