%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO620-1 : TPTP v9.3.1. Released v7.1.0.
% 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 02:28:27 PM UTC 2026
% Result : Unsatisfiable 3.97s 1.25s
% Output : Refutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 138 ( 16 unt; 4 def)
% Number of atoms : 437 ( 0 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 569 ( 270 ~; 295 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 188 ( 0 sgn 188 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : le(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ le(max(X0,X1),X2)
| le(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ le(max(X0,X1),X2)
| le(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(f4,axiom,
! [X0] :
( eq(f(X0),a3)
| eq(f(X0),a1)
| eq(f(X0),a2)
| eq(f(X0),a0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f5,axiom,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(f6,axiom,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(f7,axiom,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f8,axiom,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a3)
| ~ eq(f(X0),a3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f9,plain,
! [X0,X1] : le(X0,max(X0,X1)),
inference(resolution,[],[f2,f1]) ).
fof(f11,plain,
! [X0,X1] : le(X0,max(X1,X0)),
inference(resolution,[],[f3,f1]) ).
fof(f12,plain,
! [X2,X0,X1] : le(X0,max(max(X1,X0),X2)),
inference(resolution,[],[f3,f9]) ).
fof(f13,plain,
! [X2,X0,X1] : le(X0,max(X1,max(X2,X0))),
inference(resolution,[],[f11,f3]) ).
fof(f14,plain,
! [X2,X0,X1] : le(X0,max(X1,max(X0,X2))),
inference(resolution,[],[f11,f2]) ).
fof(f17,plain,
! [X0,X1] :
( ~ eq(f(max(X0,s(X1))),a0)
| ~ eq(f(X1),a0) ),
inference(resolution,[],[f5,f11]) ).
fof(f21,plain,
! [X0] :
( ~ eq(f(s(X0)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[],[f6,f1]) ).
fof(f22,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[],[f6,f9]) ).
fof(f23,plain,
! [X0,X1] :
( ~ eq(f(max(X0,s(X1))),a1)
| ~ eq(f(X1),a1) ),
inference(resolution,[],[f6,f11]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : le(X0,max(max(X1,max(X0,X2)),X3)),
inference(resolution,[],[f12,f2]) ).
fof(f29,plain,
! [X0] :
( ~ eq(f(s(X0)),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[],[f7,f1]) ).
fof(f30,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[],[f7,f9]) ).
fof(f31,plain,
! [X0,X1] :
( ~ eq(f(max(X0,s(X1))),a2)
| ~ eq(f(X1),a2) ),
inference(resolution,[],[f7,f11]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ eq(f(max(X0,max(X1,s(X2)))),a2)
| ~ eq(f(X2),a2) ),
inference(resolution,[],[f13,f7]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ eq(f(max(X0,max(X1,s(X2)))),a1)
| ~ eq(f(X2),a1) ),
inference(resolution,[],[f13,f6]) ).
fof(f39,plain,
! [X0] :
( ~ eq(f(s(X0)),a3)
| ~ eq(f(X0),a3) ),
inference(resolution,[],[f8,f1]) ).
fof(f40,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a3)
| ~ eq(f(X0),a3) ),
inference(resolution,[],[f8,f9]) ).
fof(f45,plain,
! [X2,X3,X0,X1] : le(X0,max(X1,max(max(X2,X0),X3))),
inference(resolution,[],[f14,f3]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : le(X0,max(X1,max(max(X0,X2),X3))),
inference(resolution,[],[f14,f2]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ eq(f(max(X0,max(s(X1),X2))),a1)
| ~ eq(f(X1),a1) ),
inference(resolution,[],[f14,f6]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ eq(f(max(X0,max(s(X1),X2))),a0)
| ~ eq(f(X1),a0) ),
inference(resolution,[],[f14,f5]) ).
fof(f51,plain,
! [X0] :
( eq(f(s(X0)),a2)
| eq(f(s(X0)),a1)
| ~ eq(f(X0),a3)
| eq(f(s(X0)),a0) ),
inference(resolution,[],[f39,f4]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X4] : le(X0,max(max(X1,max(max(X0,X2),X3)),X4)),
inference(resolution,[],[f26,f2]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ eq(f(max(X0,max(max(X1,s(X2)),X3))),a1)
| ~ eq(f(X2),a1) ),
inference(resolution,[],[f45,f6]) ).
