%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC241+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 : 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 01:05:13 PM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 11 unt; 5 def)
% Number of atoms : 284 ( 40 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 390 ( 171 ~; 164 |; 36 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 44 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( X0 != X1
& leq(X0,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) )
| ( nil != X2
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ~ ssList(X10)
| app(app(X9,cons(X8,nil)),X10) != X2
| ? [X11] :
( ssItem(X11)
& ~ leq(X11,X8)
& memberP(X9,X11)
& memberP(X10,X11)
& leq(X8,X11) ) ) ) ) ) ) ) ) ),
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
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) )
| ( nil != X2
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ~ ssList(X10)
| app(app(X9,cons(X8,nil)),X10) != X2
| ? [X11] :
( ssItem(X11)
& ~ leq(X11,X8)
& memberP(X9,X11)
& memberP(X10,X11)
& leq(X8,X11) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( X0 != X1
& leq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& memberP(X6,X7)
& lt(X4,X7)
& ~ leq(X4,X7) ) ) ) )
& ( nil = X2
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ssList(X10)
& app(app(X9,cons(X8,nil)),X10) = X2
& ! [X11] :
( ~ ssItem(X11)
| leq(X11,X8)
| ~ memberP(X9,X11)
| ~ memberP(X10,X11)
| ~ leq(X8,X11) ) )
& ssList(X9) )
& ssItem(X8) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f405,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| ~ ssItem(X1)
| leq(X0,X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f411,plain,
! [X6,X4,X5] :
( ~ leq(X4,sK54(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f412,plain,
! [X6,X4,X5] :
( lt(X4,sK54(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f415,plain,
! [X6,X4,X5] :
( ssItem(sK54(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f416,plain,
( sK49 = app(app(sK52,cons(sK51,nil)),sK53)
| nil = sK49 ),
inference(cnf_transformation,[],[f221]) ).
fof(f417,plain,
( ssList(sK53)
| nil = sK49 ),
inference(cnf_transformation,[],[f221]) ).
fof(f418,plain,
( ssList(sK52)
| nil = sK49 ),
inference(cnf_transformation,[],[f221]) ).
fof(f419,plain,
( ssItem(sK51)
| nil = sK49 ),
inference(cnf_transformation,[],[f221]) ).
fof(f420,plain,
nil != sK47,
inference(cnf_transformation,[],[f221]) ).
fof(f421,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f221]) ).
fof(f429,plain,
nil != sK49,
inference(definition_unfolding,[],[f420,f421]) ).
fof(f430,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK49
| ssItem(sK54(X4,X5,X6))
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f415,f421]) ).
fof(f433,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK49
| lt(X4,sK54(X4,X5,X6))
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f412,f421]) ).
fof(f434,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK49
| ~ leq(X4,sK54(X4,X5,X6))
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f411,f421]) ).
fof(f520,definition,
( spl55_1
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl55_1])],[avatar_definition]) ).
fof(f528,definition,
( spl55_3
<=> sK49 = app(app(sK52,cons(sK51,nil)),sK53) ),
introduced(definition,[new_symbols(definition,[spl55_3])],[avatar_definition]) ).
fof(f530,plain,
( sK49 = app(app(sK52,cons(sK51,nil)),sK53)
| ~ spl55_3 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f531,plain,
( spl55_1
| spl55_3 ),
inference(avatar_split_clause,[],[f416,f528,f520]) ).
fof(f533,definition,
( spl55_4
<=> ssList(sK53) ),
introduced(definition,[new_symbols(definition,[spl55_4])],[avatar_definition]) ).
fof(f535,plain,
( ssList(sK53)
| ~ spl55_4 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f536,plain,
( spl55_1
| spl55_4 ),
inference(avatar_split_clause,[],[f417,f533,f520]) ).
fof(f538,definition,
( spl55_5
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl55_5])],[avatar_definition]) ).
fof(f540,plain,
( ssList(sK52)
| ~ spl55_5 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f541,plain,
( spl55_1
| spl55_5 ),
inference(avatar_split_clause,[],[f418,f538,f520]) ).
fof(f543,definition,
( spl55_6
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl55_6])],[avatar_definition]) ).
fof(f545,plain,
( ssItem(sK51)
| ~ spl55_6 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f546,plain,
( spl55_1
| spl55_6 ),
inference(avatar_split_clause,[],[f419,f543,f520]) ).
fof(f547,plain,
~ spl55_1,
inference(avatar_split_clause,[],[f429,f520]) ).
fof(f583,plain,
( sK49 != sK49
| ssItem(sK54(sK51,sK52,sK53))
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3 ),
inference(superposition,[],[f430,f530]) ).
fof(f584,plain,
( ssItem(sK54(sK51,sK52,sK53))
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3 ),
inference(trivial_inequality_removal,[],[f583]) ).
