%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN252-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 3.12s 1.11s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 54
% Syntax : Number of formulae : 194 ( 51 unt; 27 def)
% Number of atoms : 459 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 529 ( 264 ~; 238 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 45 ( 44 usr; 28 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 120 ( 0 sgn 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
s0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f12,axiom,
! [X0] : m0(a,X0,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
fof(f14,axiom,
! [X0] : p0(b,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f17,axiom,
! [X0] : q0(X0,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
fof(f19,axiom,
! [X0,X1] : m0(X0,d,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
fof(f20,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
fof(f24,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
fof(f26,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
fof(f32,axiom,
k0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
fof(f37,axiom,
n0(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
fof(f39,axiom,
! [X0,X1] :
( k1(X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).
fof(f40,axiom,
! [X0,X1] :
( l1(X0,X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_002) ).
fof(f42,axiom,
! [X0,X1] :
( l1(X0,X0)
| ~ k1(X0)
| ~ l0(X1)
| ~ l1(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_004) ).
fof(f88,axiom,
! [X0,X1] :
( n1(X0,X1,X0)
| ~ s0(b)
| ~ l0(X0)
| ~ p0(b,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_050) ).
fof(f92,axiom,
! [X2,X0,X1] :
( n1(X0,X1,X1)
| ~ l0(X2)
| ~ l1(X2,X0)
| ~ n1(X0,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_054) ).
fof(f107,axiom,
! [X0,X1] :
( p1(X0,X0,X1)
| ~ p0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_069) ).
fof(f126,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_088) ).
fof(f163,axiom,
! [X0] :
( ~ p0(X0,X0)
| s1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
fof(f164,axiom,
! [X2,X0,X1] :
( s1(X0)
| ~ q0(X0,X1)
| ~ s1(X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rule_133) ).
fof(f215,axiom,
! [X0,X1] :
( ~ k0(X1)
| q2(X0,X1,X1)
| ~ p1(X0,X0,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rule_182) ).
fof(f224,axiom,
! [X0,X1] :
( ~ l1(X1,X0)
| q2(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_186) ).
fof(f227,axiom,
! [X0] :
( s2(X0)
| ~ q2(b,X0,b)
| ~ s1(b) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rule_273) ).
fof(f317,axiom,
! [X2,X0,X1] :
( ~ s3(a,X0)
| ~ l2(X2,X1)
| m4(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_279) ).
fof(f369,negated_conjecture,
! [X0] : ~ m4(X0,d),
file('/export/starexec/sandbox/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(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(f896,definition,
( spl0_133
<=> ! [X0] :
( q2(X0,X0,X0)
| ~ k1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_133])],[avatar_definition]) ).
fof(f897,plain,
( ! [X0] :
( q2(X0,X0,X0)
| ~ k1(X0) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f896]) ).
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(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(f1593,plain,
( $false
| ~ spl0_194 ),
inference(resolution,[],[f1142,f14]) ).
fof(f1594,plain,
~ spl0_194,
inference(avatar_contradiction_clause,[],[f1593]) ).
fof(f1662,plain,
( ! [X0] : ~ n0(X0,a)
| spl0_268 ),
inference(resolution,[],[f39,f1450]) ).
fof(f1670,plain,
( ! [X0] : ~ p0(X0,X0)
| ~ spl0_60 ),
inference(forward_subsumption_resolution,[],[f163,f603]) ).
fof(f1671,plain,
( spl0_194
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f1670,f602,f1141]) ).
fof(f1673,plain,
s1(b),
inference(resolution,[],[f163,f14]) ).
fof(f1677,plain,
spl0_130,
inference(avatar_split_clause,[],[f1673,f885]) ).
fof(f1678,plain,
( $false
| spl0_268 ),
inference(resolution,[],[f1662,f37]) ).
fof(f1679,plain,
spl0_268,
inference(avatar_contradiction_clause,[],[f1678]) ).
fof(f1688,plain,
( ! [X0] : ~ q0(d,X0)
| spl0_126
| ~ spl0_198 ),
inference(resolution,[],[f1158,f869]) ).
