%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n014.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 09:40:31 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 25 unt; 0 typ; 3 def)
% Number of atoms : 166 ( 69 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 150 ( 61 ~; 52 |; 26 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 34 ( 32 usr; 4 prp; 0-3 aty)
% Number of functors : 115 ( 115 usr; 9 con; 0-3 aty)
% Number of variables : 55 ( 0 sgn 47 !; 8 ?; 55 :)
% 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: vTerm > vTerm ).
tff(func_def_17,type,
sK26: vTerm > 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 > vTerm ).
tff(func_def_22,type,
sK31: vTerm > vTerm ).
tff(func_def_23,type,
sK32: vTerm > vTerm ).
tff(func_def_24,type,
sK33: vOptTerm > vTerm ).
tff(func_def_25,type,
sK34: vTerm > vTerm ).
tff(func_def_26,type,
sK35: vTerm > vTerm ).
tff(func_def_27,type,
sK36: vTerm > vTerm ).
tff(func_def_28,type,
sK37: vTerm > vTerm ).
tff(func_def_29,type,
sK38: vTerm > vTerm ).
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(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(f38,axiom,
! [X0: vTy] :
( ( X0 = vB )
| ( X0 = vNat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-Ty') ).
tff(f39,axiom,
vB != vNat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-B-Nat') ).
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(f127,plain,
! [X0: vOptTerm] :
( ? [X1: vTerm] : ( X0 = vsomeTerm(X1) )
| ~ visSomeTerm(X0) ),
inference(ennf_transformation,[],[f53]) ).
tff(f151,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(f152,plain,
! [X0: vTerm] :
( ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) )
| ( vZero = X0 )
| ? [X1: vTerm] : ( vSucc(X1) = X0 )
| ~ visSomeTerm(vreduce(X0)) ),
inference(flattening,[],[f151]) ).
tff(f179,plain,
! [X0: vTerm] :
( vptchecksimple(vIszero(X0),vB)
| ~ vptchecksimple(X0,vNat) ),
inference(ennf_transformation,[],[f98]) ).
tff(f180,plain,
! [X0: vTerm] :
( vptchecksimple(X0,vNat)
| ~ vptchecksimple(vIszero(X0),vB) ),
inference(ennf_transformation,[],[f99]) ).
tff(f181,plain,
! [X0: vTerm,X1: vTy] :
( ( X1 = vB )
| ~ vptchecksimple(vIszero(X0),X1) ),
inference(ennf_transformation,[],[f100]) ).
tff(f187,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| ~ vptchecksimple(vt1,X0)
| ( vsomeTerm(X1) != vreduce(vt1) ) ),
inference(ennf_transformation,[],[f105]) ).
tff(f188,plain,
! [X0: vTy,X1: vTerm] :
( vptchecksimple(X1,X0)
| ~ vptchecksimple(vt1,X0)
| ( vsomeTerm(X1) != vreduce(vt1) ) ),
inference(flattening,[],[f187]) ).
tff(f189,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(f190,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,[],[f189]) ).
tff(f229,plain,
! [X0: vOptTerm] :
( ( vsomeTerm(sK40(X0)) = X0 )
| ~ visSomeTerm(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X1,sK40(X0))],[f127]) ).
tff(f248,plain,
! [X0: vTerm] :
( ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) )
| ( vZero = X0 )
| ( vSucc(sK57(X0)) = X0 )
| ~ visSomeTerm(vreduce(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(X1,sK57(X0))],[f152]) ).
tff(f313,plain,
( ~ vptchecksimple(sK123,sK122)
& visSomeTerm(vreduce(vt1))
& ( vt1 != vZero )
& ! [X2: vTerm] : ( vt1 != vSucc(X2) )
& vptchecksimple(vIszero(vt1),sK122)
& ( vreduce(vIszero(vt1)) = vsomeTerm(sK123) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123]),skolemize(X0,sK122),skolemize(X1,sK123)],[f190]) ).
tff(f354,plain,
! [X0: vTy] :
( ( vB = X0 )
| ( vNat = X0 ) ),
inference(cnf_transformation,[],[f38]) ).
tff(f355,plain,
vB != vNat,
inference(cnf_transformation,[],[f39]) ).
