%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN137-1 : 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 : n009.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 01:49:45 PM UTC 2026
% Result : Unsatisfiable 2.90s 1.15s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 26
% Syntax : Number of formulae : 88 ( 26 unt; 10 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 249 ( 124 ~; 115 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 11 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f11,axiom,
n0(e,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
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(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(f39,axiom,
! [X0,X1] :
( ~ n0(X1,X0)
| k1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).
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(f169,axiom,
! [X0,X1] :
( l2(X0,X1)
| ~ s1(X0)
| ~ n0(e,X1)
| ~ l2(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_131) ).
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(f221,axiom,
! [X0,X1] :
( q2(X0,c,X1)
| ~ k1(X1)
| ~ l0(c)
| ~ l2(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_183) ).
fof(f227,axiom,
! [X0] :
( s2(X0)
| ~ q2(b,X0,b)
| ~ s1(b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_189) ).
fof(f275,axiom,
! [X0] :
( m3(X0,c,X0)
| ~ s2(c)
| ~ q2(X0,c,c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_237) ).
fof(f369,negated_conjecture,
~ m3(b,c,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f508,definition,
( spl0_41
<=> ! [X1] : ~ s1(X1) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f509,plain,
( ! [X1] : ~ s1(X1)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f614,definition,
( spl0_72
<=> s2(c) ),
introduced(definition,[new_symbols(definition,[spl0_72])],[avatar_definition]) ).
fof(f615,plain,
( ~ s2(c)
| spl0_72 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f617,definition,
( spl0_73
<=> ! [X0] :
( m3(X0,c,X0)
| ~ q2(X0,c,c) ) ),
introduced(definition,[new_symbols(definition,[spl0_73])],[avatar_definition]) ).
fof(f618,plain,
( ! [X0] :
( m3(X0,c,X0)
| ~ q2(X0,c,c) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f619,plain,
( ~ spl0_72
| spl0_73 ),
inference(avatar_split_clause,[],[f275,f617,f614]) ).
fof(f748,definition,
( spl0_110
<=> ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_110])],[avatar_definition]) ).
fof(f749,plain,
( ! [X0,X1] :
( ~ q0(X0,X1)
| s1(X0) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f750,plain,
( spl0_41
| spl0_110 ),
inference(avatar_split_clause,[],[f164,f748,f508]) ).
fof(f762,definition,
( spl0_114
<=> s1(b) ),
introduced(definition,[new_symbols(definition,[spl0_114])],[avatar_definition]) ).
fof(f763,plain,
( ~ s1(b)
| spl0_114 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f765,definition,
( spl0_115
<=> ! [X0] :
( s2(X0)
| ~ q2(b,X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl0_115])],[avatar_definition]) ).
fof(f766,plain,
( ! [X0] :
( ~ q2(b,X0,b)
| s2(X0) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f767,plain,
( ~ spl0_114
| spl0_115 ),
inference(avatar_split_clause,[],[f227,f765,f762]) ).
fof(f816,definition,
( spl0_129
<=> l0(c) ),
introduced(definition,[new_symbols(definition,[spl0_129])],[avatar_definition]) ).
fof(f817,plain,
( ~ l0(c)
| spl0_129 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f1087,definition,
( spl0_204
<=> ! [X1] : ~ p0(X1,X1) ),
introduced(definition,[new_symbols(definition,[spl0_204])],[avatar_definition]) ).
fof(f1088,plain,
( ! [X1] : ~ p0(X1,X1)
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f1087]) ).
fof(f1090,definition,
( spl0_205
<=> ! [X2,X0,X3] :
( l2(X0,X0)
| ~ s1(X2)
| ~ m0(X3,X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_205])],[avatar_definition]) ).
fof(f1091,plain,
( ! [X2,X3,X0] :
( l2(X0,X0)
| ~ s1(X2)
| ~ m0(X3,X2,X0) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f1092,plain,
( spl0_204
| spl0_205 ),
inference(avatar_split_clause,[],[f171,f1090,f1087]) ).
fof(f1139,definition,
( spl0_219
<=> ! [X0,X1] :
( q2(X0,c,X1)
| ~ l2(X1,X0)
| ~ k1(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_219])],[avatar_definition]) ).
fof(f1140,plain,
( ! [X0,X1] :
( q2(X0,c,X1)
| ~ l2(X1,X0)
| ~ k1(X1) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1141,plain,
( ~ spl0_129
| spl0_219 ),
inference(avatar_split_clause,[],[f221,f1139,f816]) ).
fof(f1402,plain,
( $false
| spl0_129 ),
inference(forward_subsumption_resolution,[],[f817,f24]) ).
fof(f1403,plain,
spl0_129,
inference(avatar_contradiction_clause,[],[f1402]) ).
fof(f1422,plain,
( $false
| ~ spl0_204 ),
inference(resolution,[],[f1088,f14]) ).
fof(f1423,plain,
~ spl0_204,
inference(avatar_contradiction_clause,[],[f1422]) ).