fof(f1691,plain,
( $false
| spl0_126
| ~ spl0_198 ),
inference(resolution,[],[f1688,f17]) ).
fof(f1696,plain,
( spl0_126
| ~ spl0_198 ),
inference(avatar_contradiction_clause,[],[f1691]) ).
fof(f1733,plain,
( ! [X0] : ~ n0(X0,c)
| spl0_287 ),
inference(resolution,[],[f40,f1530]) ).
fof(f1748,plain,
( $false
| spl0_287 ),
inference(resolution,[],[f1733,f26]) ).
fof(f1749,plain,
spl0_287,
inference(avatar_contradiction_clause,[],[f1748]) ).
fof(f1750,plain,
( ~ l0(c)
| ~ spl0_287
| ~ spl0_291 ),
inference(resolution,[],[f1529,f1545]) ).
fof(f1751,plain,
( $false
| ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(forward_subsumption_resolution,[],[f1750,f901]) ).
fof(f1752,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(avatar_contradiction_clause,[],[f1751]) ).
fof(f1826,plain,
( ! [X0] :
( q2(X0,X0,X0)
| ~ k1(X0) )
| ~ spl0_292 ),
inference(resolution,[],[f224,f1548]) ).
fof(f1830,plain,
( spl0_133
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f1826,f1547,f896]) ).
fof(f2054,plain,
( ! [X0,X1] :
( l2(X0,X0)
| ~ m0(X1,d,X0) )
| ~ spl0_126
| ~ spl0_195 ),
inference(resolution,[],[f1145,f868]) ).
fof(f2058,plain,
( ! [X0] : l2(X0,X0)
| ~ spl0_126
| ~ spl0_195 ),
inference(forward_subsumption_resolution,[],[f2054,f19]) ).
fof(f2069,plain,
( ! [X0,X1] :
( n1(X0,X1,X0)
| ~ l0(X0) )
| ~ spl0_261 ),
inference(forward_subsumption_resolution,[],[f1420,f14]) ).
fof(f2095,plain,
( ! [X0] :
( q2(X0,b,b)
| ~ p1(X0,X0,X0) )
| ~ spl0_184 ),
inference(resolution,[],[f215,f1100]) ).
fof(f2328,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(f2330,definition,
( spl0_321
<=> s2(a) ),
introduced(definition,[new_symbols(definition,[spl0_321])],[avatar_definition]) ).
fof(f2332,plain,
( ~ s2(a)
| spl0_321 ),
inference(avatar_component_clause,[],[f2330]) ).
fof(f2334,definition,
( spl0_322
<=> ! [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_322])],[avatar_definition]) ).
fof(f2335,plain,
( ! [X2,X3,X0,X1,X4] :
( m4(X2,X4)
| ~ q2(X0,a,X0)
| ~ l2(X3,X4)
| ~ m0(X0,X1,X2) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f2334]) ).
fof(f2336,plain,
( ~ spl0_321
| spl0_322 ),
inference(avatar_split_clause,[],[f2328,f2334,f2330]) ).
fof(f2473,plain,
( ! [X0,X1] :
( s2(X1)
| ~ n1(X1,b,X0)
| ~ q2(X1,X0,b)
| ~ p1(b,b,X0) )
| ~ spl0_131 ),
inference(resolution,[],[f220,f890]) ).
fof(f3086,definition,
( spl0_405
<=> p1(b,b,b) ),
introduced(definition,[new_symbols(definition,[spl0_405])],[avatar_definition]) ).
fof(f3087,plain,
( p1(b,b,b)
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f3088,plain,
( ~ p1(b,b,b)
| spl0_405 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f3090,definition,
( spl0_406
<=> n1(a,b,b) ),
introduced(definition,[new_symbols(definition,[spl0_406])],[avatar_definition]) ).
fof(f3092,plain,
( ~ n1(a,b,b)
| spl0_406 ),
inference(avatar_component_clause,[],[f3090]) ).
fof(f3095,plain,
( ~ p0(b,b)
| spl0_405 ),
inference(resolution,[],[f3088,f107]) ).
