%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN109-1 : 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 : n010.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 01:49:41 PM UTC 2026
% Result : Unsatisfiable 2.83s 1.18s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 18 unt; 6 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 55 ~; 47 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 7 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
s0(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f22,axiom,
p0(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
fof(f26,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
fof(f33,axiom,
q0(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
fof(f39,axiom,
! [X0,X1] :
( k1(X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_001) ).
fof(f67,axiom,
! [X0,X1] :
( m1(X0,X1,X0)
| ~ p0(X0,X1)
| ~ s0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_029) ).
fof(f131,axiom,
! [X0,X1] :
( q1(X0,X0,X0)
| ~ q0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_093) ).
fof(f165,axiom,
! [X2,X3,X0,X1] :
( ~ k1(X3)
| ~ m1(X2,X1,X0)
| k2(X0,X1)
| ~ k2(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_127) ).
fof(f167,axiom,
! [X0,X1] :
( k2(X0,X0)
| ~ q1(X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_129) ).
fof(f369,negated_conjecture,
~ k2(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f734,definition,
( spl0_93
<=> k2(b,c) ),
introduced(definition,[new_symbols(definition,[spl0_93])],[avatar_definition]) ).
fof(f736,plain,
( ~ k2(b,c)
| spl0_93 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f1116,definition,
( spl0_188
<=> k1(c) ),
introduced(definition,[new_symbols(definition,[spl0_188])],[avatar_definition]) ).
fof(f1117,plain,
( k1(c)
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1118,plain,
( ~ k1(c)
| spl0_188 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1170,definition,
( spl0_201
<=> s0(b) ),
introduced(definition,[new_symbols(definition,[spl0_201])],[avatar_definition]) ).
fof(f1171,plain,
( s0(b)
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f1567,plain,
spl0_201,
inference(avatar_split_clause,[],[f5,f1170]) ).
fof(f1569,plain,
~ spl0_93,
inference(avatar_split_clause,[],[f369,f734]) ).
fof(f1795,plain,
( ! [X0] : ~ n0(X0,c)
| spl0_188 ),
inference(resolution,[],[f1118,f39]) ).
fof(f1798,plain,
( $false
| spl0_188 ),
inference(resolution,[],[f1795,f26]) ).
fof(f1799,plain,
spl0_188,
inference(avatar_contradiction_clause,[],[f1798]) ).
fof(f1800,plain,
( ! [X2,X0,X1] :
( ~ k2(c,X1)
| k2(X2,X1)
| ~ m1(X0,X1,X2) )
| ~ spl0_188 ),
inference(resolution,[],[f1117,f165]) ).
fof(f1898,definition,
( spl0_306
<=> ! [X0] : ~ q0(X0,c) ),
introduced(definition,[new_symbols(definition,[spl0_306])],[avatar_definition]) ).
fof(f1899,plain,
( ! [X0] : ~ q0(X0,c)
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f1898]) ).
fof(f2321,plain,
( $false
| ~ spl0_306 ),
inference(resolution,[],[f1899,f33]) ).
fof(f2322,plain,
~ spl0_306,
inference(avatar_contradiction_clause,[],[f2321]) ).
fof(f2335,plain,
( ! [X2,X0,X1] :
( k2(X0,c)
| ~ m1(X1,c,X0)
| ~ q1(X2,c,c) )
| ~ spl0_188 ),
inference(resolution,[],[f1800,f167]) ).
fof(f2337,definition,
( spl0_331
<=> ! [X2] : ~ q1(X2,c,c) ),
introduced(definition,[new_symbols(definition,[spl0_331])],[avatar_definition]) ).
fof(f2338,plain,
( ! [X2] : ~ q1(X2,c,c)
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f2337]) ).
fof(f2340,definition,
( spl0_332
<=> ! [X0,X1] :
( k2(X0,c)
| ~ m1(X1,c,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_332])],[avatar_definition]) ).
fof(f2341,plain,
( ! [X0,X1] :
( k2(X0,c)
| ~ m1(X1,c,X0) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f2340]) ).
fof(f2342,plain,
( spl0_331
| spl0_332
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2335,f1116,f2340,f2337]) ).
fof(f2343,plain,
( ! [X0] : ~ q0(X0,c)
| ~ spl0_331 ),
inference(resolution,[],[f2338,f131]) ).
fof(f2364,plain,
( spl0_306
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f2343,f2337,f1898]) ).
