%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN254-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:50:01 PM UTC 2026
% Result : Unsatisfiable 4.13s 1.22s
% Output : Refutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 50
% Syntax : Number of formulae : 174 ( 47 unt; 24 def)
% Number of atoms : 418 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 485 ( 241 ~; 220 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 25 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 114 ( 0 sgn 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
s0(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f14,axiom,
! [X0] : p0(b,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
fof(f19,axiom,
! [X0,X1] : m0(X0,d,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
fof(f20,axiom,
l0(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
fof(f24,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
fof(f26,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
fof(f29,axiom,
q0(d,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
fof(f32,axiom,
k0(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
fof(f37,axiom,
n0(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
fof(f39,axiom,
! [X0,X1] :
( k1(X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_001) ).
fof(f40,axiom,
! [X0,X1] :
( l1(X0,X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
fof(f42,axiom,
! [X0,X1] :
( l1(X0,X0)
| ~ k1(X0)
| ~ l0(X1)
| ~ l1(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_004) ).
fof(f88,axiom,
! [X0,X1] :
( n1(X0,X1,X0)
| ~ s0(b)
| ~ l0(X0)
| ~ p0(b,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_050) ).
fof(f92,axiom,
! [X2,X0,X1] :
( ~ l0(X2)
| n1(X0,X1,X1)
| ~ l1(X2,X0)
| ~ n1(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_054) ).
fof(f106,axiom,
! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_068) ).
fof(f126,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_088) ).
fof(f163,axiom,
! [X0] :
( ~ p0(X0,X0)
| s1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_125) ).
fof(f164,axiom,
! [X2,X0,X1] :
( s1(X0)
| ~ q0(X0,X1)
| ~ s1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_126) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( l2(X0,X0)
| ~ p0(X1,X1)
| ~ s1(X2)
| ~ m0(X3,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_133) ).
fof(f215,axiom,
! [X0,X1] :
( q2(X0,X1,X1)
| ~ k0(X1)
| ~ p1(X0,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_177) ).
fof(f220,axiom,
! [X2,X0,X1] :
( q2(X0,X1,X0)
| ~ p1(X0,X0,X2)
| ~ n1(X1,X0,X2)
| ~ q2(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_182) ).
fof(f224,axiom,
! [X0,X1] :
( ~ l1(X1,X0)
| q2(X0,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_186) ).
fof(f227,axiom,
! [X0] :
( s2(X0)
| ~ q2(b,X0,b)
| ~ s1(b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_189) ).
fof(f311,axiom,
! [X2,X3,X0,X1] :
( s3(X0,X1)
| ~ q2(X2,X0,X2)
| ~ s2(X0)
| ~ m0(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_273) ).
fof(f317,axiom,
! [X2,X0,X1] :
( ~ s3(a,X0)
| ~ l2(X2,X1)
| m4(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_279) ).
fof(f369,negated_conjecture,
~ m4(e,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f602,definition,
( spl0_60
<=> ! [X1] : ~ s1(X1) ),
introduced(definition,[new_symbols(definition,[spl0_60])],[avatar_definition]) ).
fof(f603,plain,
( ! [X1] : ~ s1(X1)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f844,definition,
( spl0_120
<=> ! [X1] : ~ l2(X1,b) ),
introduced(definition,[new_symbols(definition,[spl0_120])],[avatar_definition]) ).
fof(f845,plain,
( ! [X1] : ~ l2(X1,b)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f867,definition,
( spl0_126
<=> s1(d) ),
introduced(definition,[new_symbols(definition,[spl0_126])],[avatar_definition]) ).
fof(f868,plain,
( s1(d)
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f869,plain,
( ~ s1(d)
| spl0_126 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f885,definition,
( spl0_130
<=> s1(b) ),
introduced(definition,[new_symbols(definition,[spl0_130])],[avatar_definition]) ).
fof(f889,definition,
( spl0_131
<=> ! [X0] :
( s2(X0)
| ~ q2(b,X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl0_131])],[avatar_definition]) ).
fof(f890,plain,
( ! [X0] :
( ~ q2(b,X0,b)
| s2(X0) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f889]) ).