fof(f3121,plain,
( $false
| spl0_405 ),
inference(forward_subsumption_resolution,[],[f3095,f14]) ).
fof(f3122,plain,
spl0_405,
inference(avatar_contradiction_clause,[],[f3121]) ).
fof(f3171,definition,
( spl0_415
<=> n1(a,b,a) ),
introduced(definition,[new_symbols(definition,[spl0_415])],[avatar_definition]) ).
fof(f3173,plain,
( ~ n1(a,b,a)
| spl0_415 ),
inference(avatar_component_clause,[],[f3171]) ).
fof(f3175,definition,
( spl0_416
<=> ! [X0] :
( ~ l0(X0)
| ~ l1(X0,a) ) ),
introduced(definition,[new_symbols(definition,[spl0_416])],[avatar_definition]) ).
fof(f3176,plain,
( ! [X0] :
( ~ l0(X0)
| ~ l1(X0,a) )
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f3175]) ).
fof(f3225,plain,
( ~ l0(a)
| ~ spl0_261
| spl0_415 ),
inference(resolution,[],[f3173,f2069]) ).
fof(f3226,plain,
( $false
| ~ spl0_227
| ~ spl0_261
| spl0_415 ),
inference(forward_subsumption_resolution,[],[f3225,f1277]) ).
fof(f3227,plain,
( ~ spl0_227
| ~ spl0_261
| spl0_415 ),
inference(avatar_contradiction_clause,[],[f3226]) ).
fof(f3232,definition,
( spl0_419
<=> ! [X1] : ~ l2(X1,d) ),
introduced(definition,[new_symbols(definition,[spl0_419])],[avatar_definition]) ).
fof(f3233,plain,
( ! [X1] : ~ l2(X1,d)
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f3232]) ).
fof(f3235,definition,
( spl0_420
<=> ! [X2,X0,X3] :
( ~ q2(X0,a,X0)
| ~ m0(X0,X2,X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_420])],[avatar_definition]) ).
fof(f3236,plain,
( ! [X2,X3,X0] :
( ~ q2(X0,a,X0)
| ~ m0(X0,X2,X3) )
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f3235]) ).
fof(f3238,plain,
( ! [X0] :
( ~ q2(a,X0,b)
| ~ n1(a,b,X0)
| ~ p1(b,b,X0) )
| ~ spl0_131
| spl0_321 ),
inference(resolution,[],[f2332,f2473]) ).
fof(f3239,plain,
( ~ n1(a,b,b)
| ~ p1(b,b,b)
| ~ p1(a,a,a)
| ~ spl0_131
| ~ spl0_184
| spl0_321 ),
inference(resolution,[],[f3238,f2095]) ).
fof(f3240,plain,
( ~ n1(a,b,b)
| ~ p1(a,a,a)
| ~ spl0_131
| ~ spl0_184
| spl0_321
| ~ spl0_405 ),
inference(forward_subsumption_resolution,[],[f3239,f3087]) ).
fof(f3241,plain,
( ~ n1(a,b,b)
| ~ spl0_131
| ~ spl0_184
| ~ spl0_228
| spl0_321
| ~ spl0_405 ),
inference(forward_subsumption_resolution,[],[f3240,f1282]) ).
fof(f3242,plain,
( ~ spl0_406
| ~ spl0_131
| ~ spl0_184
| ~ spl0_228
| spl0_321
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3241,f3086,f2330,f1280,f1099,f889,f3090]) ).
fof(f3243,plain,
( ! [X0] :
( ~ l0(X0)
| ~ l1(X0,a)
| ~ n1(a,b,a) )
| spl0_406 ),
inference(resolution,[],[f3092,f92]) ).
fof(f3244,plain,
( ~ spl0_415
| spl0_416
| spl0_406 ),
inference(avatar_split_clause,[],[f3243,f3090,f3175,f3171]) ).
fof(f3320,plain,
( ~ l1(a,a)
| ~ spl0_227
| ~ spl0_416 ),
inference(resolution,[],[f3176,f1277]) ).
