%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM220_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:39:49 AM UTC 2026
% Result : Theorem 6.01s 1.34s
% Output : Refutation 6.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 59 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 45 ~; 36 |; 26 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 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 : 113 ( 113 usr; 9 con; 0-3 aty)
% Number of variables : 53 ( 45 !; 8 ?; 53 :)
% 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,
vt1: vTerm ).
tff(func_def_13,type,
vreduce: vTerm > vOptTerm ).
tff(func_def_14,type,
vplusop: ( vTerm * vTerm ) > vTerm ).
tff(func_def_15,type,
vgetTerm: vOptTerm > vTerm ).
tff(func_def_16,type,
sK25: vTy ).
tff(func_def_17,type,
sK26: vTerm ).
tff(func_def_18,type,
sK27: vTerm > vTerm ).
tff(func_def_19,type,
sK28: vTerm > vTerm ).
tff(func_def_20,type,
sK29: vTerm > vTerm ).
tff(func_def_21,type,
sK30: vTerm > vOptTerm ).
tff(func_def_22,type,
sK31: vTerm > vTerm ).
tff(func_def_23,type,
sK32: vTerm > vOptTerm ).
tff(func_def_24,type,
sK33: vTerm > vTerm ).
tff(func_def_25,type,
sK34: vTerm > vTerm ).
tff(func_def_26,type,
sK35: vTerm > vTerm ).
tff(func_def_27,type,
sK36: vTerm > vOptTerm ).
tff(func_def_28,type,
sK37: vTerm > vTerm ).
tff(func_def_29,type,
sK38: vTerm > vOptTerm ).
tff(func_def_30,type,
sK39: vTerm > vTerm ).
tff(func_def_31,type,
sK40: vTerm > vOptTerm ).
tff(func_def_32,type,
sK41: vTerm > vTerm ).
tff(func_def_33,type,
sK42: vTerm > vOptTerm ).
tff(func_def_34,type,
sK43: vTerm > vTerm ).
tff(func_def_35,type,
sK44: vTerm > vTerm ).
tff(func_def_36,type,
sK45: vTerm > vOptTerm ).
tff(func_def_37,type,
sK46: vTerm > vTerm ).
tff(func_def_38,type,
sK47: vTerm > vTerm ).
tff(func_def_39,type,
sK48: vTerm > vOptTerm ).
tff(func_def_40,type,
sK49: vTerm > vTerm ).
tff(func_def_41,type,
sK50: vTerm > vTerm ).
tff(func_def_42,type,
sK51: vTerm > vTerm ).
tff(func_def_43,type,
sK52: vTerm > vOptTerm ).
tff(func_def_44,type,
sK53: vTerm > vTerm ).
tff(func_def_45,type,
sK54: vTerm > vTerm ).
tff(func_def_46,type,
sK55: vTerm > vTerm ).
tff(func_def_47,type,
sK56: vTerm > vOptTerm ).
tff(func_def_48,type,
sK57: vTerm > vTerm ).
tff(func_def_49,type,
sK58: vTerm > vOptTerm ).
tff(func_def_50,type,
sK59: vTerm > vTerm ).
tff(func_def_51,type,
sK60: vTerm > vOptTerm ).
tff(func_def_52,type,
sK61: vTerm > vTerm ).
tff(func_def_53,type,
sK62: vTerm > vOptTerm ).
tff(func_def_54,type,
sK63: vTerm > vTerm ).
tff(func_def_55,type,
sK64: vTerm > vOptTerm ).
tff(func_def_56,type,
sK65: vTerm > vTerm ).
tff(func_def_57,type,
sK66: vTerm > vTerm ).
tff(func_def_58,type,
sK67: vTerm > vOptTerm ).
tff(func_def_59,type,
sK68: vTerm > vTerm ).
tff(func_def_60,type,
sK69: vTerm > vTerm ).
tff(func_def_61,type,
sK70: vTerm > vOptTerm ).
