%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC010+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 0.08s 0.46s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 14 unt; 7 def)
% Number of atoms : 229 ( 51 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 293 ( 121 ~; 107 |; 44 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 37 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
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)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X3
| app(X8,X9) != X2
| ? [X10] :
( ssItem(X10)
& X7 != X10
& memberP(X3,X10)
& geq(X10,X7) ) ) ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X3
| app(X8,X9) != X2
| ? [X10] :
( ssItem(X10)
& X7 != X10
& memberP(X3,X10)
& geq(X10,X7) ) ) ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ! [X10] :
( ~ ssItem(X10)
| X7 = X10
| ~ memberP(X3,X10)
| ~ geq(X10,X7) )
& ssList(X9) )
& ssList(X8) )
& 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] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ! [X10] :
( ~ ssItem(X10)
| X7 = X10
| ~ memberP(X3,X10)
| ~ geq(X10,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f413,plain,
! [X6,X4,X5] :
( ~ neq(sK50,nil)
| app(X5,X6) != sK47
| app(app(X5,cons(X4,nil)),X6) != sK48
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| ssList(sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
( ~ neq(sK50,nil)
| sK49 = app(sK52,sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
( ~ neq(sK50,nil)
| sK50 = app(app(sK52,cons(sK51,nil)),sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f428,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f429,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f436,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f425,f429]) ).
fof(f443,plain,
! [X6,X4,X5] :
( ~ neq(sK50,nil)
| app(X5,X6) != sK49
| app(app(X5,cons(X4,nil)),X6) != sK50
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f413,f428,f429]) ).
fof(f481,definition,
( spl54_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl54_2])],[avatar_definition]) ).
fof(f487,definition,
( spl54_3
<=> ! [X6,X4,X5] :
( app(X5,X6) != sK49
| ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK50 ) ),
introduced(definition,[new_symbols(definition,[spl54_3])],[avatar_definition]) ).
fof(f488,plain,
( ! [X6,X4,X5] :
( ~ ssItem(X4)
| app(X5,X6) != sK49
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK50 )
| ~ spl54_3 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f489,plain,
( spl54_3
| ~ spl54_2 ),
inference(avatar_split_clause,[],[f443,f481,f487]) ).
fof(f492,definition,
( spl54_4
<=> ssList(sK53) ),
introduced(definition,[new_symbols(definition,[spl54_4])],[avatar_definition]) ).
fof(f494,plain,
( ssList(sK53)
| ~ spl54_4 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f495,plain,
( spl54_4
| ~ spl54_2 ),
inference(avatar_split_clause,[],[f415,f481,f492]) ).
fof(f497,definition,
( spl54_5
<=> sK49 = app(sK52,sK53) ),
introduced(definition,[new_symbols(definition,[spl54_5])],[avatar_definition]) ).
fof(f499,plain,
( sK49 = app(sK52,sK53)
| ~ spl54_5 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f500,plain,
( spl54_5
| ~ spl54_2 ),
inference(avatar_split_clause,[],[f416,f481,f497]) ).
fof(f502,definition,
( spl54_6
<=> sK50 = app(app(sK52,cons(sK51,nil)),sK53) ),
introduced(definition,[new_symbols(definition,[spl54_6])],[avatar_definition]) ).
fof(f504,plain,
( sK50 = app(app(sK52,cons(sK51,nil)),sK53)
| ~ spl54_6 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f505,plain,
( spl54_6
| ~ spl54_2 ),
inference(avatar_split_clause,[],[f417,f481,f502]) ).
fof(f510,definition,
( spl54_7
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl54_7])],[avatar_definition]) ).
fof(f512,plain,
( ssList(sK52)
| ~ spl54_7 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f514,plain,
( spl54_7
| ~ spl54_2 ),
inference(avatar_split_clause,[],[f422,f481,f510]) ).
fof(f516,definition,
( spl54_8
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl54_8])],[avatar_definition]) ).
fof(f518,plain,
( ssItem(sK51)
| ~ spl54_8 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f519,plain,
( spl54_8
| ~ spl54_2 ),
inference(avatar_split_clause,[],[f423,f481,f516]) ).
fof(f521,plain,
spl54_2,
inference(avatar_split_clause,[],[f436,f481]) ).
fof(f554,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sK49
| sK50 != app(app(X0,cons(sK51,nil)),X1) )
| ~ spl54_3
| ~ spl54_8 ),
inference(resolution,[],[f488,f518]) ).