fof(f3324,plain,
( ~ k1(a)
| ~ spl0_227
| ~ spl0_292
| ~ spl0_416 ),
inference(resolution,[],[f3320,f1548]) ).
fof(f3327,plain,
( $false
| ~ spl0_227
| ~ spl0_268
| ~ spl0_292
| ~ spl0_416 ),
inference(forward_subsumption_resolution,[],[f3324,f1449]) ).
fof(f3328,plain,
( ~ spl0_227
| ~ spl0_268
| ~ spl0_292
| ~ spl0_416 ),
inference(avatar_contradiction_clause,[],[f3327]) ).
fof(f3330,plain,
( $false
| ~ spl0_126
| ~ spl0_195
| ~ spl0_419 ),
inference(resolution,[],[f3233,f2058]) ).
fof(f3331,plain,
( ~ spl0_126
| ~ spl0_195
| ~ spl0_419 ),
inference(avatar_contradiction_clause,[],[f3330]) ).
fof(f3332,plain,
( ! [X2,X3,X0,X1] :
( ~ q2(X0,a,X0)
| ~ l2(X1,d)
| ~ m0(X0,X2,X3) )
| ~ spl0_322 ),
inference(resolution,[],[f2335,f369]) ).
fof(f3335,plain,
( spl0_419
| spl0_420
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f3332,f2334,f3235,f3232]) ).
fof(f3341,plain,
( ! [X0,X1] :
( ~ m0(a,X0,X1)
| ~ k1(a) )
| ~ spl0_133
| ~ spl0_420 ),
inference(resolution,[],[f3236,f897]) ).
fof(f3343,plain,
( ! [X0,X1] : ~ m0(a,X0,X1)
| ~ spl0_133
| ~ spl0_268
| ~ spl0_420 ),
inference(forward_subsumption_resolution,[],[f3341,f1449]) ).
fof(f3345,definition,
( spl0_429
<=> ! [X0,X1] : ~ m0(a,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl0_429])],[avatar_definition]) ).
fof(f3346,plain,
( ! [X0,X1] : ~ m0(a,X0,X1)
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f3345]) ).
fof(f3361,plain,
( spl0_429
| ~ spl0_133
| ~ spl0_268
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f3343,f3235,f1448,f896,f3345]) ).
fof(f3363,plain,
( $false
| ~ spl0_429 ),
inference(resolution,[],[f3346,f12]) ).
fof(f3368,plain,
~ spl0_429,
inference(avatar_contradiction_clause,[],[f3363]) ).
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(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(s176,plain,
~ spl0_194,
inference(sat_conversion,[],[f1594]) ).
cnf(s202,plain,
( ~ spl0_60
| spl0_194 ),
inference(sat_conversion,[],[f1671]) ).
cnf(s204,plain,
spl0_130,
inference(sat_conversion,[],[f1677]) ).
cnf(s205,plain,
spl0_268,
inference(sat_conversion,[],[f1679]) ).
cnf(s212,plain,
( spl0_126
| ~ spl0_198 ),
inference(sat_conversion,[],[f1696]) ).
cnf(s231,plain,
spl0_287,
inference(sat_conversion,[],[f1749]) ).
cnf(s232,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(sat_conversion,[],[f1752]) ).
cnf(s253,plain,
( spl0_133
| ~ spl0_292 ),
inference(sat_conversion,[],[f1830]) ).
cnf(s326,plain,
( ~ spl0_321
| spl0_322 ),
inference(sat_conversion,[],[f2336]) ).
cnf(s453,plain,
spl0_405,
inference(sat_conversion,[],[f3122]) ).
cnf(s470,plain,
( ~ spl0_227
| ~ spl0_261
| spl0_415 ),
inference(sat_conversion,[],[f3227]) ).
cnf(s472,plain,
( ~ spl0_131
| ~ spl0_184
| ~ spl0_228
| spl0_321
| ~ spl0_405
| ~ spl0_406 ),
inference(sat_conversion,[],[f3242]) ).
