%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC012+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 01:04:16 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 18 unt; 5 def)
% Number of atoms : 210 ( 52 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 267 ( 113 ~; 98 |; 40 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 37 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(X5,X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> app(X2,cons(X7,nil)) != X3 ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(X5,X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> app(X2,cons(X7,nil)) != X3 ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(X5,X6) != X0 ) ) )
& ? [X7] :
( app(X2,cons(X7,nil)) = X3
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(X5,X6) != X0 ) ) )
& ? [X7] :
( app(X2,cons(X7,nil)) = X3
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( neq(sK54,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK54
| app(X5,X6) != sK53 ) ) )
& sK56 = app(sK55,cons(sK57,nil))
& ssItem(sK57) )
| ( neq(sK54,nil)
& ~ neq(sK56,nil) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57)],[f222]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( sK56 = app(sK55,cons(sK57,nil))
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK54
| app(X5,X6) != sK53
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( neq(sK54,nil)
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
( neq(sK56,nil)
| neq(sK56,nil) ),
inference(definition_unfolding,[],[f507,f509,f509]) ).
fof(f513,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK56
| app(X5,X6) != sK55
| ~ neq(sK56,nil) ),
inference(definition_unfolding,[],[f504,f509,f508]) ).
fof(f545,plain,
neq(sK56,nil),
inference(duplicate_literal_removal,[],[f510]) ).
fof(f554,definition,
( spl58_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f558,definition,
( spl58_2
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f560,plain,
( ssItem(sK57)
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f561,plain,
( ~ spl58_1
| spl58_2 ),
inference(avatar_split_clause,[],[f500,f558,f554]) ).
fof(f564,definition,
( spl58_3
<=> sK56 = app(sK55,cons(sK57,nil)) ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f566,plain,
( sK56 = app(sK55,cons(sK57,nil))
| ~ spl58_3 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f567,plain,
( ~ spl58_1
| spl58_3 ),
inference(avatar_split_clause,[],[f502,f564,f554]) ).
fof(f570,definition,
( spl58_4
<=> ! [X6,X4,X5] :
( ~ ssItem(X4)
| app(X5,X6) != sK55
| app(app(X5,cons(X4,nil)),X6) != sK56
| ~ ssList(X6)
| ~ ssList(X5) ) ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f571,plain,
( ! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK56
| app(X5,X6) != sK55
| ~ ssItem(X4)
| ~ ssList(X6)
| ~ ssList(X5) )
| ~ spl58_4 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f572,plain,
( ~ spl58_1
| spl58_4 ),
inference(avatar_split_clause,[],[f513,f570,f554]) ).
fof(f574,plain,
spl58_1,
inference(avatar_split_clause,[],[f545,f554]) ).
fof(f576,definition,
( spl58_5
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f577,plain,
( ssList(nil)
| ~ spl58_5 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f609,plain,
spl58_5,
inference(avatar_split_clause,[],[f389,f576]) ).
fof(f610,plain,
( ! [X0] :
( sK56 != app(sK56,X0)
| sK55 != app(sK55,X0)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(sK55) )
| ~ spl58_3
| ~ spl58_4 ),
inference(superposition,[],[f571,f566]) ).
fof(f611,plain,
( ! [X0] :
( sK56 != app(sK56,X0)
| sK55 != app(sK55,X0)
| ~ ssList(X0)
| ~ ssList(sK55) )
| ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f610,f560]) ).
fof(f612,plain,
( ! [X0] :
( sK56 != app(sK56,X0)
| sK55 != app(sK55,X0)
| ~ ssList(X0) )
| ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f611,f498]) ).
fof(f856,plain,
sK55 = app(sK55,nil),
inference(resolution,[],[f482,f498]) ).
fof(f857,plain,
sK56 = app(sK56,nil),
inference(resolution,[],[f482,f499]) ).
fof(f863,plain,
( sK56 != sK56
| sK55 != app(sK55,nil)
| ~ ssList(nil)
| ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(superposition,[],[f612,f857]) ).
fof(f864,plain,
( sK55 != app(sK55,nil)
| ~ ssList(nil)
| ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(trivial_inequality_removal,[],[f863]) ).
fof(f865,plain,
( ~ ssList(nil)
| ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f864,f856]) ).
fof(f866,plain,
( $false
| ~ spl58_2
| ~ spl58_3
| ~ spl58_4
| ~ spl58_5 ),
inference(forward_subsumption_resolution,[],[f865,f577]) ).
fof(f867,plain,
( ~ spl58_2
| ~ spl58_3
| ~ spl58_4
| ~ spl58_5 ),
inference(avatar_contradiction_clause,[],[f866]) ).
cnf(s1,plain,
( ~ spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f561]) ).
cnf(s3,plain,
( ~ spl58_1
| spl58_3 ),
inference(sat_conversion,[],[f567]) ).
cnf(s5,plain,
( ~ spl58_1
| spl58_4 ),
inference(sat_conversion,[],[f572]) ).
cnf(s7,plain,
spl58_1,
inference(sat_conversion,[],[f574]) ).
cnf(s16,plain,
spl58_5,
inference(sat_conversion,[],[f609]) ).
cnf(s29,plain,
( ~ spl58_2
| ~ spl58_3
| ~ spl58_4
| ~ spl58_5 ),
inference(sat_conversion,[],[f867]) ).
cnf(s34,plain,
spl58_4,
inference(rat,[],[s5,s7]) ).
cnf(s35,plain,
spl58_3,
inference(rat,[],[s3,s7]) ).
cnf(s36,plain,
~ spl58_2,
inference(rat,[],[s29,s16,s34,s35]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s1,s36,s7]) ).
fof(f868,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC012+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 07:25:21 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % (999658)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (999666)dis+10_1_sil=32000:sp=arity:random_seed=2738504133:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (999666) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-999658-999666"...
% 0.11/0.44 % (999664)% WARNING: option uhcvi not known.
% 0.11/0.44 % (999663)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3907808118_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.44 % (999665)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3684117426:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (999666)...printing done.
% 0.11/0.44 % (999667)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=21781077:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.44 % (999668)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1220308843:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.44 % (999669)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1416859280:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % (999666)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (999666)------------------------------
% 0.11/0.44 % (999666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (999666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (999666)CaDiCaL version: 2.1.3
% 0.11/0.44 % (999666)Termination reason: Refutation
% 0.11/0.44 % (999666)Time elapsed: 0.007 s
% 0.11/0.44 % (999666)Peak memory usage: 13 MB
% 0.11/0.44 % (999666)Instructions burned: 19 (million)
% 0.11/0.44 % (999658)Success in time 0.038 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------