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 > vTerm ).
tff(func_def_68,type,
sK77: vTerm > vTerm ).
tff(func_def_69,type,
sK78: vTerm > vTerm ).
tff(func_def_70,type,
sK79: vTerm > vTerm ).
tff(func_def_71,type,
sK80: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_72,type,
sK81: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_73,type,
sK82: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_74,type,
sK83: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_75,type,
sK84: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_76,type,
sK85: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_77,type,
sK86: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_78,type,
sK87: ( vTerm * vTerm * vTerm ) > vTerm ).
tff(func_def_79,type,
sK88: vOptTerm > vTerm ).
tff(func_def_80,type,
sK89: vOptTerm > vTerm ).
tff(func_def_81,type,
sK90: vTerm > vTerm ).
tff(func_def_82,type,
sK91: vTerm > vTerm ).
tff(func_def_83,type,
sK92: vTerm > vTerm ).
tff(func_def_84,type,
sK93: vTerm > vTerm ).
tff(func_def_85,type,
sK94: vTerm > vTerm ).
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 > vTerm ).
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 > vTerm ).
tff(func_def_94,type,
sK103: vTerm > vTerm ).
tff(func_def_95,type,
sK104: ( vTerm * vTerm ) > vTerm ).
tff(func_def_96,type,
sK105: ( vTerm * vTerm ) > vTerm ).
tff(func_def_97,type,
sK106: ( vTerm * vTerm ) > vTerm ).
tff(func_def_98,type,
sK107: ( vTerm * vTerm ) > vTerm ).
tff(func_def_99,type,
sK108: ( vTerm * vTerm ) > vTerm ).
tff(func_def_100,type,
sK109: vTerm > vTerm ).
tff(func_def_101,type,
sK110: vTerm > vTerm ).
tff(func_def_102,type,
sK111: vTerm > vTerm ).
tff(func_def_103,type,
sK112: vTerm > vTerm ).
tff(func_def_104,type,
sK113: vTerm > vTerm ).
tff(func_def_105,type,
sK114: vTerm > vTerm ).
tff(func_def_106,type,
sK115: vTerm > vTerm ).
tff(func_def_107,type,
sK116: vTerm > vTerm ).
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(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 > $o ).
tff(pred_def_6,type,
sP1: vTerm > $o ).
tff(pred_def_7,type,
sP2: vTerm > $o ).
tff(pred_def_8,type,
sP3: 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 * vTerm * vTerm ) > $o ).
tff(pred_def_27,type,
sP22: ( vTerm * vTerm * vTerm ) > $o ).
tff(pred_def_28,type,
sP23: ( vTerm * vTerm ) > $o ).
tff(pred_def_29,type,
sP24: ( vTerm * vTerm ) > $o ).
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] :
( ( ( X0 != vZero )
& ! [X1: vTerm] : ( X0 != vSucc(X1) )
& visSomeTerm(vreduce(X0)) )
=> ( 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] :
( ( vptchecksimple(vt1,X0)
& ( vreduce(vt1) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-IH0') ).
tff(f106,conjecture,
! [X0: vTy,X1: vTerm] :
( ( visSomeTerm(vreduce(vt1))
& ( vt1 != vZero )
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& vptchecksimple(vIszero(vt1),X0)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-t1-isSomeTerm-True') ).
tff(f107,negated_conjecture,
~ ! [X0: vTy,X1: vTerm] :
( ( visSomeTerm(vreduce(vt1))
& ( vt1 != vZero )
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& vptchecksimple(vIszero(vt1),X0)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X1) ) )
=> vptchecksimple(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f110,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& visSomeTerm(vreduce(vt1))
& ( vt1 != vZero )
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& vptchecksimple(vIszero(vt1),X0)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X1) ) ),
inference(ennf_transformation,[],[f107]) ).