fof(f585,plain,
( ssItem(sK54(sK51,sK52,sK53))
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f584,f535]) ).
fof(f586,plain,
( ssItem(sK54(sK51,sK52,sK53))
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f585,f540]) ).
fof(f587,plain,
( ssItem(sK54(sK51,sK52,sK53))
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_subsumption_resolution,[],[f586,f545]) ).
fof(f588,plain,
( sK49 != sK49
| lt(sK51,sK54(sK51,sK52,sK53))
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3 ),
inference(superposition,[],[f433,f530]) ).
fof(f589,plain,
( lt(sK51,sK54(sK51,sK52,sK53))
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3 ),
inference(trivial_inequality_removal,[],[f588]) ).
fof(f590,plain,
( lt(sK51,sK54(sK51,sK52,sK53))
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f589,f535]) ).
fof(f591,plain,
( lt(sK51,sK54(sK51,sK52,sK53))
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f590,f540]) ).
fof(f592,plain,
( lt(sK51,sK54(sK51,sK52,sK53))
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_subsumption_resolution,[],[f591,f545]) ).
fof(f593,plain,
( sK49 != sK49
| ~ leq(sK51,sK54(sK51,sK52,sK53))
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3 ),
inference(superposition,[],[f434,f530]) ).
fof(f594,plain,
( ~ leq(sK51,sK54(sK51,sK52,sK53))
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3 ),
inference(trivial_inequality_removal,[],[f593]) ).
fof(f595,plain,
( ~ leq(sK51,sK54(sK51,sK52,sK53))
| ~ ssList(sK52)
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f594,f535]) ).
fof(f596,plain,
( ~ leq(sK51,sK54(sK51,sK52,sK53))
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f595,f540]) ).
fof(f597,plain,
( ~ leq(sK51,sK54(sK51,sK52,sK53))
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_subsumption_resolution,[],[f596,f545]) ).
fof(f873,plain,
( ~ ssItem(sK54(sK51,sK52,sK53))
| leq(sK51,sK54(sK51,sK52,sK53))
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(resolution,[],[f405,f592]) ).
fof(f874,plain,
( leq(sK51,sK54(sK51,sK52,sK53))
| ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_subsumption_resolution,[],[f873,f587]) ).
fof(f875,plain,
( ~ ssItem(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_subsumption_resolution,[],[f874,f597]) ).
fof(f876,plain,
( $false
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_subsumption_resolution,[],[f875,f545]) ).
fof(f877,plain,
( ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(avatar_contradiction_clause,[],[f876]) ).
cnf(s2,plain,
( spl55_1
| spl55_3 ),
inference(sat_conversion,[],[f531]) ).
cnf(s3,plain,
( spl55_1
| spl55_4 ),
inference(sat_conversion,[],[f536]) ).
cnf(s4,plain,
( spl55_1
| spl55_5 ),
inference(sat_conversion,[],[f541]) ).
cnf(s5,plain,
( spl55_1
| spl55_6 ),
inference(sat_conversion,[],[f546]) ).
cnf(s6,plain,
~ spl55_1,
inference(sat_conversion,[],[f547]) ).
cnf(s22,plain,
( ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6 ),
inference(sat_conversion,[],[f877]) ).
cnf(s27,plain,
spl55_6,
inference(rat,[],[s5,s6]) ).
cnf(s28,plain,
spl55_5,
inference(rat,[],[s4,s6]) ).
cnf(s29,plain,
spl55_4,
inference(rat,[],[s3,s6]) ).
cnf(s30,plain,
~ spl55_3,
inference(rat,[],[s22,s27,s28,s29]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s2,s30,s6]) ).
fof(f878,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC241+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 08:43:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.29 % (3480524)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (3480533)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1613545932:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (3480530)% WARNING: option uhcvi not known.
% 0.20/0.29 % (3480529)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=474511306_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (3480530)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2947095383:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (3480532)dis+10_1_sil=32000:sp=arity:random_seed=3237075795:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (3480531)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3985598681:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (3480535)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3073019882:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (3480534)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2695826944:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (3480530) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3480524-3480530"...
% 0.20/0.29 % TRYING [1]
% 0.20/0.29 % TRYING [2]
% 0.20/0.29 % (3480530)...printing done.
% 0.20/0.29 % (3480530)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (3480530)------------------------------
% 0.20/0.29 % (3480530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3480530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3480530)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3480530)Termination reason: Refutation
% 0.20/0.29 % (3480530)Time elapsed: 0.017 s
% 0.20/0.29 % (3480530)Peak memory usage: 13 MB
% 0.20/0.29 % (3480530)Instructions burned: 26 (million)
% 0.20/0.29 % (3480524)Success in time 0.053 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------