%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN206-1 : 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 : n014.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 01:49:55 PM UTC 2026
% Result : Unsatisfiable 2.31s 0.89s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 76 ( 22 unt; 9 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 182 ( 91 ~; 82 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 10 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
n0(d,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
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(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(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(f163,axiom,
! [X0] :
( ~ p0(X0,X0)
| s1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_125) ).
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] :
( ~ s2(X0)
| ~ q2(X2,X0,X2)
| s3(X0,X1)
| ~ m0(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_273) ).
fof(f369,negated_conjecture,
~ s3(b,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
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] :
( s2(X0)
| ~ q2(b,X0,b) )
| ~ 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(f1129,definition,
( spl0_191
<=> k1(b) ),
introduced(definition,[new_symbols(definition,[spl0_191])],[avatar_definition]) ).
fof(f1130,plain,
( k1(b)
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f1131,plain,
( ~ k1(b)
| spl0_191 ),
inference(avatar_component_clause,[],[f1129]) ).
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(f1558,plain,
spl0_134,
inference(avatar_split_clause,[],[f24,f900]) ).
fof(f1661,plain,
( ! [X0] : ~ n0(X0,b)
| spl0_191 ),
inference(resolution,[],[f39,f1131]) ).
fof(f1685,plain,
( $false
| spl0_191 ),
inference(resolution,[],[f1661,f7]) ).
fof(f1690,plain,
spl0_191,
inference(avatar_contradiction_clause,[],[f1685]) ).
fof(f1701,plain,
s1(b),
inference(resolution,[],[f163,f14]) ).
fof(f1705,plain,
spl0_130,
inference(avatar_split_clause,[],[f1701,f885]) ).
fof(f1826,plain,
( ! [X0] : ~ n0(X0,c)
| spl0_287 ),
inference(resolution,[],[f40,f1530]) ).
fof(f1847,plain,
( $false
| spl0_287 ),
inference(resolution,[],[f1826,f26]) ).
fof(f1848,plain,
spl0_287,
inference(avatar_contradiction_clause,[],[f1847]) ).
fof(f1851,plain,
( ~ l0(c)
| ~ spl0_287
| ~ spl0_291 ),
inference(resolution,[],[f1529,f1545]) ).
fof(f1852,plain,
( $false
| ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(forward_subsumption_resolution,[],[f1851,f901]) ).
fof(f1853,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(avatar_contradiction_clause,[],[f1852]) ).
fof(f1885,plain,
( ! [X0] :
( ~ k1(X0)
| q2(X0,X0,X0) )
| ~ spl0_292 ),
inference(resolution,[],[f1548,f224]) ).
fof(f1887,plain,
( spl0_133
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f1885,f1547,f896]) ).
fof(f2100,definition,
( spl0_309
<=> s2(b) ),
introduced(definition,[new_symbols(definition,[spl0_309])],[avatar_definition]) ).
fof(f2101,plain,
( s2(b)
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f2100]) ).
fof(f2102,plain,
( ~ s2(b)
| spl0_309 ),
inference(avatar_component_clause,[],[f2100]) ).
fof(f2107,plain,
( ~ q2(b,b,b)
| ~ spl0_131
| spl0_309 ),
inference(resolution,[],[f2102,f890]) ).
fof(f2132,plain,
( ~ k1(b)
| ~ spl0_131
| ~ spl0_133
| spl0_309 ),
inference(resolution,[],[f2107,f897]) ).
fof(f2142,plain,
( $false
| ~ spl0_131
| ~ spl0_133
| ~ spl0_191
| spl0_309 ),
inference(forward_subsumption_resolution,[],[f2132,f1130]) ).
fof(f2143,plain,
( ~ spl0_131
| ~ spl0_133
| ~ spl0_191
| spl0_309 ),
inference(avatar_contradiction_clause,[],[f2142]) ).
fof(f2147,plain,
( ! [X2,X0,X1] :
( s3(b,X1)
| ~ q2(X0,b,X0)
| ~ m0(X0,X2,X1) )
| ~ spl0_309 ),
inference(resolution,[],[f2101,f311]) ).
fof(f2575,plain,
( ! [X0,X1] :
( ~ m0(X0,X1,b)
| ~ q2(X0,b,X0) )
| ~ spl0_309 ),
inference(resolution,[],[f2147,f369]) ).
fof(f2576,plain,
( ! [X0] : ~ q2(X0,b,X0)
| ~ spl0_309 ),
inference(resolution,[],[f2575,f19]) ).
fof(f2579,plain,
( ~ k1(b)
| ~ spl0_133
| ~ spl0_309 ),
inference(resolution,[],[f2576,f897]) ).
