%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM219_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 : n002.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 3.36s 1.34s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 20 unt; 0 typ; 8 def)
% Number of atoms : 213 ( 44 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 243 ( 98 ~; 100 |; 33 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 40 ( 38 usr; 7 prp; 0-3 aty)
% Number of functors : 116 ( 116 usr; 10 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn 53 !; 6 ?; 59 :)
% 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: vTerm ).
tff(func_def_114,type,
sK123: vTy ).
tff(func_def_115,type,
sK124: 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(pred_def_30,type,
sQ125_eqProxy: ( vTerm * vTerm ) > $o ).
tff(pred_def_31,type,
sQ126_eqProxy: ( vOptTerm * vOptTerm ) > $o ).
tff(pred_def_32,type,
sQ127_eqProxy: ( vTy * vTy ) > $o ).
tff(f106,axiom,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( visSomeTerm(vreduce(vSucc(X0)))
& ~ visNV(X0)
& ( vt1 != vZero )
& ( vt1 = vSucc(X0) )
& vptchecksimple(vIszero(vt1),X1)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X2) ) )
=> vptchecksimple(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-Succ-isNV-False-isSomeTerm-True') ).
tff(f107,axiom,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ~ visSomeTerm(vreduce(vSucc(X0)))
& ~ visNV(X0)
& ( vt1 != vZero )
& ( vt1 = vSucc(X0) )
& vptchecksimple(vIszero(vt1),X1)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X2) ) )
=> vptchecksimple(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-Succ-isNV-False-isSomeTerm-False') ).
tff(f108,conjecture,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ~ visNV(X0)
& ( vt1 != vZero )
& ( vt1 = vSucc(X0) )
& vptchecksimple(vIszero(vt1),X1)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X2) ) )
=> vptchecksimple(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Iszero-Succ-isNV-False') ).
tff(f109,negated_conjecture,
~ ! [X0: vTerm,X1: vTy,X2: vTerm] :
( ( ~ visNV(X0)
& ( vt1 != vZero )
& ( vt1 = vSucc(X0) )
& vptchecksimple(vIszero(vt1),X1)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X2) ) )
=> vptchecksimple(X2,X1) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f191,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( vptchecksimple(X2,X1)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| ( vZero = vt1 )
| ( vSucc(X0) != vt1 )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vreduce(vIszero(vt1)) != vsomeTerm(X2) ) ),
inference(ennf_transformation,[],[f106]) ).
tff(f192,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( vptchecksimple(X2,X1)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| ( vZero = vt1 )
| ( vSucc(X0) != vt1 )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vreduce(vIszero(vt1)) != vsomeTerm(X2) ) ),
inference(flattening,[],[f191]) ).
tff(f193,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( vptchecksimple(X2,X1)
| visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| ( vZero = vt1 )
| ( vSucc(X0) != vt1 )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vreduce(vIszero(vt1)) != vsomeTerm(X2) ) ),
inference(ennf_transformation,[],[f107]) ).
tff(f194,plain,
! [X0: vTerm,X1: vTy,X2: vTerm] :
( vptchecksimple(X2,X1)
| visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| ( vZero = vt1 )
| ( vSucc(X0) != vt1 )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vreduce(vIszero(vt1)) != vsomeTerm(X2) ) ),
inference(flattening,[],[f193]) ).
tff(f195,plain,
? [X0: vTerm,X1: vTy,X2: vTerm] :
( ~ vptchecksimple(X2,X1)
& ~ visNV(X0)
& ( vt1 != vZero )
& ( vt1 = vSucc(X0) )
& vptchecksimple(vIszero(vt1),X1)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X2) ) ),
inference(ennf_transformation,[],[f109]) ).
tff(f196,plain,
? [X0: vTerm,X1: vTy,X2: vTerm] :
( ~ vptchecksimple(X2,X1)
& ~ visNV(X0)
& ( vt1 != vZero )
& ( vt1 = vSucc(X0) )
& vptchecksimple(vIszero(vt1),X1)
& ( vreduce(vIszero(vt1)) = vsomeTerm(X2) ) ),
inference(flattening,[],[f195]) ).