fof(f1478,plain,
k1(b),
inference(resolution,[],[f39,f7]) ).
fof(f1479,plain,
k1(c),
inference(resolution,[],[f39,f26]) ).
fof(f1503,plain,
( ! [X0] : ~ p0(X0,X0)
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[],[f163,f509]) ).
fof(f1504,plain,
( spl0_204
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f1503,f508,f1087]) ).
fof(f1506,plain,
s1(b),
inference(resolution,[],[f163,f14]) ).
fof(f1507,plain,
( $false
| spl0_114 ),
inference(forward_subsumption_resolution,[],[f1506,f763]) ).
fof(f1508,plain,
spl0_114,
inference(avatar_contradiction_clause,[],[f1507]) ).
fof(f1510,plain,
( ! [X0] : s1(X0)
| ~ spl0_110 ),
inference(resolution,[],[f749,f17]) ).
fof(f1649,plain,
( ! [X2,X3,X0] :
( ~ m0(X3,X2,X0)
| l2(X0,X0) )
| ~ spl0_110
| ~ spl0_205 ),
inference(forward_subsumption_resolution,[],[f1091,f1510]) ).
fof(f1753,plain,
( ! [X0] : l2(X0,X0)
| ~ spl0_110
| ~ spl0_205 ),
inference(resolution,[],[f1649,f19]) ).
fof(f2190,plain,
( ~ l2(b,b)
| ~ k1(b)
| s2(c)
| ~ spl0_115
| ~ spl0_219 ),
inference(resolution,[],[f1140,f766]) ).
fof(f2191,plain,
( ~ k1(b)
| s2(c)
| ~ spl0_110
| ~ spl0_115
| ~ spl0_205
| ~ spl0_219 ),
inference(forward_subsumption_resolution,[],[f2190,f1753]) ).
fof(f2193,plain,
( s2(c)
| ~ spl0_110
| ~ spl0_115
| ~ spl0_205
| ~ spl0_219 ),
inference(forward_subsumption_resolution,[],[f2191,f1478]) ).
fof(f2194,plain,
( $false
| spl0_72
| ~ spl0_110
| ~ spl0_115
| ~ spl0_205
| ~ spl0_219 ),
inference(forward_subsumption_resolution,[],[f2193,f615]) ).
fof(f2195,plain,
( spl0_72
| ~ spl0_110
| ~ spl0_115
| ~ spl0_205
| ~ spl0_219 ),
inference(avatar_contradiction_clause,[],[f2194]) ).
fof(f2196,plain,
( ~ q2(b,c,c)
| ~ spl0_73 ),
inference(resolution,[],[f618,f369]) ).
fof(f2205,plain,
( ~ l2(c,b)
| ~ k1(c)
| ~ spl0_73
| ~ spl0_219 ),
inference(resolution,[],[f2196,f1140]) ).
fof(f2206,plain,
( ~ l2(c,b)
| ~ spl0_73
| ~ spl0_219 ),
inference(forward_subsumption_resolution,[],[f2205,f1479]) ).
fof(f2431,plain,
( ! [X0,X1] :
( l2(X0,X1)
| ~ n0(e,X1)
| ~ l2(X1,X1) )
| ~ spl0_110 ),
inference(forward_subsumption_resolution,[],[f169,f1510]) ).
fof(f2432,plain,
( ! [X0,X1] :
( l2(X0,X1)
| ~ n0(e,X1) )
| ~ spl0_110
| ~ spl0_205 ),
inference(forward_subsumption_resolution,[],[f2431,f1753]) ).
fof(f2444,plain,
( ~ n0(e,b)
| ~ spl0_73
| ~ spl0_110
| ~ spl0_205
| ~ spl0_219 ),
inference(resolution,[],[f2432,f2206]) ).
fof(f2445,plain,
( $false
| ~ spl0_73
| ~ spl0_110
| ~ spl0_205
| ~ spl0_219 ),
inference(forward_subsumption_resolution,[],[f2444,f11]) ).
fof(f2446,plain,
( ~ spl0_73
| ~ spl0_110
| ~ spl0_205
| ~ spl0_219 ),
inference(avatar_contradiction_clause,[],[f2445]) ).
cnf(s30,plain,
( ~ spl0_72
| spl0_73 ),
inference(sat_conversion,[],[f619]) ).
cnf(s48,plain,
( spl0_41
| spl0_110 ),
inference(sat_conversion,[],[f750]) ).
cnf(s50,plain,
( ~ spl0_114
| spl0_115 ),
inference(sat_conversion,[],[f767]) ).
cnf(s103,plain,
( spl0_204
| spl0_205 ),
inference(sat_conversion,[],[f1092]) ).
cnf(s110,plain,
( ~ spl0_129
| spl0_219 ),
inference(sat_conversion,[],[f1141]) ).
cnf(s160,plain,
spl0_129,
inference(sat_conversion,[],[f1403]) ).
cnf(s170,plain,
~ spl0_204,
inference(sat_conversion,[],[f1423]) ).