fof(f2472,plain,
( ! [X0] : ~ m1(X0,c,b)
| spl0_93
| ~ spl0_332 ),
inference(resolution,[],[f2341,f736]) ).
fof(f2474,plain,
( ~ p0(b,c)
| ~ s0(b)
| spl0_93
| ~ spl0_332 ),
inference(resolution,[],[f2472,f67]) ).
fof(f2481,plain,
( ~ s0(b)
| spl0_93
| ~ spl0_332 ),
inference(forward_subsumption_resolution,[],[f2474,f22]) ).
fof(f2485,plain,
( $false
| spl0_93
| ~ spl0_201
| ~ spl0_332 ),
inference(forward_subsumption_resolution,[],[f2481,f1171]) ).
fof(f2486,plain,
( spl0_93
| ~ spl0_201
| ~ spl0_332 ),
inference(avatar_contradiction_clause,[],[f2485]) ).
cnf(s167,plain,
spl0_201,
inference(sat_conversion,[],[f1567]) ).
cnf(s169,plain,
~ spl0_93,
inference(sat_conversion,[],[f1569]) ).
cnf(s250,plain,
spl0_188,
inference(sat_conversion,[],[f1799]) ).
cnf(s340,plain,
~ spl0_306,
inference(sat_conversion,[],[f2322]) ).
cnf(s341,plain,
( ~ spl0_188
| spl0_331
| spl0_332 ),
inference(sat_conversion,[],[f2342]) ).
cnf(s347,plain,
( spl0_306
| ~ spl0_331 ),
inference(sat_conversion,[],[f2364]) ).
cnf(s362,plain,
( spl0_93
| ~ spl0_201
| ~ spl0_332 ),
inference(sat_conversion,[],[f2486]) ).
cnf(s365,plain,
~ spl0_331,
inference(rat,[],[s347,s340]) ).
cnf(s369,plain,
spl0_332,
inference(rat,[],[s341,s365,s250]) ).
cnf(s374,plain,
~ spl0_201,
inference(rat,[],[s362,s369,s169]) ).
cnf(s376,plain,
$false,
inference(rat,[],[s167,s374]) ).
fof(f2487,plain,
$false,
inference(avatar_sat_refutation,[],[s376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN109-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.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 15:34:47 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.83/1.18 % (2011416)Input is clausal, will run a generic CNF schedule.
% 2.83/1.18 % (2011426)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1272526904:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.83/1.18 % (2011426)First to succeed.
% 2.83/1.18 % (2011426)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2011416"
% 2.83/1.18 % (2011422)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3023230306:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.83/1.18 % (2011423)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1528806477:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.83/1.18 % (2011424)lrs+10_1_sil=8000:sp=occurrence:random_seed=4105902088:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.83/1.18 % (2011421)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=528166528:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.83/1.18 % (2011425)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=844253253:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.83/1.18 % (2011427)dis-21_1_sil=8000:lcm=predicate:random_seed=660157203: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)
% 2.83/1.18 % (2011424)Also succeeded, but the first one will report.
% 2.83/1.18 % (2011425)Also succeeded, but the first one will report.
% 2.83/1.18 % (2011427)Instruction limit reached!
% 2.83/1.18 % (2011427)------------------------------
% 2.83/1.18 % (2011427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.18 % (2011427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.18 % (2011427)CaDiCaL version: 2.1.3
% 2.83/1.18 % (2011427)Termination reason: Instruction limit
% 2.83/1.18 % (2011427)Termination phase: Saturation
% 2.83/1.18 % (2011427)Time elapsed: 0.056 s
% 2.83/1.18 % (2011427)Peak memory usage: 89 MB
% 2.83/1.18 % (2011427)Instructions burned: 118 (million)
% 2.83/1.18 % (2011426)Refutation found. Thanks to Tanya!
% 2.83/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.83/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.18 % (2011426)------------------------------
% 2.83/1.18 % (2011426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.18 % (2011426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.18 % (2011426)CaDiCaL version: 2.1.3
% 2.83/1.18 % (2011426)Termination reason: Refutation
% 2.83/1.18 % (2011426)Time elapsed: 0.019 s
% 2.83/1.18 % (2011426)Peak memory usage: 90 MB
% 2.83/1.18 % (2011426)Instructions burned: 48 (million)
% 2.83/1.18 % (2011426)------------------------------
% 2.83/1.18 % (2011426)------------------------------
% 2.83/1.18 % (2011416)Success in time 0.314 s
% 2.83/1.18 % Vampire exiting
%------------------------------------------------------------------------------