tff(f111,plain,
? [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(X1,X0)
& visSomeTerm(vreduce(vt1))
& ( vt1 != vZero )
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& vptchecksimple(vIszero(vt1),X0)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X1) ) ),
inference(flattening,[],[f110]) ).
tff(f123,plain,
! [X0: vTerm] :
( ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) )
| ( vZero = X0 )
| ? [X1: vTerm] : ( vSucc(X1) = X0 )
| ~ visSomeTerm(vreduce(X0)) ),
inference(ennf_transformation,[],[f75]) ).
tff(f124,plain,
! [X0: vTerm] :
( ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) )
| ( vZero = X0 )
| ? [X1: vTerm] : ( vSucc(X1) = X0 )
| ~ visSomeTerm(vreduce(X0)) ),
inference(flattening,[],[f123]) ).
tff(f144,plain,
! [X0: vOptTerm] :
( ? [X1: vTerm] : ( X0 = vsomeTerm(X1) )
| ~ visSomeTerm(X0) ),
inference(ennf_transformation,[],[f53]) ).
tff(f145,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| ~ vptchecksimple(vt1,X0)
| ( vsomeTerm(X1) != vreduce(vt1) ) ),
inference(ennf_transformation,[],[f105]) ).
tff(f146,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| ~ vptchecksimple(vt1,X0)
| ( vsomeTerm(X1) != vreduce(vt1) ) ),
inference(flattening,[],[f145]) ).
tff(f157,plain,
! [X0: vTerm,X1: vTy] :
( ( X1 = vB )
| ~ vptchecksimple(vIszero(X0),X1) ),
inference(ennf_transformation,[],[f100]) ).
tff(f158,plain,
! [X0: vTerm] :
( vptchecksimple(X0,vNat)
| ~ vptchecksimple(vIszero(X0),vB) ),
inference(ennf_transformation,[],[f99]) ).
tff(f159,plain,
! [X0: vTerm] :
( vptchecksimple(vIszero(X0),vB)
| ~ vptchecksimple(X0,vNat) ),
inference(ennf_transformation,[],[f98]) ).
tff(f212,plain,
( ~ vptchecksimple(sK26,sK25)
& visSomeTerm(vreduce(vt1))
& ( vt1 != vZero )
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& vptchecksimple(vIszero(vt1),sK25)
& ( vreduce(vIszero(vt1)) = vsomeTerm(sK26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26]),skolemize(X0,sK25),skolemize(X1,sK26)],[f111]) ).
tff(f276,plain,
! [X0: vTerm] :
( ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) )
| ( vZero = X0 )
| ( vSucc(sK77(X0)) = X0 )
| ~ visSomeTerm(vreduce(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(X1,sK77(X0))],[f124]) ).
tff(f287,plain,
! [X0: vOptTerm] :
( ( vsomeTerm(sK88(X0)) = X0 )
| ~ visSomeTerm(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(X1,sK88(X0))],[f144]) ).
tff(f302,plain,
vreduce(vIszero(vt1)) = vsomeTerm(sK26),
inference(cnf_transformation,[],[f212]) ).
tff(f303,plain,
vptchecksimple(vIszero(vt1),sK25),
inference(cnf_transformation,[],[f212]) ).
tff(f304,plain,
! [X2: vTerm] : ( vSucc(X2) != vt1 ),
inference(cnf_transformation,[],[f212]) ).
tff(f305,plain,
vZero != vt1,
inference(cnf_transformation,[],[f212]) ).
tff(f306,plain,
visSomeTerm(vreduce(vt1)),
inference(cnf_transformation,[],[f212]) ).
tff(f307,plain,
~ vptchecksimple(sK26,sK25),
inference(cnf_transformation,[],[f212]) ).
tff(f433,plain,
! [X0: vTerm] :
( ~ visSomeTerm(vreduce(X0))
| ( vZero = X0 )
| ( vSucc(sK77(X0)) = X0 )
| ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) ) ),
inference(cnf_transformation,[],[f276]) ).
