%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC011+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 : 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 01:04:16 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 15 unt; 7 def)
% Number of atoms : 237 ( 50 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 281 ( 109 ~; 115 |; 36 &)
% ( 7 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 35 !; 20 ?)
% 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 ) ) ) ) )
& ( ~ 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)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X3
| app(X8,X9) != X2 ) ) ) ) )
& ( ~ 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
& 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
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f411,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(f413,plain,
( ~ neq(sK50,nil)
| ssList(sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
( ~ neq(sK50,nil)
| sK49 = app(sK52,sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| sK50 = app(app(sK52,cons(sK51,nil)),sK53) ),
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f427,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f434,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f423,f427]) ).
fof(f441,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,[],[f411,f426,f427]) ).
fof(f598,plain,
~ neq(sK50,nil),
inference(consistent_polarity_flipping,[],[f434]) ).
fof(f600,plain,
( neq(sK50,nil)
| ~ ssItem(sK51) ),
inference(consistent_polarity_flipping,[],[f421]) ).
fof(f601,plain,
( neq(sK50,nil)
| ssList(sK52) ),
inference(consistent_polarity_flipping,[],[f420]) ).
fof(f606,plain,
( neq(sK50,nil)
| sK50 = app(app(sK52,cons(sK51,nil)),sK53) ),
inference(consistent_polarity_flipping,[],[f415]) ).
fof(f607,plain,
( neq(sK50,nil)
| sK49 = app(sK52,sK53) ),
inference(consistent_polarity_flipping,[],[f414]) ).
fof(f608,plain,
( neq(sK50,nil)
| ssList(sK53) ),
inference(consistent_polarity_flipping,[],[f413]) ).
fof(f610,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(consistent_polarity_flipping,[],[f441]) ).
fof(f619,definition,
( spl54_1
<=> ! [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_1])],[avatar_definition]) ).
fof(f620,plain,
( ! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK50
| ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(X5,X6) != sK49 )
| ~ spl54_1 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f622,definition,
( spl54_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl54_2])],[avatar_definition]) ).
fof(f625,plain,
( spl54_1
| spl54_2 ),
inference(avatar_split_clause,[],[f610,f622,f619]) ).
fof(f628,definition,
( spl54_3
<=> ssList(sK53) ),
introduced(definition,[new_symbols(definition,[spl54_3])],[avatar_definition]) ).
fof(f630,plain,
( ssList(sK53)
| ~ spl54_3 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f631,plain,
( spl54_3
| spl54_2 ),
inference(avatar_split_clause,[],[f608,f622,f628]) ).
fof(f633,definition,
( spl54_4
<=> sK49 = app(sK52,sK53) ),
introduced(definition,[new_symbols(definition,[spl54_4])],[avatar_definition]) ).
fof(f635,plain,
( sK49 = app(sK52,sK53)
| ~ spl54_4 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f636,plain,
( spl54_4
| spl54_2 ),
inference(avatar_split_clause,[],[f607,f622,f633]) ).
fof(f638,definition,
( spl54_5
<=> sK50 = app(app(sK52,cons(sK51,nil)),sK53) ),
introduced(definition,[new_symbols(definition,[spl54_5])],[avatar_definition]) ).
fof(f640,plain,
( sK50 = app(app(sK52,cons(sK51,nil)),sK53)
| ~ spl54_5 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f641,plain,
( spl54_5
| spl54_2 ),
inference(avatar_split_clause,[],[f606,f622,f638]) ).
fof(f646,definition,
( spl54_6
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl54_6])],[avatar_definition]) ).
fof(f648,plain,
( ssList(sK52)
| ~ spl54_6 ),
inference(avatar_component_clause,[],[f646]) ).
fof(f650,plain,
( spl54_6
| spl54_2 ),
inference(avatar_split_clause,[],[f601,f622,f646]) ).
fof(f652,definition,
( spl54_7
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl54_7])],[avatar_definition]) ).
fof(f654,plain,
( ~ ssItem(sK51)
| spl54_7 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f655,plain,
( ~ spl54_7
| spl54_2 ),
inference(avatar_split_clause,[],[f600,f622,f652]) ).
fof(f657,plain,
~ spl54_2,
inference(avatar_split_clause,[],[f598,f622]) ).