fof(f891,plain,
( ~ spl0_130
| spl0_131 ),
inference(avatar_split_clause,[],[f227,f889,f885]) ).
fof(f900,definition,
( spl0_134
<=> l0(c) ),
introduced(definition,[new_symbols(definition,[spl0_134])],[avatar_definition]) ).
fof(f901,plain,
( l0(c)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f1099,definition,
( spl0_184
<=> k0(b) ),
introduced(definition,[new_symbols(definition,[spl0_184])],[avatar_definition]) ).
fof(f1100,plain,
( k0(b)
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1141,definition,
( spl0_194
<=> ! [X1] : ~ p0(X1,X1) ),
introduced(definition,[new_symbols(definition,[spl0_194])],[avatar_definition]) ).
fof(f1142,plain,
( ! [X1] : ~ p0(X1,X1)
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f1144,definition,
( spl0_195
<=> ! [X2,X0,X3] :
( l2(X0,X0)
| ~ s1(X2)
| ~ m0(X3,X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_195])],[avatar_definition]) ).
fof(f1145,plain,
( ! [X2,X3,X0] :
( ~ s1(X2)
| l2(X0,X0)
| ~ m0(X3,X2,X0) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1144]) ).
fof(f1146,plain,
( spl0_194
| spl0_195 ),
inference(avatar_split_clause,[],[f171,f1144,f1141]) ).
fof(f1157,definition,
( spl0_198
<=> ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_198])],[avatar_definition]) ).
fof(f1158,plain,
( ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f1159,plain,
( spl0_60
| spl0_198 ),
inference(avatar_split_clause,[],[f164,f1157,f602]) ).
fof(f1170,definition,
( spl0_201
<=> s0(b) ),
introduced(definition,[new_symbols(definition,[spl0_201])],[avatar_definition]) ).
fof(f1276,definition,
( spl0_227
<=> l0(a) ),
introduced(definition,[new_symbols(definition,[spl0_227])],[avatar_definition]) ).
fof(f1277,plain,
( l0(a)
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1280,definition,
( spl0_228
<=> p1(a,a,a) ),
introduced(definition,[new_symbols(definition,[spl0_228])],[avatar_definition]) ).
fof(f1282,plain,
( p1(a,a,a)
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f1283,plain,
( ~ spl0_227
| spl0_228 ),
inference(avatar_split_clause,[],[f126,f1280,f1276]) ).
fof(f1340,definition,
( spl0_242
<=> ! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_242])],[avatar_definition]) ).
fof(f1341,plain,
( ! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1360,plain,
spl0_242,
inference(avatar_split_clause,[],[f106,f1340]) ).
fof(f1419,definition,
( spl0_261
<=> ! [X0,X1] :
( n1(X0,X1,X0)
| ~ p0(b,X1)
| ~ l0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_261])],[avatar_definition]) ).
fof(f1420,plain,
( ! [X0,X1] :
( n1(X0,X1,X0)
| ~ p0(b,X1)
| ~ l0(X0) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f1421,plain,
( ~ spl0_201
| spl0_261 ),
inference(avatar_split_clause,[],[f88,f1419,f1170]) ).
fof(f1448,definition,
( spl0_268
<=> k1(a) ),
introduced(definition,[new_symbols(definition,[spl0_268])],[avatar_definition]) ).
fof(f1449,plain,
( k1(a)
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f1450,plain,
( ~ k1(a)
| spl0_268 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f1528,definition,
( spl0_287
<=> l1(c,c) ),
introduced(definition,[new_symbols(definition,[spl0_287])],[avatar_definition]) ).
fof(f1529,plain,
( l1(c,c)
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f1530,plain,
( ~ l1(c,c)
| spl0_287 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f1544,definition,
( spl0_291
<=> ! [X1] :
( ~ l0(X1)
| ~ l1(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_291])],[avatar_definition]) ).
fof(f1545,plain,
( ! [X1] :
( ~ l1(X1,X1)
| ~ l0(X1) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f1547,definition,
( spl0_292
<=> ! [X0] :
( l1(X0,X0)
| ~ k1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_292])],[avatar_definition]) ).