tff(f455,plain,
! [X0: vOptTerm] :
( ( vsomeTerm(sK88(X0)) = X0 )
| ~ visSomeTerm(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f458,plain,
! [X0: vTy,X1: vTerm] :
( ~ vptchecksimple(vt1,X0)
| vptchecksimple(X1,X0)
| ( vsomeTerm(X1) != vreduce(vt1) ) ),
inference(cnf_transformation,[],[f146]) ).
tff(f466,plain,
! [X0: vTerm] : ( vgetTerm(vsomeTerm(X0)) = X0 ),
inference(cnf_transformation,[],[f40]) ).
tff(f474,plain,
! [X0: vTerm,X1: vTy] :
( ~ vptchecksimple(vIszero(X0),X1)
| ( vB = X1 ) ),
inference(cnf_transformation,[],[f157]) ).
tff(f475,plain,
! [X0: vTerm] :
( ~ vptchecksimple(vIszero(X0),vB)
| vptchecksimple(X0,vNat) ),
inference(cnf_transformation,[],[f158]) ).
tff(f476,plain,
! [X0: vTerm] :
( ~ vptchecksimple(X0,vNat)
| vptchecksimple(vIszero(X0),vB) ),
inference(cnf_transformation,[],[f159]) ).
tff(f548,plain,
! [X0: vOptTerm] :
( ( sK88(X0) = vgetTerm(X0) )
| ~ visSomeTerm(X0) ),
inference(superposition,[],[f466,f455]) ).
tff(f552,plain,
vB = sK25,
inference(resolution,[],[f474,f303]) ).
tff(f553,plain,
vptchecksimple(vIszero(vt1),vB),
inference(superposition,[],[f303,f552]) ).
tff(f554,plain,
~ vptchecksimple(sK26,vB),
inference(superposition,[],[f307,f552]) ).
tff(f556,plain,
vptchecksimple(vt1,vNat),
inference(resolution,[],[f553,f475]) ).
tff(f829,plain,
! [X0: vTerm] :
( ( vsomeTerm(X0) != vreduce(vt1) )
| vptchecksimple(X0,vNat) ),
inference(resolution,[],[f458,f556]) ).
tff(f830,plain,
! [X0: vOptTerm] :
( ( vreduce(vt1) != X0 )
| vptchecksimple(sK88(X0),vNat)
| ~ visSomeTerm(X0) ),
inference(superposition,[],[f829,f455]) ).
tff(f837,plain,
( vptchecksimple(sK88(vreduce(vt1)),vNat)
| ~ visSomeTerm(vreduce(vt1)) ),
inference(equality_resolution,[],[f830]) ).
tff(f838,plain,
vptchecksimple(sK88(vreduce(vt1)),vNat),
inference(forward_subsumption_resolution,[],[f837,f306]) ).
tff(f840,plain,
vptchecksimple(vIszero(sK88(vreduce(vt1))),vB),
inference(resolution,[],[f838,f476]) ).
tff(f1089,plain,
( ( vZero = vt1 )
| ( vt1 = vSucc(sK77(vt1)) )
| ( vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))) ) ),
inference(resolution,[],[f433,f306]) ).
tff(f1120,plain,
( ( vt1 = vSucc(sK77(vt1)) )
| ( vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))) ) ),
inference(forward_subsumption_resolution,[],[f1089,f305]) ).
tff(f1132,plain,
vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))),
inference(forward_subsumption_resolution,[],[f1120,f304]) ).
tff(f1143,plain,
vsomeTerm(sK26) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))),
inference(forward_demodulation,[],[f1132,f302]) ).
tff(f1244,plain,
vgetTerm(vsomeTerm(sK26)) = vIszero(vgetTerm(vreduce(vt1))),
inference(superposition,[],[f466,f1143]) ).