fof(f693,plain,
( sK50 != sK50
| ssItem(sK51)
| ~ ssList(sK52)
| ~ ssList(sK53)
| sK49 != app(sK52,sK53)
| ~ spl54_1
| ~ spl54_5 ),
inference(superposition,[],[f620,f640]) ).
fof(f694,plain,
( ssItem(sK51)
| ~ ssList(sK52)
| ~ ssList(sK53)
| sK49 != app(sK52,sK53)
| ~ spl54_1
| ~ spl54_5 ),
inference(trivial_inequality_removal,[],[f693]) ).
fof(f695,plain,
( ~ ssList(sK52)
| ~ ssList(sK53)
| sK49 != app(sK52,sK53)
| ~ spl54_1
| ~ spl54_5
| spl54_7 ),
inference(forward_subsumption_resolution,[],[f694,f654]) ).
fof(f696,plain,
( ~ ssList(sK53)
| sK49 != app(sK52,sK53)
| ~ spl54_1
| ~ spl54_5
| ~ spl54_6
| spl54_7 ),
inference(forward_subsumption_resolution,[],[f695,f648]) ).
fof(f697,plain,
( sK49 != app(sK52,sK53)
| ~ spl54_1
| ~ spl54_3
| ~ spl54_5
| ~ spl54_6
| spl54_7 ),
inference(forward_subsumption_resolution,[],[f696,f630]) ).
fof(f698,plain,
( $false
| ~ spl54_1
| ~ spl54_3
| ~ spl54_4
| ~ spl54_5
| ~ spl54_6
| spl54_7 ),
inference(forward_subsumption_resolution,[],[f697,f635]) ).
fof(f699,plain,
( ~ spl54_1
| ~ spl54_3
| ~ spl54_4
| ~ spl54_5
| ~ spl54_6
| spl54_7 ),
inference(avatar_contradiction_clause,[],[f698]) ).
cnf(s1,plain,
( spl54_1
| spl54_2 ),
inference(sat_conversion,[],[f625]) ).
cnf(s3,plain,
( spl54_2
| spl54_3 ),
inference(sat_conversion,[],[f631]) ).
cnf(s4,plain,
( spl54_2
| spl54_4 ),
inference(sat_conversion,[],[f636]) ).
cnf(s5,plain,
( spl54_2
| spl54_5 ),
inference(sat_conversion,[],[f641]) ).
cnf(s10,plain,
( spl54_2
| spl54_6 ),
inference(sat_conversion,[],[f650]) ).
cnf(s11,plain,
( spl54_2
| ~ spl54_7 ),
inference(sat_conversion,[],[f655]) ).
cnf(s13,plain,
~ spl54_2,
inference(sat_conversion,[],[f657]) ).
cnf(s23,plain,
( ~ spl54_1
| ~ spl54_3
| ~ spl54_4
| ~ spl54_5
| ~ spl54_6
| spl54_7 ),
inference(sat_conversion,[],[f699]) ).
cnf(s28,plain,
~ spl54_7,
inference(rat,[],[s11,s13]) ).
cnf(s29,plain,
spl54_6,
inference(rat,[],[s10,s13]) ).
cnf(s30,plain,
spl54_5,
inference(rat,[],[s5,s13]) ).
cnf(s31,plain,
spl54_4,
inference(rat,[],[s4,s13]) ).
cnf(s32,plain,
spl54_3,
inference(rat,[],[s3,s13]) ).
cnf(s33,plain,
~ spl54_1,
inference(rat,[],[s23,s28,s29,s30,s31,s32]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s13,s33]) ).
fof(f700,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC011+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:25:46 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.18/0.47 % (2859411)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (2859417)% WARNING: option uhcvi not known.
% 0.18/0.47 % (2859417)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=847884263:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (2859417) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2859411-2859417"...
% 0.18/0.47 % (2859417)...printing done.
% 0.18/0.47 % (2859417)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (2859417)------------------------------
% 0.18/0.47 % (2859417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (2859417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (2859417)CaDiCaL version: 2.1.3
% 0.18/0.47 % (2859417)Termination reason: Refutation
% 0.18/0.47 % (2859417)Time elapsed: 0.004 s
% 0.18/0.47 % (2859417)Peak memory usage: 12 MB
% 0.18/0.47 % (2859417)Instructions burned: 11 (million)
% 0.18/0.47 % (2859411)Success in time 0.036 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------