fof(f1548,plain,
( ! [X0] :
( l1(X0,X0)
| ~ k1(X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f1547]) ).
fof(f1549,plain,
( spl0_291
| spl0_292 ),
inference(avatar_split_clause,[],[f42,f1547,f1544]) ).
fof(f1555,plain,
spl0_184,
inference(avatar_split_clause,[],[f32,f1099]) ).
fof(f1558,plain,
spl0_134,
inference(avatar_split_clause,[],[f24,f900]) ).
fof(f1560,plain,
spl0_227,
inference(avatar_split_clause,[],[f20,f1276]) ).
fof(f1567,plain,
spl0_201,
inference(avatar_split_clause,[],[f5,f1170]) ).
fof(f1578,plain,
( $false
| ~ spl0_194 ),
inference(resolution,[],[f1142,f14]) ).
fof(f1579,plain,
~ spl0_194,
inference(avatar_contradiction_clause,[],[f1578]) ).
fof(f1631,plain,
( ! [X0] : ~ n0(X0,a)
| spl0_268 ),
inference(resolution,[],[f39,f1450]) ).
fof(f1633,plain,
( ! [X0] : ~ p0(X0,X0)
| ~ spl0_60 ),
inference(forward_subsumption_resolution,[],[f163,f603]) ).
fof(f1634,plain,
( spl0_194
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f1633,f602,f1141]) ).
fof(f1651,plain,
( $false
| spl0_268 ),
inference(resolution,[],[f1631,f37]) ).
fof(f1652,plain,
spl0_268,
inference(avatar_contradiction_clause,[],[f1651]) ).
fof(f1692,plain,
s1(b),
inference(resolution,[],[f163,f14]) ).
fof(f1696,plain,
spl0_130,
inference(avatar_split_clause,[],[f1692,f885]) ).
fof(f1708,plain,
( ! [X0] : ~ q0(d,X0)
| spl0_126
| ~ spl0_198 ),
inference(resolution,[],[f1158,f869]) ).
fof(f1711,plain,
( $false
| spl0_126
| ~ spl0_198 ),
inference(resolution,[],[f1708,f29]) ).
fof(f1716,plain,
( spl0_126
| ~ spl0_198 ),
inference(avatar_contradiction_clause,[],[f1711]) ).
fof(f1775,plain,
( ! [X0] : ~ n0(X0,c)
| spl0_287 ),
inference(resolution,[],[f40,f1530]) ).
fof(f1784,plain,
( $false
| spl0_287 ),
inference(resolution,[],[f1775,f26]) ).
fof(f1785,plain,
spl0_287,
inference(avatar_contradiction_clause,[],[f1784]) ).
fof(f1786,plain,
( ~ l0(c)
| ~ spl0_287
| ~ spl0_291 ),
inference(resolution,[],[f1529,f1545]) ).
fof(f1787,plain,
( $false
| ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(forward_subsumption_resolution,[],[f1786,f901]) ).
fof(f1788,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(avatar_contradiction_clause,[],[f1787]) ).
fof(f1891,plain,
! [X0,X1] :
( q2(X0,X0,X0)
| ~ n0(X1,X0) ),
inference(resolution,[],[f224,f40]) ).
fof(f2110,plain,
( ! [X0,X1] :
( l2(X0,X0)
| ~ m0(X1,d,X0) )
| ~ spl0_126
| ~ spl0_195 ),
inference(resolution,[],[f1145,f868]) ).
fof(f2114,plain,
( ! [X0] : l2(X0,X0)
| ~ spl0_126
| ~ spl0_195 ),
inference(forward_subsumption_resolution,[],[f2110,f19]) ).
fof(f2116,plain,
( $false
| ~ spl0_120
| ~ spl0_126
| ~ spl0_195 ),
inference(resolution,[],[f2114,f845]) ).
fof(f2126,plain,
( ~ spl0_120
| ~ spl0_126
| ~ spl0_195 ),
inference(avatar_contradiction_clause,[],[f2116]) ).
fof(f2160,plain,
( ! [X0,X1] :
( ~ l0(X0)
| n1(X0,X1,X0) )
| ~ spl0_261 ),
inference(forward_subsumption_resolution,[],[f1420,f14]) ).