tff(f1247,plain,
sK26 = vIszero(vgetTerm(vreduce(vt1))),
inference(forward_demodulation,[],[f1244,f466]) ).
tff(f1453,plain,
( vptchecksimple(vIszero(vgetTerm(vreduce(vt1))),vB)
| ~ visSomeTerm(vreduce(vt1)) ),
inference(superposition,[],[f840,f548]) ).
tff(f1471,plain,
vptchecksimple(vIszero(vgetTerm(vreduce(vt1))),vB),
inference(forward_subsumption_resolution,[],[f1453,f306]) ).
tff(f1474,plain,
vptchecksimple(sK26,vB),
inference(forward_demodulation,[],[f1471,f1247]) ).
tff(f1476,plain,
$false,
inference(forward_subsumption_resolution,[],[f1474,f554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM220_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n009.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Mon Sep 28 22:02:15 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running first-order theorem proving
% 0.11/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.01/1.34 % (3539090)Detected formulas, will run a generic FOF schedule.
% 6.01/1.34 % (3539183)dis-21_1_sil=8000:lcm=predicate:random_seed=1951745803: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)
% 6.01/1.34 % (3539182)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1892947923:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.01/1.34 % (3539178)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=3389350159:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.01/1.34 % (3539181)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2092629229:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.01/1.34 % (3539177)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=2966667468:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.01/1.34 % (3539181)Refutation not found, incomplete strategy
% 6.01/1.34 % (3539181)------------------------------
% 6.01/1.34 % (3539181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539181)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539181)Termination reason: Refutation not found, incomplete strategy
% 6.01/1.34 % (3539181)Time elapsed: 0.003 s
% 6.01/1.34 % (3539181)Peak memory usage: 88 MB
% 6.01/1.34 % (3539181)Instructions burned: 1 (million)
% 6.01/1.34 % (3539183)Instruction limit reached!
% 6.01/1.34 % (3539183)------------------------------
% 6.01/1.34 % (3539183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539183)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539183)Termination reason: Instruction limit
% 6.01/1.34 % (3539183)Termination phase: Saturation
% 6.01/1.34 % (3539183)Time elapsed: 0.042 s
% 6.01/1.34 % (3539183)Peak memory usage: 91 MB
% 6.01/1.34 % (3539183)Instructions burned: 131 (million)
% 6.01/1.34 % (3539176)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=163601892:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.01/1.34 % (3539179)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=731211338:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.01/1.34 % (3539179)Refutation not found, incomplete strategy
% 6.01/1.34 % (3539179)------------------------------
% 6.01/1.34 % (3539179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539179)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539179)Termination reason: Refutation not found, incomplete strategy
% 6.01/1.34 % (3539179)Time elapsed: 0.002 s
% 6.01/1.34 % (3539179)Peak memory usage: 88 MB
% 6.01/1.34 % (3539179)Instructions burned: 2 (million)
% 6.01/1.34 % (3539182)Instruction limit reached!
% 6.01/1.34 % (3539182)------------------------------
% 6.01/1.34 % (3539182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539182)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539182)Termination reason: Instruction limit
% 6.01/1.34 % (3539182)Termination phase: Saturation
% 6.01/1.34 % (3539182)Time elapsed: 0.088 s
% 6.01/1.34 % (3539182)Peak memory usage: 90 MB
% 6.01/1.34 % (3539182)Instructions burned: 140 (million)
% 6.01/1.34 % (3539219)lrs+10_1_sil=8000:sp=occurrence:random_seed=343200853:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.01/1.34 % (3539219)Refutation not found, incomplete strategy
% 6.01/1.34 % (3539219)------------------------------
% 6.01/1.34 % (3539219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539219)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539219)Termination reason: Refutation not found, incomplete strategy
% 6.01/1.34 % (3539219)Time elapsed: 0.002 s
% 6.01/1.34 % (3539219)Peak memory usage: 88 MB
% 6.01/1.34 % (3539219)Instructions burned: 2 (million)
% 6.01/1.34 % (3539228)lrs+10_1_sil=32000:urr=on:br=off:random_seed=599364636:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.01/1.34 % (3539181)------------------------------
% 6.01/1.34 % (3539181)------------------------------
% 6.01/1.34 % (3539219)------------------------------
% 6.01/1.34 % (3539219)------------------------------
% 6.01/1.34 % (3539179)------------------------------
% 6.01/1.34 % (3539179)------------------------------
% 6.01/1.34 % (3539228)Instruction limit reached!