cnf(s473,plain,
( spl0_406
| ~ spl0_415
| spl0_416 ),
inference(sat_conversion,[],[f3244]) ).
cnf(s490,plain,
( ~ spl0_227
| ~ spl0_268
| ~ spl0_292
| ~ spl0_416 ),
inference(sat_conversion,[],[f3328]) ).
cnf(s492,plain,
( ~ spl0_126
| ~ spl0_195
| ~ spl0_419 ),
inference(sat_conversion,[],[f3331]) ).
cnf(s493,plain,
( ~ spl0_322
| spl0_419
| spl0_420 ),
inference(sat_conversion,[],[f3335]) ).
cnf(s498,plain,
( ~ spl0_133
| ~ spl0_268
| ~ spl0_420
| spl0_429 ),
inference(sat_conversion,[],[f3361]) ).
cnf(s502,plain,
~ spl0_429,
inference(sat_conversion,[],[f3368]) ).
cnf(s504,plain,
( ~ spl0_133
| ~ spl0_268
| ~ spl0_420 ),
inference(rat,[],[s498,s502]) ).
cnf(s523,plain,
~ spl0_60,
inference(rat,[],[s202,s176]) ).
cnf(s533,plain,
~ spl0_291,
inference(rat,[],[s232,s231,s158]) ).
cnf(s540,plain,
spl0_292,
inference(rat,[],[s152,s533]) ).
cnf(s541,plain,
spl0_133,
inference(rat,[],[s253,s540]) ).
cnf(s542,plain,
~ spl0_416,
inference(rat,[],[s490,s160,s205,s540]) ).
cnf(s543,plain,
~ spl0_420,
inference(rat,[],[s504,s205,s541]) ).
cnf(s568,plain,
spl0_261,
inference(rat,[],[s131,s167]) ).
cnf(s569,plain,
spl0_415,
inference(rat,[],[s470,s160,s568]) ).
cnf(s570,plain,
spl0_406,
inference(rat,[],[s473,s542,s569]) ).
cnf(s583,plain,
spl0_228,
inference(rat,[],[s111,s160]) ).
cnf(s619,plain,
spl0_198,
inference(rat,[],[s91,s523]) ).
cnf(s622,plain,
spl0_126,
inference(rat,[],[s212,s619]) ).
cnf(s625,plain,
spl0_195,
inference(rat,[],[s89,s176]) ).
cnf(s626,plain,
~ spl0_419,
inference(rat,[],[s492,s622,s625]) ).
cnf(s635,plain,
~ spl0_322,
inference(rat,[],[s493,s543,s626]) ).
cnf(s636,plain,
~ spl0_321,
inference(rat,[],[s326,s635]) ).
cnf(s637,plain,
~ spl0_131,
inference(rat,[],[s472,s570,s453,s583,s155,s636]) ).
cnf(s668,plain,
$false,
inference(rat,[],[s60,s637,s204]) ).
fof(f3369,plain,
$false,
inference(avatar_sat_refutation,[],[s668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN252-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:39:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.12/1.11 % (4104210)Input is clausal, will run a generic CNF schedule.
% 3.12/1.11 % (4104265)lrs+10_1_sil=8000:sp=occurrence:random_seed=462518369:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.12/1.11 % (4104265)Refutation not found, incomplete strategy
% 3.12/1.11 % (4104265)------------------------------
% 3.12/1.11 % (4104265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.11 % (4104265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.11 % (4104265)CaDiCaL version: 2.1.3
% 3.12/1.11 % (4104265)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.11 % (4104265)Time elapsed: 0.016 s
% 3.12/1.11 % (4104265)Peak memory usage: 89 MB
% 3.12/1.11 % (4104265)Instructions burned: 41 (million)
% 3.12/1.11 % (4104263)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1675035403:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.12/1.11 % (4104262)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=4262588476:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.12/1.11 % (4104266)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1694582891:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.12/1.11 % (4104268)dis-21_1_sil=8000:lcm=predicate:random_seed=3252334552: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)
% 3.12/1.11 % (4104264)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1392510332:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.12/1.11 % (4104267)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=726098753:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.12/1.11 % (4104267)First to succeed.