fof(f2162,plain,
( ! [X0] : n1(a,X0,a)
| ~ spl0_227
| ~ spl0_261 ),
inference(resolution,[],[f2160,f1277]) ).
fof(f2215,definition,
( spl0_320
<=> ! [X0] : ~ n0(X0,a) ),
introduced(definition,[new_symbols(definition,[spl0_320])],[avatar_definition]) ).
fof(f2216,plain,
( ! [X0] : ~ n0(X0,a)
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f2215]) ).
fof(f2489,plain,
( ! [X0,X1] :
( ~ l1(a,X0)
| n1(X0,X1,X1)
| ~ n1(X0,X1,X0) )
| ~ spl0_227 ),
inference(resolution,[],[f92,f1277]) ).
fof(f2525,plain,
! [X2,X3,X0,X1,X4] :
( ~ q2(X0,a,X0)
| ~ s2(a)
| ~ m0(X0,X1,X2)
| ~ l2(X3,X4)
| m4(X2,X4) ),
inference(resolution,[],[f311,f317]) ).
fof(f2527,definition,
( spl0_347
<=> s2(a) ),
introduced(definition,[new_symbols(definition,[spl0_347])],[avatar_definition]) ).
fof(f2529,plain,
( ~ s2(a)
| spl0_347 ),
inference(avatar_component_clause,[],[f2527]) ).
fof(f2531,definition,
( spl0_348
<=> ! [X4,X0,X3,X2,X1] :
( ~ q2(X0,a,X0)
| m4(X2,X4)
| ~ l2(X3,X4)
| ~ m0(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_348])],[avatar_definition]) ).
fof(f2532,plain,
( ! [X2,X3,X0,X1,X4] :
( m4(X2,X4)
| ~ q2(X0,a,X0)
| ~ l2(X3,X4)
| ~ m0(X0,X1,X2) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f2531]) ).
fof(f2533,plain,
( ~ spl0_347
| spl0_348 ),
inference(avatar_split_clause,[],[f2525,f2531,f2527]) ).
fof(f2660,plain,
( $false
| ~ spl0_320 ),
inference(resolution,[],[f2216,f37]) ).
fof(f2661,plain,
~ spl0_320,
inference(avatar_contradiction_clause,[],[f2660]) ).
fof(f2663,plain,
( ! [X0,X1] :
( s2(X1)
| ~ n1(X1,b,X0)
| ~ q2(X1,X0,b)
| ~ p1(b,b,X0) )
| ~ spl0_131 ),
inference(resolution,[],[f220,f890]) ).
fof(f2875,plain,
( ! [X0] :
( n1(a,X0,X0)
| ~ n1(a,X0,a)
| ~ k1(a) )
| ~ spl0_227
| ~ spl0_292 ),
inference(resolution,[],[f2489,f1548]) ).
fof(f2878,plain,
( ! [X0] :
( n1(a,X0,X0)
| ~ n1(a,X0,a) )
| ~ spl0_227
| ~ spl0_268
| ~ spl0_292 ),
inference(forward_subsumption_resolution,[],[f2875,f1449]) ).
fof(f2880,definition,
( spl0_375
<=> ! [X0] : n1(a,X0,X0) ),
introduced(definition,[new_symbols(definition,[spl0_375])],[avatar_definition]) ).
fof(f2881,plain,
( ! [X0] : n1(a,X0,X0)
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f2880]) ).
fof(f2883,plain,
( ! [X0] : n1(a,X0,X0)
| ~ spl0_227
| ~ spl0_261
| ~ spl0_268
| ~ spl0_292 ),
inference(forward_subsumption_resolution,[],[f2878,f2162]) ).
fof(f2884,plain,
( spl0_375
| ~ spl0_227
| ~ spl0_261
| ~ spl0_268
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2883,f1547,f1448,f1419,f1276,f2880]) ).
fof(f2971,plain,
( ! [X0] :
( ~ q2(a,X0,b)
| ~ n1(a,b,X0)
| ~ p1(b,b,X0) )
| ~ spl0_131
| spl0_347 ),
inference(resolution,[],[f2663,f2529]) ).