% 6.01/1.34 % (3539228)------------------------------
% 6.01/1.34 % (3539228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539228)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539228)Termination reason: Instruction limit
% 6.01/1.34 % (3539228)Termination phase: Saturation
% 6.01/1.34 % (3539228)Time elapsed: 0.083 s
% 6.01/1.34 % (3539228)Peak memory usage: 89 MB
% 6.01/1.34 % (3539228)Instructions burned: 157 (million)
% 6.01/1.34 % (3539305)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=520609378:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.01/1.34 % (3539295)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1657515094:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.01/1.34 % (3539313)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=610649752:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.01/1.34 % (3539295)First to succeed.
% 6.01/1.34 % (3539295)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3539090"
% 6.01/1.34 % (3539305)Instruction limit reached!
% 6.01/1.34 % (3539305)------------------------------
% 6.01/1.34 % (3539305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539305)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539305)Termination reason: Instruction limit
% 6.01/1.34 % (3539305)Termination phase: Saturation
% 6.01/1.34 % (3539305)Time elapsed: 0.074 s
% 6.01/1.34 % (3539305)Peak memory usage: 91 MB
% 6.01/1.34 % (3539305)Instructions burned: 249 (million)
% 6.01/1.34 % (3539325)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1783067478:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.01/1.34 % (3539343)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4098279902:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.01/1.34 % (3539313)Instruction limit reached!
% 6.01/1.34 % (3539313)------------------------------
% 6.01/1.34 % (3539313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539313)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539313)Termination reason: Instruction limit
% 6.01/1.34 % (3539313)Termination phase: Saturation
% 6.01/1.34 % (3539313)Time elapsed: 0.158 s
% 6.01/1.34 % (3539313)Peak memory usage: 89 MB
% 6.01/1.34 % (3539313)Instructions burned: 296 (million)
% 6.01/1.34 % (3539343)Instruction limit reached!
% 6.01/1.34 % (3539343)------------------------------
% 6.01/1.34 % (3539343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.34 % (3539343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.34 % (3539343)CaDiCaL version: 2.1.3
% 6.01/1.34 % (3539343)Termination reason: Instruction limit
% 6.01/1.34 % (3539343)Termination phase: Saturation
% 6.01/1.34 % (3539343)Time elapsed: 0.037 s
% 6.01/1.34 % (3539343)Peak memory usage: 91 MB
% 6.01/1.34 % (3539343)Instructions burned: 114 (million)
% 6.01/1.34 % (3539295)Refutation found. Thanks to Tanya!
% 6.01/1.34 % SZS status Theorem for theBenchmark
% 6.01/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 6.57/1.53 % (3539295)------------------------------
% 6.57/1.53 % (3539295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.53 % (3539295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.53 % (3539295)CaDiCaL version: 2.1.3
% 6.57/1.53 % (3539295)Termination reason: Refutation
% 6.57/1.53 % (3539295)Time elapsed: 0.047 s
% 6.57/1.53 % (3539295)Peak memory usage: 90 MB
% 6.57/1.53 % (3539295)Instructions burned: 84 (million)
% 6.57/1.53 % (3539295)------------------------------
% 6.57/1.53 % (3539295)------------------------------
% 6.57/1.53 % (3539090)Success in time 0.883 s
% 6.57/1.53 % Vampire exiting
%------------------------------------------------------------------------------