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))
| ( vZero = X0 )
| ( vSucc(sK57(X0)) = X0 )
| ( vreduce(vIszero(X0)) = vsomeTerm(vIszero(vgetTerm(vreduce(X0)))) ) ),
inference(cnf_transformation,[],[f248]) ).
tff(f566,plain,
! [X0: vTerm] :
( vptchecksimple(vIszero(X0),vB)
| ~ vptchecksimple(X0,vNat) ),
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]) ).
tff(f603,plain,
( ~ vptchecksimple(sK123,vB)
| ( vNat = sK122 ) ),
inference(superposition,[],[f579,f354]) ).
tff(f606,definition,
( spl124_1
<=> ( vNat = sK122 ) ),
introduced(definition,[new_symbols(definition,[spl124_1])],[avatar_definition]) ).
tff(f608,plain,
( ( vNat = sK122 )
| ~ spl124_1 ),
inference(avatar_component_clause,[],[f606]) ).
tff(f610,definition,
( spl124_2
<=> vptchecksimple(sK123,vB) ),
introduced(definition,[new_symbols(definition,[spl124_2])],[avatar_definition]) ).
tff(f612,plain,
( ~ vptchecksimple(sK123,vB)
| spl124_2 ),
inference(avatar_component_clause,[],[f610]) ).
tff(f613,plain,
( spl124_1
| ~ spl124_2 ),
inference(avatar_split_clause,[],[f603,f610,f606]) ).
tff(f615,definition,
( spl124_3
<=> vptchecksimple(vIszero(vt1),vB) ),
introduced(definition,[new_symbols(definition,[spl124_3])],[avatar_definition]) ).
tff(f617,plain,
( vptchecksimple(vIszero(vt1),vB)
| ~ spl124_3 ),
inference(avatar_component_clause,[],[f615]) ).
tff(f624,plain,
vreduce(vt1) = vsomeTerm(sK40(vreduce(vt1))),
inference(resolution,[],[f383,f578]) ).
tff(f633,plain,
sK40(vreduce(vt1)) = vgetTerm(vreduce(vt1)),
inference(superposition,[],[f356,f624]) ).
tff(f644,plain,
( vptchecksimple(vt1,vNat)
| ~ spl124_3 ),
inference(resolution,[],[f567,f617]) ).
tff(f649,plain,
vB = sK122,
inference(resolution,[],[f568,f575]) ).
tff(f653,plain,
vptchecksimple(vIszero(vt1),vB),
inference(superposition,[],[f575,f649]) ).
tff(f1138,plain,
! [X0: vTy] :
( ( vreduce(vt1) != vreduce(vt1) )
| ~ vptchecksimple(vt1,X0)
| vptchecksimple(sK40(vreduce(vt1)),X0) ),
inference(superposition,[],[f573,f624]) ).
tff(f1145,plain,
! [X0: vTy] :
( ~ vptchecksimple(vt1,X0)
| vptchecksimple(sK40(vreduce(vt1)),X0) ),
inference(trivial_inequality_removal,[],[f1138]) ).
tff(f1147,plain,
! [X0: vTy] :
( vptchecksimple(vgetTerm(vreduce(vt1)),X0)
| ~ vptchecksimple(vt1,X0) ),
inference(forward_demodulation,[],[f1145,f633]) ).
tff(f1744,plain,
( ( vZero = vt1 )
| ( vt1 = vSucc(sK57(vt1)) )
| ( vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))) ) ),
inference(resolution,[],[f425,f578]) ).
tff(f1774,plain,
( ( vt1 = vSucc(sK57(vt1)) )
| ( vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))) ) ),
inference(forward_subsumption_resolution,[],[f1744,f577]) ).
tff(f1784,plain,
vreduce(vIszero(vt1)) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))),
inference(forward_subsumption_resolution,[],[f1774,f576]) ).
tff(f1798,plain,
vsomeTerm(sK123) = vsomeTerm(vIszero(vgetTerm(vreduce(vt1)))),
inference(forward_demodulation,[],[f1784,f574]) ).
tff(f1965,plain,
spl124_3,
inference(avatar_split_clause,[],[f653,f615]) ).
tff(f1972,plain,
( ( vB = vNat )
| ~ spl124_1 ),
inference(superposition,[],[f608,f649]) ).