fof(f94,plain,
! [X0,X1] :
( eq(f(max(s(X0),X1)),a2)
| eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a3)
| eq(f(max(s(X0),X1)),a0) ),
inference(resolution,[],[f40,f4]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( ~ eq(f(max(X0,max(max(s(X1),X2),X3))),a0)
| ~ eq(f(X1),a0) ),
inference(resolution,[],[f46,f5]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( ~ eq(f(max(max(X0,max(max(s(X1),X2),X3)),X4)),a0)
| ~ eq(f(X1),a0) ),
inference(resolution,[],[f71,f5]) ).
fof(f211,plain,
! [X0,X1] :
( eq(f(max(s(X0),s(X1))),a1)
| ~ eq(f(X0),a3)
| eq(f(max(s(X0),s(X1))),a0)
| ~ eq(f(X1),a2) ),
inference(resolution,[],[f94,f31]) ).
fof(f212,plain,
! [X2,X0,X1] :
( eq(f(max(s(X0),max(X1,s(X2)))),a1)
| ~ eq(f(X0),a3)
| eq(f(max(s(X0),max(X1,s(X2)))),a0)
| ~ eq(f(X2),a2) ),
inference(resolution,[],[f94,f36]) ).
fof(f479,plain,
! [X2,X0,X1] :
( eq(f(max(s(X0),max(s(X1),s(X2)))),a0)
| ~ eq(f(X0),a3)
| ~ eq(f(X2),a2)
| ~ eq(f(X1),a1) ),
inference(resolution,[],[f212,f49]) ).
fof(f480,plain,
! [X2,X3,X0,X1] :
( eq(f(max(s(X0),max(max(X1,s(X2)),s(X3)))),a0)
| ~ eq(f(X0),a3)
| ~ eq(f(X3),a2)
| ~ eq(f(X2),a1) ),
inference(resolution,[],[f212,f92]) ).
fof(f1025,definition,
( spl0_1
<=> ! [X1] : ~ eq(f(X1),a0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1026,plain,
( ! [X1] : ~ eq(f(X1),a0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f1068,definition,
( spl0_5
<=> ! [X1] : ~ eq(f(X1),a1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f1069,plain,
( ! [X1] : ~ eq(f(X1),a1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f1077,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),s(X1))),a0)
| ~ eq(f(X0),a3)
| ~ eq(f(X1),a2) )
| ~ spl0_5 ),
inference(resolution,[],[f1069,f211]) ).
fof(f1078,plain,
( ! [X2,X0,X1] :
( eq(f(max(s(X0),max(X1,s(X2)))),a0)
| ~ eq(f(X0),a3)
| ~ eq(f(X2),a2) )
| ~ spl0_5 ),
inference(resolution,[],[f1069,f212]) ).
fof(f1134,definition,
( spl0_7
<=> ! [X1] : ~ eq(f(X1),a2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f1135,plain,
( ! [X1] : ~ eq(f(X1),a2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f1137,definition,
( spl0_8
<=> ! [X0] : ~ eq(f(X0),a3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f1138,plain,
( ! [X0] : ~ eq(f(X0),a3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f1137]) ).
fof(f1148,plain,
( ! [X0] :
( eq(f(s(X0)),a1)
| ~ eq(f(X0),a3)
| eq(f(s(X0)),a0) )
| ~ spl0_7 ),
inference(resolution,[],[f1135,f51]) ).
fof(f1155,plain,
( ! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_8 ),
inference(resolution,[],[f1138,f4]) ).
fof(f1187,plain,
( ! [X0] :
( eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f1155,f1135]) ).
fof(f1219,plain,
( ! [X0] : eq(f(X0),a0)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f1187,f1069]) ).
fof(f1250,plain,
( ! [X0] : ~ eq(f(X0),a0)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f1219,f150]) ).
fof(f1251,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1250,f1137,f1134,f1068,f1025]) ).
fof(f1258,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f1026,f1219]) ).
fof(f1259,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f1258]) ).
fof(f1261,plain,
( ! [X0] :
( eq(f(s(X0)),a0)
| ~ eq(f(X0),a3) )
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f1148,f1069]) ).
fof(f1263,plain,
( ! [X0] : ~ eq(f(X0),a3)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f1261,f1026]) ).
fof(f1264,plain,
( spl0_8
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1263,f1134,f1068,f1025,f1137]) ).
fof(f1268,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a3)
| ~ eq(f(X1),a2) )
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f1077,f1026]) ).
fof(f1269,plain,
( spl0_7
| spl0_8
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f1268,f1068,f1025,f1137,f1134]) ).