fof(f2596,plain,
( $false
| ~ spl0_133
| ~ spl0_191
| ~ spl0_309 ),
inference(forward_subsumption_resolution,[],[f2579,f1130]) ).
fof(f2597,plain,
( ~ spl0_133
| ~ spl0_191
| ~ spl0_309 ),
inference(avatar_contradiction_clause,[],[f2596]) ).
cnf(s60,plain,
( ~ spl0_130
| spl0_131 ),
inference(sat_conversion,[],[f891]) ).
cnf(s152,plain,
( spl0_291
| spl0_292 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s158,plain,
spl0_134,
inference(sat_conversion,[],[f1558]) ).
cnf(s212,plain,
spl0_191,
inference(sat_conversion,[],[f1690]) ).
cnf(s216,plain,
spl0_130,
inference(sat_conversion,[],[f1705]) ).
cnf(s245,plain,
spl0_287,
inference(sat_conversion,[],[f1848]) ).
cnf(s246,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(sat_conversion,[],[f1853]) ).
cnf(s251,plain,
( spl0_133
| ~ spl0_292 ),
inference(sat_conversion,[],[f1887]) ).
cnf(s304,plain,
( ~ spl0_131
| ~ spl0_133
| ~ spl0_191
| spl0_309 ),
inference(sat_conversion,[],[f2143]) ).
cnf(s376,plain,
( ~ spl0_133
| ~ spl0_191
| ~ spl0_309 ),
inference(sat_conversion,[],[f2597]) ).
cnf(s390,plain,
~ spl0_291,
inference(rat,[],[s246,s245,s158]) ).
cnf(s396,plain,
spl0_292,
inference(rat,[],[s152,s390]) ).
cnf(s397,plain,
spl0_133,
inference(rat,[],[s251,s396]) ).
cnf(s398,plain,
~ spl0_309,
inference(rat,[],[s376,s212,s397]) ).
cnf(s400,plain,
~ spl0_131,
inference(rat,[],[s304,s398,s212,s397]) ).
cnf(s506,plain,
$false,
inference(rat,[],[s60,s400,s216]) ).
fof(f2601,plain,
$false,
inference(avatar_sat_refutation,[],[s506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN206-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n014.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 15:38:16 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 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
% 2.31/0.88 % (1863206)Input is clausal, will run a generic CNF schedule.
% 2.31/0.88 % (1863224)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2549356253:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.31/0.88 % (1863224)First to succeed.
% 2.31/0.88 % (1863224)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1863206"
% 2.31/0.88 % (1863222)lrs+10_1_sil=8000:sp=occurrence:random_seed=3849162505:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.31/0.88 % (1863225)dis-21_1_sil=8000:lcm=predicate:random_seed=3875534522: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)
% 2.31/0.88 % (1863219)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=1917111252:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.31/0.88 % (1863220)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2182007872:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.31/0.88 % (1863221)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3149576944:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.31/0.89 % (1863223)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4163282646:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.31/0.89 % (1863222)Also succeeded, but the first one will report.
% 2.31/0.89 % (1863223)Also succeeded, but the first one will report.
% 2.31/0.89 % (1863225)Instruction limit reached!
% 2.31/0.89 % (1863225)------------------------------
% 2.31/0.89 % (1863225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.89 % (1863225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.89 % (1863225)CaDiCaL version: 2.1.3
% 2.31/0.89 % (1863225)Termination reason: Instruction limit
% 2.31/0.89 % (1863225)Termination phase: Saturation
% 2.31/0.89 % (1863225)Time elapsed: 0.055 s
% 2.31/0.89 % (1863225)Peak memory usage: 89 MB
% 2.31/0.89 % (1863225)Instructions burned: 118 (million)
% 2.31/0.89 % (1863224)Refutation found. Thanks to Tanya!
% 2.31/0.89 % SZS status Unsatisfiable for theBenchmark
% 2.31/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.89 % (1863224)------------------------------
% 2.31/0.89 % (1863224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.89 % (1863224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.89 % (1863224)CaDiCaL version: 2.1.3
% 2.31/0.89 % (1863224)Termination reason: Refutation
% 2.31/0.89 % (1863224)Time elapsed: 0.019 s
% 2.31/0.89 % (1863224)Peak memory usage: 91 MB
% 2.31/0.89 % (1863224)Instructions burned: 49 (million)
% 2.31/0.89 % (1863224)------------------------------
% 2.31/0.89 % (1863224)------------------------------
% 2.31/0.89 % (1863206)Success in time 0.272 s
% 2.31/0.89 % Vampire exiting
%------------------------------------------------------------------------------