tff(f319,plain,
( ~ vptchecksimple(sK124,sK123)
& ~ visNV(sK122)
& ( vt1 != vZero )
& ( vt1 = vSucc(sK122) )
& vptchecksimple(vIszero(vt1),sK123)
& ( vreduce(vIszero(vt1)) = vsomeTerm(sK124) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123,sK124]),skolemize(X0,sK122),skolemize(X1,sK123),skolemize(X2,sK124)],[f196]) ).
tff(f580,plain,
! [X2: vTerm,X0: vTerm,X1: vTy] :
( vptchecksimple(X2,X1)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| ( vZero = vt1 )
| ( vSucc(X0) != vt1 )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vreduce(vIszero(vt1)) != vsomeTerm(X2) ) ),
inference(cnf_transformation,[],[f192]) ).
tff(f581,plain,
! [X2: vTerm,X0: vTerm,X1: vTy] :
( vptchecksimple(X2,X1)
| visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| ( vZero = vt1 )
| ( vSucc(X0) != vt1 )
| ~ vptchecksimple(vIszero(vt1),X1)
| ( vreduce(vIszero(vt1)) != vsomeTerm(X2) ) ),
inference(cnf_transformation,[],[f194]) ).
tff(f582,plain,
vreduce(vIszero(vt1)) = vsomeTerm(sK124),
inference(cnf_transformation,[],[f319]) ).
tff(f583,plain,
vptchecksimple(vIszero(vt1),sK123),
inference(cnf_transformation,[],[f319]) ).
tff(f584,plain,
vt1 = vSucc(sK122),
inference(cnf_transformation,[],[f319]) ).
tff(f585,plain,
vZero != vt1,
inference(cnf_transformation,[],[f319]) ).
tff(f586,plain,
~ visNV(sK122),
inference(cnf_transformation,[],[f319]) ).
tff(f587,plain,
~ vptchecksimple(sK124,sK123),
inference(cnf_transformation,[],[f319]) ).
tff(f596,definition,
! [X0: vTerm,X1: vTerm] :
( sQ125_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ125_eqProxy])],[equality_proxy_definition]) ).
tff(f634,definition,
! [X0: vOptTerm,X1: vOptTerm] :
( sQ126_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ126_eqProxy])],[equality_proxy_definition]) ).
tff(f805,plain,
! [X2: vTerm,X0: vTerm,X1: vTy] :
( vptchecksimple(X2,X1)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| sQ125_eqProxy(vZero,vt1)
| ~ sQ125_eqProxy(vSucc(X0),vt1)
| ~ vptchecksimple(vIszero(vt1),X1)
| ~ sQ126_eqProxy(vreduce(vIszero(vt1)),vsomeTerm(X2)) ),
inference(equality_proxy_replacement,[],[f580,f596,f596,f634]) ).
tff(f806,plain,
! [X2: vTerm,X0: vTerm,X1: vTy] :
( vptchecksimple(X2,X1)
| visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0)
| sQ125_eqProxy(vZero,vt1)
| ~ sQ125_eqProxy(vSucc(X0),vt1)
| ~ vptchecksimple(vIszero(vt1),X1)
| ~ sQ126_eqProxy(vreduce(vIszero(vt1)),vsomeTerm(X2)) ),
inference(equality_proxy_replacement,[],[f581,f596,f596,f634]) ).
tff(f807,plain,
~ sQ125_eqProxy(vZero,vt1),
inference(equality_proxy_replacement,[],[f585,f596]) ).
tff(f808,plain,
sQ125_eqProxy(vt1,vSucc(sK122)),
inference(equality_proxy_replacement,[],[f584,f596]) ).
tff(f809,plain,
sQ126_eqProxy(vreduce(vIszero(vt1)),vsomeTerm(sK124)),
inference(equality_proxy_replacement,[],[f582,f634]) ).
tff(f813,plain,
! [X0: vTerm,X1: vTerm] :
( sQ125_eqProxy(X1,X0)
| ~ sQ125_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f596]) ).
tff(f817,definition,
( spl128_1
<=> sQ125_eqProxy(vZero,vt1) ),
introduced(definition,[new_symbols(definition,[spl128_1])],[avatar_definition]) ).