fof(f2975,plain,
( ~ n1(a,b,b)
| ~ p1(b,b,b)
| ~ k0(b)
| ~ p1(a,a,a)
| ~ spl0_131
| spl0_347 ),
inference(resolution,[],[f2971,f215]) ).
fof(f2976,plain,
( ~ p1(b,b,b)
| ~ k0(b)
| ~ p1(a,a,a)
| ~ spl0_131
| spl0_347
| ~ spl0_375 ),
inference(forward_subsumption_resolution,[],[f2975,f2881]) ).
fof(f2977,plain,
( ~ k0(b)
| ~ p1(a,a,a)
| ~ spl0_131
| ~ spl0_242
| spl0_347
| ~ spl0_375 ),
inference(forward_subsumption_resolution,[],[f2976,f1341]) ).
fof(f2978,plain,
( ~ p1(a,a,a)
| ~ spl0_131
| ~ spl0_184
| ~ spl0_242
| spl0_347
| ~ spl0_375 ),
inference(forward_subsumption_resolution,[],[f2977,f1100]) ).
fof(f2979,plain,
( $false
| ~ spl0_131
| ~ spl0_184
| ~ spl0_228
| ~ spl0_242
| spl0_347
| ~ spl0_375 ),
inference(forward_subsumption_resolution,[],[f2978,f1282]) ).
fof(f2980,plain,
( ~ spl0_131
| ~ spl0_184
| ~ spl0_228
| ~ spl0_242
| spl0_347
| ~ spl0_375 ),
inference(avatar_contradiction_clause,[],[f2979]) ).
fof(f2981,plain,
( ! [X2,X0,X1] :
( ~ q2(X0,a,X0)
| ~ l2(X1,b)
| ~ m0(X0,X2,e) )
| ~ spl0_348 ),
inference(resolution,[],[f2532,f369]) ).
fof(f2985,definition,
( spl0_387
<=> ! [X2,X0] :
( ~ q2(X0,a,X0)
| ~ m0(X0,X2,e) ) ),
introduced(definition,[new_symbols(definition,[spl0_387])],[avatar_definition]) ).
fof(f2986,plain,
( ! [X2,X0] :
( ~ m0(X0,X2,e)
| ~ q2(X0,a,X0) )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f2985]) ).
fof(f2987,plain,
( spl0_120
| spl0_387
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f2981,f2531,f2985,f844]) ).
fof(f2988,plain,
( ! [X0] : ~ q2(X0,a,X0)
| ~ spl0_387 ),
inference(resolution,[],[f2986,f19]) ).
fof(f3024,plain,
( ! [X0] : ~ n0(X0,a)
| ~ spl0_387 ),
inference(resolution,[],[f2988,f1891]) ).
fof(f3030,plain,
( spl0_320
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f3024,f2985,f2215]) ).
cnf(s60,plain,
( ~ spl0_130
| spl0_131 ),
inference(sat_conversion,[],[f891]) ).
cnf(s89,plain,
( spl0_194
| spl0_195 ),
inference(sat_conversion,[],[f1146]) ).
cnf(s91,plain,
( spl0_60
| spl0_198 ),
inference(sat_conversion,[],[f1159]) ).
cnf(s111,plain,
( ~ spl0_227
| spl0_228 ),
inference(sat_conversion,[],[f1283]) ).
cnf(s124,plain,
spl0_242,
inference(sat_conversion,[],[f1360]) ).
cnf(s131,plain,
( ~ spl0_201
| spl0_261 ),
inference(sat_conversion,[],[f1421]) ).
cnf(s152,plain,
( spl0_291
| spl0_292 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s155,plain,
spl0_184,
inference(sat_conversion,[],[f1555]) ).
cnf(s158,plain,
spl0_134,
inference(sat_conversion,[],[f1558]) ).
cnf(s160,plain,
spl0_227,
inference(sat_conversion,[],[f1560]) ).
cnf(s167,plain,
spl0_201,
inference(sat_conversion,[],[f1567]) ).