fof(f1270,plain,
( ! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_8 ),
inference(resolution,[],[f1138,f4]) ).
fof(f1271,plain,
( ! [X0] :
( eq(f(s(X0)),a1)
| eq(f(s(X0)),a0)
| ~ eq(f(X0),a2) )
| ~ spl0_8 ),
inference(resolution,[],[f1270,f29]) ).
fof(f1272,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a2) )
| ~ spl0_8 ),
inference(resolution,[],[f1270,f30]) ).
fof(f1303,plain,
( ! [X0] :
( eq(f(s(X0)),a0)
| ~ eq(f(X0),a2) )
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f1271,f1069]) ).
fof(f1305,plain,
( ! [X0] : ~ eq(f(X0),a2)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f1303,f1026]) ).
fof(f1306,plain,
( spl0_7
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1305,f1137,f1068,f1025,f1134]) ).
fof(f1332,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a2) )
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f1272,f1069]) ).
fof(f1334,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a2)
| ~ eq(f(X1),a0) )
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f1332,f17]) ).
fof(f1363,plain,
( spl0_1
| spl0_7
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1334,f1137,f1068,f1134,f1025]) ).
fof(f1367,plain,
( ! [X2,X0,X1] :
( ~ eq(f(X0),a3)
| ~ eq(f(X1),a2)
| ~ eq(f(X2),a0) )
| ~ spl0_5 ),
inference(resolution,[],[f1078,f50]) ).
fof(f1380,plain,
( spl0_1
| spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f1367,f1068,f1137,f1134,f1025]) ).
fof(f1383,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a3)
| eq(f(max(s(X0),X1)),a0) )
| ~ spl0_7 ),
inference(resolution,[],[f1135,f94]) ).
fof(f1415,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a3) )
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f1383,f1069]) ).
fof(f1417,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a3)
| ~ eq(f(X1),a0) )
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f1415,f17]) ).
fof(f1446,plain,
( spl0_1
| spl0_8
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1417,f1134,f1068,f1137,f1025]) ).
fof(f1548,plain,
( ! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_8 ),
inference(resolution,[],[f1138,f4]) ).
fof(f1550,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a2) )
| ~ spl0_8 ),
inference(resolution,[],[f1548,f30]) ).
fof(f1584,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),s(X1))),a0)
| ~ eq(f(X0),a2)
| ~ eq(f(X1),a1) )
| ~ spl0_8 ),
inference(resolution,[],[f1550,f23]) ).
fof(f1636,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a2)
| ~ eq(f(X1),a1) )
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f1584,f1026]) ).
fof(f1637,plain,
( spl0_5
| spl0_7
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1636,f1137,f1025,f1134,f1068]) ).
fof(f1683,plain,
( ! [X2,X0,X1] :
( ~ eq(f(X0),a3)
| ~ eq(f(X1),a2)
| ~ eq(f(X2),a1) )
| ~ spl0_1 ),
inference(resolution,[],[f479,f1026]) ).
fof(f1684,plain,
( spl0_5
| spl0_7
| spl0_8
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f1683,f1025,f1137,f1134,f1068]) ).
fof(f1686,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a3)
| eq(f(max(s(X0),X1)),a0) )
| ~ spl0_7 ),
inference(resolution,[],[f1135,f94]) ).
fof(f1695,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),s(X1))),a0)
| ~ eq(f(X0),a3)
| ~ eq(f(X1),a1) )
| ~ spl0_7 ),
inference(resolution,[],[f1686,f23]) ).
fof(f1713,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a3)
| ~ eq(f(X1),a1) )
| ~ spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f1695,f1026]) ).
fof(f1714,plain,
( spl0_5
| spl0_8
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1713,f1134,f1025,f1137,f1068]) ).
fof(f1715,plain,
( ! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_8 ),
inference(resolution,[],[f1138,f4]) ).
fof(f1717,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a2) )
| ~ spl0_8 ),
inference(resolution,[],[f1715,f30]) ).
fof(f1747,plain,
( ! [X0] :
( eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f1715,f1135]) ).
fof(f1750,plain,
( ! [X0] :
( eq(f(s(X0)),a0)
| ~ eq(f(X0),a1) )
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f1747,f21]) ).
fof(f1783,plain,
( ! [X0] : ~ eq(f(X0),a1)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f1750,f1026]) ).
fof(f1784,plain,
( spl0_5
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1783,f1137,f1134,f1025,f1068]) ).