tff(f818,plain,
( sQ125_eqProxy(vZero,vt1)
| ~ spl128_1 ),
inference(avatar_component_clause,[],[f817]) ).
tff(f820,definition,
( spl128_2
<=> ! [X0: vTerm] :
( visSomeTerm(vreduce(vSucc(X0)))
| ~ sQ125_eqProxy(vSucc(X0),vt1)
| visNV(X0) ) ),
introduced(definition,[new_symbols(definition,[spl128_2])],[avatar_definition]) ).
tff(f821,plain,
( ! [X0: vTerm] :
( ~ sQ125_eqProxy(vSucc(X0),vt1)
| visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0) )
| ~ spl128_2 ),
inference(avatar_component_clause,[],[f820]) ).
tff(f823,definition,
( spl128_3
<=> ! [X2: vTerm,X1: vTy] :
( vptchecksimple(X2,X1)
| ~ sQ126_eqProxy(vreduce(vIszero(vt1)),vsomeTerm(X2))
| ~ vptchecksimple(vIszero(vt1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl128_3])],[avatar_definition]) ).
tff(f824,plain,
( ! [X2: vTerm,X1: vTy] :
( ~ sQ126_eqProxy(vreduce(vIszero(vt1)),vsomeTerm(X2))
| vptchecksimple(X2,X1)
| ~ vptchecksimple(vIszero(vt1),X1) )
| ~ spl128_3 ),
inference(avatar_component_clause,[],[f823]) ).
tff(f825,plain,
( spl128_1
| spl128_2
| spl128_3 ),
inference(avatar_split_clause,[],[f806,f823,f820,f817]) ).
tff(f827,definition,
( spl128_4
<=> ! [X0: vTerm] :
( ~ visSomeTerm(vreduce(vSucc(X0)))
| ~ sQ125_eqProxy(vSucc(X0),vt1)
| visNV(X0) ) ),
introduced(definition,[new_symbols(definition,[spl128_4])],[avatar_definition]) ).
tff(f828,plain,
( ! [X0: vTerm] :
( ~ sQ125_eqProxy(vSucc(X0),vt1)
| ~ visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0) )
| ~ spl128_4 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f829,plain,
( spl128_1
| spl128_4
| spl128_3 ),
inference(avatar_split_clause,[],[f805,f823,f827,f817]) ).
tff(f830,plain,
( ! [X0: vTy] :
( ~ vptchecksimple(vIszero(vt1),X0)
| vptchecksimple(sK124,X0) )
| ~ spl128_3 ),
inference(resolution,[],[f809,f824]) ).
tff(f831,plain,
( vptchecksimple(sK124,sK123)
| ~ spl128_3 ),
inference(resolution,[],[f830,f583]) ).
tff(f832,plain,
( $false
| ~ spl128_3 ),
inference(resolution,[],[f831,f587]) ).
tff(f833,plain,
~ spl128_3,
inference(avatar_contradiction_clause,[],[f832]) ).
tff(f834,plain,
( $false
| ~ spl128_1 ),
inference(resolution,[],[f818,f807]) ).
tff(f835,plain,
~ spl128_1,
inference(avatar_contradiction_clause,[],[f834]) ).
tff(f868,plain,
( ! [X0: vTerm] :
( ~ sQ125_eqProxy(vt1,vSucc(X0))
| ~ visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0) )
| ~ spl128_4 ),
inference(resolution,[],[f813,f828]) ).
tff(f869,plain,
( ! [X0: vTerm] :
( ~ sQ125_eqProxy(vt1,vSucc(X0))
| visSomeTerm(vreduce(vSucc(X0)))
| visNV(X0) )
| ~ spl128_2 ),
inference(resolution,[],[f813,f821]) ).
tff(f880,plain,
( ~ visSomeTerm(vreduce(vSucc(sK122)))
| visNV(sK122)
| ~ spl128_4 ),
inference(resolution,[],[f868,f808]) ).
tff(f883,definition,
( spl128_5
<=> visNV(sK122) ),
introduced(definition,[new_symbols(definition,[spl128_5])],[avatar_definition]) ).