% 3.12/1.11 % (4104267)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4104210"
% 3.12/1.11 % (4104268)Instruction limit reached!
% 3.12/1.11 % (4104268)------------------------------
% 3.12/1.11 % (4104268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.11 % (4104268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.11 % (4104268)CaDiCaL version: 2.1.3
% 3.12/1.11 % (4104268)Termination reason: Instruction limit
% 3.12/1.11 % (4104268)Termination phase: Saturation
% 3.12/1.11 % (4104268)Time elapsed: 0.055 s
% 3.12/1.11 % (4104268)Peak memory usage: 89 MB
% 3.12/1.11 % (4104268)Instructions burned: 118 (million)
% 3.12/1.11 % (4104266)Instruction limit reached!
% 3.12/1.11 % (4104266)------------------------------
% 3.12/1.11 % (4104266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.11 % (4104266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.11 % (4104266)CaDiCaL version: 2.1.3
% 3.12/1.11 % (4104266)Termination reason: Instruction limit
% 3.12/1.11 % (4104266)Termination phase: Saturation
% 3.12/1.11 % (4104266)Time elapsed: 0.072 s
% 3.12/1.11 % (4104266)Peak memory usage: 89 MB
% 3.12/1.11 % (4104266)Instructions burned: 115 (million)
% 3.12/1.11 % (4104265)------------------------------
% 3.12/1.11 % (4104265)------------------------------
% 3.12/1.11 % (4104276)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=3504468872:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.12/1.11 % (4104276)Refutation not found, incomplete strategy
% 3.12/1.11 % (4104276)------------------------------
% 3.12/1.11 % (4104276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.11 % (4104276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.11 % (4104276)CaDiCaL version: 2.1.3
% 3.12/1.11 % (4104276)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.11 % (4104276)Time elapsed: 0.002 s
% 3.12/1.11 % (4104276)Peak memory usage: 87 MB
% 3.12/1.11 % (4104276)Instructions burned: 1 (million)
% 3.12/1.11 % (4104277)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=94485317:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.12/1.11 % (4104277)Refutation not found, incomplete strategy
% 3.12/1.11 % (4104277)------------------------------
% 3.12/1.11 % (4104277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.11 % (4104277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.11 % (4104277)CaDiCaL version: 2.1.3
% 3.12/1.11 % (4104277)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.11 % (4104277)Time elapsed: 0.014 s
% 3.12/1.11 % (4104277)Peak memory usage: 88 MB
% 3.12/1.11 % (4104277)Instructions burned: 23 (million)
% 3.12/1.11 % (4104278)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1886210143:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.12/1.11 % (4104278)Refutation not found, incomplete strategy
% 3.12/1.11 % (4104278)------------------------------
% 3.12/1.11 % (4104278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.11 % (4104278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.11 % (4104278)CaDiCaL version: 2.1.3
% 3.12/1.11 % (4104278)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.11 % (4104278)Time elapsed: 0.003 s
% 3.12/1.11 % (4104278)Peak memory usage: 88 MB
% 3.12/1.11 % (4104278)Instructions burned: 9 (million)
% 3.12/1.11 % (4104267)Refutation found. Thanks to Tanya!
% 3.12/1.11 % SZS status Unsatisfiable for theBenchmark
% 3.12/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.25 % (4104267)------------------------------
% 3.81/1.25 % (4104267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.25 % (4104267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.25 % (4104267)CaDiCaL version: 2.1.3
% 3.81/1.25 % (4104267)Termination reason: Refutation
% 3.81/1.25 % (4104267)Time elapsed: 0.046 s
% 3.81/1.25 % (4104267)Peak memory usage: 91 MB
% 3.81/1.25 % (4104267)Instructions burned: 70 (million)
% 3.81/1.25 % (4104267)------------------------------
% 3.81/1.25 % (4104267)------------------------------
% 3.81/1.25 % (4104210)Success in time 0.459 s
% 3.81/1.25 % Vampire exiting
%------------------------------------------------------------------------------