fof(f1789,plain,
( ! [X2,X0,X1] :
( eq(f(max(s(X0),max(X1,s(X2)))),a0)
| ~ eq(f(X0),a2)
| ~ eq(f(X2),a1) )
| ~ spl0_8 ),
inference(resolution,[],[f1717,f37]) ).
fof(f1881,plain,
( ! [X2,X0,X1] :
( ~ eq(f(X0),a2)
| ~ eq(f(X1),a1)
| ~ eq(f(X2),a0) )
| ~ spl0_8 ),
inference(resolution,[],[f1789,f50]) ).
fof(f1894,plain,
( spl0_1
| spl0_5
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1881,f1137,f1134,f1068,f1025]) ).
fof(f1972,plain,
! [X2,X3,X0,X1] :
( ~ eq(f(X0),a3)
| ~ eq(f(X1),a2)
| ~ eq(f(X2),a1)
| ~ eq(f(X3),a0) ),
inference(resolution,[],[f480,f100]) ).
fof(f1978,plain,
( spl0_1
| spl0_5
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f1972,f1137,f1134,f1068,f1025]) ).
fof(f1980,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a3)
| eq(f(max(s(X0),X1)),a0) )
| ~ spl0_7 ),
inference(resolution,[],[f1135,f94]) ).
fof(f1990,plain,
( ! [X2,X0,X1] :
( eq(f(max(s(X0),max(X1,s(X2)))),a0)
| ~ eq(f(X0),a3)
| ~ eq(f(X2),a1) )
| ~ spl0_7 ),
inference(resolution,[],[f1980,f37]) ).
fof(f2052,plain,
( ! [X2,X0,X1] :
( ~ eq(f(X0),a3)
| ~ eq(f(X1),a1)
| ~ eq(f(X2),a0) )
| ~ spl0_7 ),
inference(resolution,[],[f1990,f50]) ).
fof(f2065,plain,
( spl0_1
| spl0_5
| spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f2052,f1134,f1137,f1068,f1025]) ).
fof(f2072,plain,
( ! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_8 ),
inference(resolution,[],[f1138,f4]) ).
fof(f2104,plain,
( ! [X0] :
( eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f2072,f1135]) ).
fof(f2108,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a1) )
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f2104,f22]) ).
fof(f2141,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a1)
| ~ eq(f(X1),a0) )
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f2108,f17]) ).
fof(f2170,plain,
( spl0_1
| spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f2141,f1137,f1134,f1068,f1025]) ).
cnf(s39,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1251]) ).
cnf(s70,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1259]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1264]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1269]) ).
cnf(s74,plain,
( ~ spl0_1
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1306]) ).
cnf(s90,plain,
( spl0_1
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1363]) ).
cnf(s98,plain,
( spl0_1
| ~ spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1380]) ).
cnf(s114,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1446]) ).
cnf(s128,plain,
( ~ spl0_1
| spl0_5
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1637]) ).
cnf(s129,plain,
( ~ spl0_1
| spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1684]) ).
cnf(s130,plain,
( ~ spl0_1
| spl0_5
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1714]) ).
cnf(s131,plain,
( ~ spl0_1
| spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1784]) ).
cnf(s138,plain,
( spl0_1
| spl0_5
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1894]) ).
cnf(s141,plain,
( spl0_1
| spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1978]) ).
cnf(s148,plain,
( spl0_1
| spl0_5
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f2065]) ).
cnf(s163,plain,
( spl0_1
| spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f2170]) ).
cnf(s164,plain,
( spl0_7
| spl0_5
| spl0_1 ),
inference(rat,[],[s141,s138]) ).
cnf(s165,plain,
( ~ spl0_7
| spl0_5
| spl0_1 ),
inference(rat,[],[s163,s148]) ).
cnf(s166,plain,
( spl0_5
| spl0_1 ),
inference(rat,[],[s165,s164]) ).
cnf(s167,plain,
( spl0_7
| ~ spl0_5
| spl0_1 ),
inference(rat,[],[s90,s98]) ).
cnf(s168,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_1 ),
inference(rat,[],[s114,s39]) ).
cnf(s169,plain,
( ~ spl0_5
| spl0_1 ),
inference(rat,[],[s168,s167]) ).
cnf(s170,plain,
spl0_1,
inference(rat,[],[s169,s166]) ).
cnf(s171,plain,
( spl0_7
| spl0_5 ),
inference(rat,[],[s128,s129,s170]) ).