cnf(s173,plain,
~ spl0_194,
inference(sat_conversion,[],[f1579]) ).
cnf(s194,plain,
( ~ spl0_60
| spl0_194 ),
inference(sat_conversion,[],[f1634]) ).
cnf(s199,plain,
spl0_268,
inference(sat_conversion,[],[f1652]) ).
cnf(s210,plain,
spl0_130,
inference(sat_conversion,[],[f1696]) ).
cnf(s214,plain,
( spl0_126
| ~ spl0_198 ),
inference(sat_conversion,[],[f1716]) ).
cnf(s236,plain,
spl0_287,
inference(sat_conversion,[],[f1785]) ).
cnf(s237,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(sat_conversion,[],[f1788]) ).
cnf(s307,plain,
( ~ spl0_120
| ~ spl0_126
| ~ spl0_195 ),
inference(sat_conversion,[],[f2126]) ).
cnf(s365,plain,
( ~ spl0_347
| spl0_348 ),
inference(sat_conversion,[],[f2533]) ).
cnf(s384,plain,
~ spl0_320,
inference(sat_conversion,[],[f2661]) ).
cnf(s430,plain,
( ~ spl0_227
| ~ spl0_261
| ~ spl0_268
| ~ spl0_292
| spl0_375 ),
inference(sat_conversion,[],[f2884]) ).
cnf(s442,plain,
( ~ spl0_131
| ~ spl0_184
| ~ spl0_228
| ~ spl0_242
| spl0_347
| ~ spl0_375 ),
inference(sat_conversion,[],[f2980]) ).
cnf(s443,plain,
( spl0_120
| ~ spl0_348
| spl0_387 ),
inference(sat_conversion,[],[f2987]) ).
cnf(s451,plain,
( spl0_320
| ~ spl0_387 ),
inference(sat_conversion,[],[f3030]) ).
cnf(s456,plain,
~ spl0_387,
inference(rat,[],[s451,s384]) ).
cnf(s469,plain,
~ spl0_60,
inference(rat,[],[s194,s173]) ).
cnf(s477,plain,
~ spl0_291,
inference(rat,[],[s237,s236,s158]) ).
cnf(s483,plain,
spl0_292,
inference(rat,[],[s152,s477]) ).
cnf(s509,plain,
spl0_261,
inference(rat,[],[s131,s167]) ).
cnf(s510,plain,
spl0_375,
inference(rat,[],[s430,s483,s160,s199,s509]) ).
cnf(s530,plain,
spl0_228,
inference(rat,[],[s111,s160]) ).
cnf(s559,plain,
spl0_198,
inference(rat,[],[s91,s469]) ).
cnf(s562,plain,
spl0_126,
inference(rat,[],[s214,s559]) ).
cnf(s565,plain,
spl0_195,
inference(rat,[],[s89,s173]) ).
cnf(s570,plain,
~ spl0_120,
inference(rat,[],[s307,s562,s565]) ).
cnf(s573,plain,
~ spl0_348,
inference(rat,[],[s443,s456,s570]) ).
cnf(s574,plain,
~ spl0_347,
inference(rat,[],[s365,s573]) ).
cnf(s575,plain,
~ spl0_131,
inference(rat,[],[s442,s510,s530,s124,s155,s574]) ).
cnf(s606,plain,
$false,
inference(rat,[],[s60,s575,s210]) ).
fof(f3036,plain,
$false,
inference(avatar_sat_refutation,[],[s606]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN254-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.20 % Computer : n015.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Mon Sep 28 15:42:17 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.24 Running first-order theorem proving
% 0.12/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.13/1.22 % (2730123)Input is clausal, will run a generic CNF schedule.
% 4.13/1.22 % (2730143)dis-21_1_sil=8000:lcm=predicate:random_seed=3761494165: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)
% 4.13/1.22 % (2730137)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=1913104306:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.13/1.22 % (2730143)Instruction limit reached!