cnf(s205,plain,
( ~ spl0_41
| spl0_204 ),
inference(sat_conversion,[],[f1504]) ).
cnf(s206,plain,
spl0_114,
inference(sat_conversion,[],[f1508]) ).
cnf(s324,plain,
( spl0_72
| ~ spl0_110
| ~ spl0_115
| ~ spl0_205
| ~ spl0_219 ),
inference(sat_conversion,[],[f2195]) ).
cnf(s344,plain,
( ~ spl0_73
| ~ spl0_110
| ~ spl0_205
| ~ spl0_219 ),
inference(sat_conversion,[],[f2446]) ).
cnf(s350,plain,
~ spl0_41,
inference(rat,[],[s205,s170]) ).
cnf(s384,plain,
spl0_219,
inference(rat,[],[s110,s160]) ).
cnf(s385,plain,
spl0_205,
inference(rat,[],[s103,s170]) ).
cnf(s432,plain,
spl0_115,
inference(rat,[],[s50,s206]) ).
cnf(s434,plain,
spl0_110,
inference(rat,[],[s48,s350]) ).
cnf(s438,plain,
~ spl0_73,
inference(rat,[],[s344,s384,s385,s434]) ).
cnf(s439,plain,
spl0_72,
inference(rat,[],[s324,s384,s385,s432,s434]) ).
cnf(s466,plain,
$false,
inference(rat,[],[s30,s438,s439]) ).
fof(f2454,plain,
$false,
inference(avatar_sat_refutation,[],[s466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN137-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:36:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.90/1.15 % (3158030)Input is clausal, will run a generic CNF schedule.
% 2.90/1.15 % (3158123)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1094809221:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.90/1.15 % (3158118)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=4263093448:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.90/1.15 % (3158124)dis-21_1_sil=8000:lcm=predicate:random_seed=73140160: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)
% 2.90/1.15 % (3158122)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=781701143:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.90/1.15 % (3158120)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1222503677:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.90/1.15 % (3158121)lrs+10_1_sil=8000:sp=occurrence:random_seed=166607502:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.90/1.15 % (3158121)Refutation not found, incomplete strategy
% 2.90/1.15 % (3158121)------------------------------
% 2.90/1.15 % (3158121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.15 % (3158121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.15 % (3158121)CaDiCaL version: 2.1.3
% 2.90/1.15 % (3158121)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.15 % (3158121)Time elapsed: 0.007 s
% 2.90/1.15 % (3158121)Peak memory usage: 88 MB
% 2.90/1.15 % (3158121)Instructions burned: 9 (million)
% 2.90/1.15 % (3158119)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4130733786:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.90/1.15 % (3158122)First to succeed.
% 2.90/1.15 % (3158122)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3158030"
% 2.90/1.15 % (3158123)Also succeeded, but the first one will report.
% 2.90/1.15 % (3158124)Instruction limit reached!
% 2.90/1.15 % (3158124)------------------------------
% 2.90/1.15 % (3158124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.15 % (3158124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.15 % (3158124)CaDiCaL version: 2.1.3
% 2.90/1.15 % (3158124)Termination reason: Instruction limit
% 2.90/1.15 % (3158124)Termination phase: Saturation
% 2.90/1.15 % (3158124)Time elapsed: 0.056 s
% 2.90/1.15 % (3158124)Peak memory usage: 89 MB
% 2.90/1.15 % (3158124)Instructions burned: 118 (million)
% 2.90/1.15 % (3158179)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=3792526438:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.90/1.15 % (3158179)Refutation not found, incomplete strategy
% 2.90/1.15 % (3158179)------------------------------
% 2.90/1.15 % (3158179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.15 % (3158179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.15 % (3158179)CaDiCaL version: 2.1.3
% 2.90/1.15 % (3158179)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.15 % (3158179)Time elapsed: 0.001 s
% 2.90/1.15 % (3158179)Peak memory usage: 87 MB
% 2.90/1.15 % (3158179)Instructions burned: 1 (million)
% 2.90/1.15 % (3158121)------------------------------
% 2.90/1.15 % (3158121)------------------------------
% 2.90/1.15 % (3158122)Refutation found. Thanks to Tanya!
% 2.90/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.90/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.32 % (3158122)------------------------------
% 3.78/1.32 % (3158122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.32 % (3158122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.32 % (3158122)CaDiCaL version: 2.1.3
% 3.78/1.32 % (3158122)Termination reason: Refutation
% 3.78/1.32 % (3158122)Time elapsed: 0.025 s
% 3.78/1.32 % (3158122)Peak memory usage: 90 MB
% 3.78/1.32 % (3158122)Instructions burned: 38 (million)
% 3.78/1.32 % (3158122)------------------------------
% 3.78/1.32 % (3158122)------------------------------
% 3.78/1.32 % (3158030)Success in time 0.459 s
% 3.78/1.32 % Vampire exiting
%------------------------------------------------------------------------------