tff(f884,plain,
( visNV(sK122)
| ~ spl128_5 ),
inference(avatar_component_clause,[],[f883]) ).
tff(f886,definition,
( spl128_6
<=> visSomeTerm(vreduce(vSucc(sK122))) ),
introduced(definition,[new_symbols(definition,[spl128_6])],[avatar_definition]) ).
tff(f888,plain,
( spl128_5
| ~ spl128_6
| ~ spl128_4 ),
inference(avatar_split_clause,[],[f880,f827,f886,f883]) ).
tff(f889,plain,
( visSomeTerm(vreduce(vSucc(sK122)))
| visNV(sK122)
| ~ spl128_2 ),
inference(resolution,[],[f869,f808]) ).
tff(f892,plain,
( spl128_5
| spl128_6
| ~ spl128_2 ),
inference(avatar_split_clause,[],[f889,f820,f886,f883]) ).
tff(f893,plain,
( $false
| ~ spl128_5 ),
inference(resolution,[],[f884,f586]) ).
tff(f894,plain,
~ spl128_5,
inference(avatar_contradiction_clause,[],[f893]) ).
cnf(s1,plain,
( spl128_1
| spl128_2
| spl128_3 ),
inference(sat_conversion,[],[f825]) ).
cnf(s2,plain,
( spl128_1
| spl128_3
| spl128_4 ),
inference(sat_conversion,[],[f829]) ).
cnf(s3,plain,
~ spl128_3,
inference(sat_conversion,[],[f833]) ).
cnf(s4,plain,
~ spl128_1,
inference(sat_conversion,[],[f835]) ).
cnf(s5,plain,
( ~ spl128_4
| spl128_5
| ~ spl128_6 ),
inference(sat_conversion,[],[f888]) ).
cnf(s6,plain,
( ~ spl128_2
| spl128_5
| spl128_6 ),
inference(sat_conversion,[],[f892]) ).
cnf(s7,plain,
~ spl128_5,
inference(sat_conversion,[],[f894]) ).
cnf(s8,plain,
( ~ spl128_2
| spl128_6 ),
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
( ~ spl128_4
| ~ spl128_6 ),
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
spl128_4,
inference(rat,[],[s2,s3,s4]) ).
cnf(s11,plain,
~ spl128_6,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
~ spl128_2,
inference(rat,[],[s8,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s3,s12,s4]) ).
tff(f895,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM219_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n002.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Mon Sep 28 22:04:37 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running first-order theorem proving
% 0.25/0.29 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
% 3.36/1.34 % (821986)Detected formulas, will run a generic FOF schedule.
% 3.36/1.34 % (821998)dis-21_1_sil=8000:lcm=predicate:random_seed=437846879: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)
% 3.36/1.34 % (821998)First to succeed.
% 3.36/1.34 % (821998)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-821986"
% 3.36/1.34 % (821993)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=686033800:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.36/1.34 % (821994)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=3090544148:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.36/1.34 % (821992)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=1902924628:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.36/1.34 % (821995)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2072830489:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.36/1.34 % (821996)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2115161401:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.36/1.34 % (821997)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1538946904:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.36/1.34 % (821995)Also succeeded, but the first one will report.
% 3.36/1.34 % (821996)Also succeeded, but the first one will report.
% 3.36/1.34 % (821997)Also succeeded, but the first one will report.
% 3.36/1.34 % (821998)Refutation found. Thanks to Tanya!
% 3.36/1.34 % SZS status Theorem for theBenchmark
% 3.36/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.84/1.54 % (821998)------------------------------
% 3.84/1.54 % (821998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.84/1.54 % (821998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.54 % (821998)CaDiCaL version: 2.1.3
% 3.84/1.54 % (821998)Termination reason: Refutation
% 3.84/1.54 % (821998)Time elapsed: 0.011 s
% 3.84/1.54 % (821998)Peak memory usage: 90 MB
% 3.84/1.54 % (821998)Instructions burned: 18 (million)
% 3.84/1.54 % (821998)------------------------------
% 3.84/1.54 % (821998)------------------------------
% 3.84/1.54 % (821986)Success in time 0.415 s
% 3.84/1.54 % Vampire exiting
%------------------------------------------------------------------------------