% 4.13/1.22 % (2730143)------------------------------
% 4.13/1.22 % (2730143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.22 % (2730143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.22 % (2730143)CaDiCaL version: 2.1.3
% 4.13/1.22 % (2730143)Termination reason: Instruction limit
% 4.13/1.22 % (2730143)Termination phase: Saturation
% 4.13/1.22 % (2730143)Time elapsed: 0.046 s
% 4.13/1.22 % (2730143)Peak memory usage: 89 MB
% 4.13/1.22 % (2730143)Instructions burned: 118 (million)
% 4.13/1.22 % (2730139)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=388698387:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.13/1.22 % (2730138)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1843681223:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.13/1.22 % (2730140)lrs+10_1_sil=8000:sp=occurrence:random_seed=2477039826:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.13/1.22 % (2730142)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3914251119:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.13/1.22 % (2730141)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3553730686:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.13/1.22 % (2730140)Refutation not found, incomplete strategy
% 4.13/1.22 % (2730140)------------------------------
% 4.13/1.22 % (2730140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.22 % (2730140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.22 % (2730140)CaDiCaL version: 2.1.3
% 4.13/1.22 % (2730140)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.22 % (2730140)Time elapsed: 0.032 s
% 4.13/1.22 % (2730140)Peak memory usage: 89 MB
% 4.13/1.22 % (2730140)Instructions burned: 41 (million)
% 4.13/1.22 % (2730142)First to succeed.
% 4.13/1.22 % (2730142)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2730123"
% 4.13/1.22 % (2730141)Instruction limit reached!
% 4.13/1.22 % (2730141)------------------------------
% 4.13/1.22 % (2730141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.22 % (2730141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.22 % (2730141)CaDiCaL version: 2.1.3
% 4.13/1.22 % (2730141)Termination reason: Instruction limit
% 4.13/1.22 % (2730141)Termination phase: Saturation
% 4.13/1.22 % (2730141)Time elapsed: 0.075 s
% 4.13/1.22 % (2730141)Peak memory usage: 90 MB
% 4.13/1.22 % (2730141)Instructions burned: 115 (million)
% 4.13/1.22 % (2730152)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=1667917987:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.13/1.22 % (2730152)Refutation not found, incomplete strategy
% 4.13/1.22 % (2730152)------------------------------
% 4.13/1.22 % (2730152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.22 % (2730152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.22 % (2730152)CaDiCaL version: 2.1.3
% 4.13/1.22 % (2730152)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.22 % (2730152)Time elapsed: 0.001 s
% 4.13/1.22 % (2730152)Peak memory usage: 87 MB
% 4.13/1.22 % (2730152)Instructions burned: 1 (million)
% 4.13/1.22 % (2730158)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2581563961:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 4.13/1.22 % (2730158)Refutation not found, incomplete strategy
% 4.13/1.22 % (2730158)------------------------------
% 4.13/1.22 % (2730158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.22 % (2730158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.22 % (2730158)CaDiCaL version: 2.1.3
% 4.13/1.22 % (2730158)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.22 % (2730158)Time elapsed: 0.013 s
% 4.13/1.22 % (2730158)Peak memory usage: 88 MB
% 4.13/1.22 % (2730158)Instructions burned: 23 (million)
% 4.13/1.22 % (2730140)------------------------------
% 4.13/1.22 % (2730140)------------------------------
% 4.13/1.22 % (2730152)------------------------------
% 4.13/1.22 % (2730152)------------------------------
% 4.13/1.22 % (2730142)Refutation found. Thanks to Tanya!
% 4.13/1.22 % SZS status Unsatisfiable for theBenchmark
% 4.13/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 4.38/1.32 % (2730142)------------------------------
% 4.38/1.32 % (2730142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.32 % (2730142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.32 % (2730142)CaDiCaL version: 2.1.3
% 4.38/1.32 % (2730142)Termination reason: Refutation
% 4.38/1.32 % (2730142)Time elapsed: 0.048 s
% 4.38/1.32 % (2730142)Peak memory usage: 91 MB
% 4.38/1.32 % (2730142)Instructions burned: 65 (million)
% 4.38/1.32 % (2730142)------------------------------
% 4.38/1.32 % (2730142)------------------------------
% 4.38/1.32 % (2730123)Success in time 0.54 s
% 4.38/1.32 % Vampire exiting
%------------------------------------------------------------------------------