fof(f557,plain,
( ! [X0] :
( ~ ssList(X0)
| sK49 != app(sK52,X0)
| sK50 != app(app(sK52,cons(sK51,nil)),X0) )
| ~ spl54_3
| ~ spl54_7
| ~ spl54_8 ),
inference(resolution,[],[f554,f512]) ).
fof(f671,plain,
( sK49 != app(sK52,sK53)
| sK50 != app(app(sK52,cons(sK51,nil)),sK53)
| ~ spl54_3
| ~ spl54_4
| ~ spl54_7
| ~ spl54_8 ),
inference(resolution,[],[f557,f494]) ).
fof(f672,plain,
( sK50 != app(app(sK52,cons(sK51,nil)),sK53)
| ~ spl54_3
| ~ spl54_4
| ~ spl54_5
| ~ spl54_7
| ~ spl54_8 ),
inference(forward_subsumption_resolution,[],[f671,f499]) ).
fof(f709,plain,
( $false
| ~ spl54_3
| ~ spl54_4
| ~ spl54_5
| ~ spl54_6
| ~ spl54_7
| ~ spl54_8 ),
inference(forward_subsumption_resolution,[],[f672,f504]) ).
fof(f710,plain,
( ~ spl54_3
| ~ spl54_4
| ~ spl54_5
| ~ spl54_6
| ~ spl54_7
| ~ spl54_8 ),
inference(avatar_contradiction_clause,[],[f709]) ).
cnf(s3,plain,
( ~ spl54_2
| spl54_3 ),
inference(sat_conversion,[],[f489]) ).
cnf(s5,plain,
( ~ spl54_2
| spl54_4 ),
inference(sat_conversion,[],[f495]) ).
cnf(s6,plain,
( ~ spl54_2
| spl54_5 ),
inference(sat_conversion,[],[f500]) ).
cnf(s7,plain,
( ~ spl54_2
| spl54_6 ),
inference(sat_conversion,[],[f505]) ).
cnf(s12,plain,
( ~ spl54_2
| spl54_7 ),
inference(sat_conversion,[],[f514]) ).
cnf(s13,plain,
( ~ spl54_2
| spl54_8 ),
inference(sat_conversion,[],[f519]) ).
cnf(s15,plain,
spl54_2,
inference(sat_conversion,[],[f521]) ).
cnf(s38,plain,
( ~ spl54_3
| ~ spl54_4
| ~ spl54_5
| ~ spl54_6
| ~ spl54_7
| ~ spl54_8 ),
inference(sat_conversion,[],[f710]) ).
cnf(s42,plain,
spl54_8,
inference(rat,[],[s13,s15]) ).
cnf(s43,plain,
spl54_7,
inference(rat,[],[s12,s15]) ).
cnf(s44,plain,
spl54_6,
inference(rat,[],[s7,s15]) ).
cnf(s45,plain,
spl54_5,
inference(rat,[],[s6,s15]) ).
cnf(s46,plain,
spl54_4,
inference(rat,[],[s5,s15]) ).
cnf(s47,plain,
~ spl54_3,
inference(rat,[],[s38,s42,s43,s44,s45,s46]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s3,s47,s15]) ).
fof(f711,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC010+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.37 % Computer : n016.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 28 07:30:03 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.41 Running first-order model finding
% 0.08/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.46 % (3454766)Will run a generic schedule for satisfiability detection.
% 0.08/0.46 % (3454775)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=974569108:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.46 % (3454772)% WARNING: option uhcvi not known.
% 0.08/0.46 % (3454771)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=54004015_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.46 % (3454772)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2016505097:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.46 % (3454773)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1556588522:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.46 % (3454774)dis+10_1_sil=32000:sp=arity:random_seed=2653747995:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.46 % (3454775) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3454766-3454775"...
% 0.08/0.46 % (3454777)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2610215817:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.46 % (3454776)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=883406495:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.46 % (3454775)...printing done.
% 0.08/0.46 % (3454775)Refutation found. Thanks to Tanya!
% 0.08/0.46 % SZS status Theorem for theBenchmark
% 0.08/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.46 % (3454775)------------------------------
% 0.08/0.46 % (3454775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.46 % (3454775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.46 % (3454775)CaDiCaL version: 2.1.3
% 0.08/0.46 % (3454775)Termination reason: Refutation
% 0.08/0.46 % (3454775)Time elapsed: 0.008 s
% 0.08/0.46 % (3454775)Peak memory usage: 13 MB
% 0.08/0.46 % (3454775)Instructions burned: 23 (million)
% 0.08/0.46 % (3454766)Success in time 0.041 s
% 0.08/0.46 % Vampire exiting
%------------------------------------------------------------------------------