cnf(s172,plain,
( ~ spl0_7
| spl0_5 ),
inference(rat,[],[s130,s131,s170]) ).
cnf(s173,plain,
spl0_5,
inference(rat,[],[s172,s171]) ).
cnf(s176,plain,
spl0_7,
inference(rat,[],[s74,s73,s170,s173]) ).
cnf(s177,plain,
spl0_8,
inference(rat,[],[s71,s173,s170,s176]) ).
cnf(s178,plain,
$false,
inference(rat,[],[s70,s173,s170,s177,s176]) ).
fof(f2171,plain,
$false,
inference(avatar_sat_refutation,[],[s178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO620-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n002.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 17:59:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 3.97/1.25 % (596959)Input is clausal, will run a generic CNF schedule.
% 3.97/1.25 % (597032)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=348943960:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.97/1.25 % (597030)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=2979293978:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.97/1.25 % (597035)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3392922019:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.97/1.25 % (597031)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3294211338:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.97/1.25 % (597033)lrs+10_1_sil=8000:sp=occurrence:random_seed=1964651159:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.97/1.25 % (597033)Refutation not found, incomplete strategy
% 3.97/1.25 % (597033)------------------------------
% 3.97/1.25 % (597033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.25 % (597033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.25 % (597033)CaDiCaL version: 2.1.3
% 3.97/1.25 % (597033)Termination reason: Refutation not found, incomplete strategy
% 3.97/1.25 % (597033)Time elapsed: 0.0000 s
% 3.97/1.25 % (597033)Peak memory usage: 86 MB
% 3.97/1.25 % (597034)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3769642174:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.97/1.25 % (597034)Refutation not found, incomplete strategy
% 3.97/1.25 % (597034)------------------------------
% 3.97/1.25 % (597034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.25 % (597034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.25 % (597034)CaDiCaL version: 2.1.3
% 3.97/1.25 % (597034)Termination reason: Refutation not found, incomplete strategy
% 3.97/1.25 % (597034)Time elapsed: 0.001 s
% 3.97/1.25 % (597034)Peak memory usage: 86 MB
% 3.97/1.25 % (597037)dis-21_1_sil=8000:lcm=predicate:random_seed=701533601:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.97/1.25 % (597037)First to succeed.
% 3.97/1.25 % (597037)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-596959"
% 3.97/1.25 % (597035)Instruction limit reached!
% 3.97/1.25 % (597035)------------------------------
% 3.97/1.25 % (597035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.25 % (597035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.25 % (597035)CaDiCaL version: 2.1.3
% 3.97/1.25 % (597035)Termination reason: Instruction limit
% 3.97/1.25 % (597035)Termination phase: Saturation
% 3.97/1.25 % (597035)Time elapsed: 0.078 s
% 3.97/1.25 % (597035)Peak memory usage: 88 MB
% 3.97/1.25 % (597035)Instructions burned: 182 (million)
% 3.97/1.25 % (597090)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1323910351:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.97/1.25 % (597090)Refutation not found, incomplete strategy
% 3.97/1.25 % (597090)------------------------------
% 3.97/1.25 % (597090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.25 % (597090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.25 % (597090)CaDiCaL version: 2.1.3
% 3.97/1.25 % (597090)Termination reason: Refutation not found, incomplete strategy
% 3.97/1.25 % (597090)Time elapsed: 0.001 s
% 3.97/1.25 % (597090)Peak memory usage: 86 MB
% 3.97/1.25 % (597033)------------------------------
% 3.97/1.25 % (597033)------------------------------
% 3.97/1.25 % (597034)------------------------------
% 3.97/1.25 % (597034)------------------------------
% 3.97/1.25 % (597037)Refutation found. Thanks to Tanya!
% 3.97/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.97/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 4.50/1.45 % (597037)------------------------------
% 4.50/1.45 % (597037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.45 % (597037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.45 % (597037)CaDiCaL version: 2.1.3
% 4.50/1.45 % (597037)Termination reason: Refutation
% 4.50/1.45 % (597037)Time elapsed: 0.043 s
% 4.50/1.45 % (597037)Peak memory usage: 90 MB
% 4.50/1.45 % (597037)Instructions burned: 71 (million)
% 4.50/1.45 % (597037)------------------------------
% 4.50/1.45 % (597037)------------------------------
% 4.50/1.45 % (596959)Success in time 0.558 s
% 4.50/1.45 % Vampire exiting
%------------------------------------------------------------------------------