tff(f1983,plain,
( $false
| ~ spl124_1 ),
inference(forward_subsumption_resolution,[],[f1972,f355]) ).
tff(f1984,plain,
~ spl124_1,
inference(avatar_contradiction_clause,[],[f1983]) ).
tff(f2082,plain,
vgetTerm(vsomeTerm(sK123)) = vIszero(vgetTerm(vreduce(vt1))),
inference(superposition,[],[f356,f1798]) ).
tff(f2104,plain,
sK123 = vIszero(vgetTerm(vreduce(vt1))),
inference(forward_demodulation,[],[f2082,f356]) ).
tff(f2149,plain,
( vptchecksimple(sK123,vB)
| ~ vptchecksimple(vgetTerm(vreduce(vt1)),vNat) ),
inference(superposition,[],[f566,f2104]) ).
tff(f2152,plain,
( ~ vptchecksimple(vgetTerm(vreduce(vt1)),vNat)
| spl124_2 ),
inference(forward_subsumption_resolution,[],[f2149,f612]) ).
tff(f2494,plain,
( ~ vptchecksimple(vt1,vNat)
| spl124_2 ),
inference(resolution,[],[f2152,f1147]) ).
tff(f2497,plain,
( $false
| spl124_2
| ~ spl124_3 ),
inference(forward_subsumption_resolution,[],[f2494,f644]) ).
tff(f2498,plain,
( spl124_2
| ~ spl124_3 ),
inference(avatar_contradiction_clause,[],[f2497]) ).
cnf(s1,plain,
( spl124_1
| ~ spl124_2 ),
inference(sat_conversion,[],[f613]) ).
cnf(s66,plain,
spl124_3,
inference(sat_conversion,[],[f1965]) ).
cnf(s68,plain,
~ spl124_1,
inference(sat_conversion,[],[f1984]) ).
cnf(s100,plain,
( spl124_2
| ~ spl124_3 ),
inference(sat_conversion,[],[f2498]) ).
cnf(s107,plain,
spl124_2,
inference(rat,[],[s100,s66]) ).
cnf(s128,plain,
$false,
inference(rat,[],[s1,s107,s68]) ).
tff(f2499,plain,
$false,
inference(avatar_sat_refutation,[],[s128]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 22:02:01 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.32 % (2227589)Will run a generic schedule for satisfiability detection.
% 0.22/0.32 % (2227605)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=554173215:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.32 % (2227601)% WARNING: option uhcvi not known.
% 0.22/0.32 % (2227604)dis+10_1_sil=32000:sp=arity:random_seed=3108347957:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.32 % (2227602)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2399999953:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.32 % (2227600)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3630299419_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.32 % (2227606)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1190242709:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.32 % (2227601)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4071277780:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.32 % (2227607)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4000633707:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.33 % (2227605)Instruction limit reached!
% 0.22/0.33 % (2227605)------------------------------
% 0.22/0.33 % (2227605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2227605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2227605)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2227605)Termination reason: Instruction limit
% 0.22/0.33 % (2227605)Termination phase: Saturation
% 0.22/0.33 % (2227605)Time elapsed: 0.029 s
% 0.22/0.33 % (2227605)Peak memory usage: 12 MB
% 0.22/0.33 % (2227605)Instructions burned: 118 (million)
% 0.22/0.33 % Detected minimum model sizes of [1,3,1]
% 0.22/0.33 % Detected maximum model sizes of [3,max,max]
% 0.22/0.33 % TRYING [1,3,1]
% 0.22/0.33 % (2227631)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3336392372:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.33 % TRYING [1,3,2]
% 0.22/0.33 % TRYING [1]
% 0.22/0.33 % TRYING [2]
% 0.22/0.33 % TRYING [3]
% 0.22/0.33 % (2227604) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2227589-2227604"...
% 0.22/0.33 % (2227604)...printing done.
% 0.22/0.33 % (2227604)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.33 % (2227604)------------------------------
% 0.22/0.33 % (2227604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2227604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2227604)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2227604)Termination reason: Refutation
% 0.22/0.33 % (2227604)Time elapsed: 0.057 s
% 0.22/0.33 % (2227604)Peak memory usage: 13 MB
% 0.22/0.33 % (2227604)Instructions burned: 95 (million)
% 0.22/0.33 % (2227589)Success in time 0.085 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------