%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC219+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 : n008.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 01:05:09 PM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 16 unt; 4 def)
% Number of atoms : 297 ( 71 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 390 ( 158 ~; 149 |; 64 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 77 ( 0 sgn 57 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/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
| 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)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X9,X8) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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
| 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)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X9,X8) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
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
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X3,X9)
| ~ leq(X9,X8) )
& ssItem(X8) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [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] :
( memberP(X5,X7)
& memberP(X6,X7)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X3,X9)
| ~ leq(X9,X8) )
& ssItem(X8) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& nil != sK53
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ( memberP(X5,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& leq(X4,sK57(X4,X5,X6))
& ~ leq(sK57(X4,X5,X6),X4)
& ssItem(sK57(X4,X5,X6)) ) ) ) )
& ( ( sK55 = cons(sK58,nil)
& memberP(sK56,sK58)
& ! [X9] :
( ~ ssItem(X9)
| sK58 = X9
| ~ memberP(sK56,X9)
| ~ leq(X9,sK58) )
& ssItem(sK58) )
| ( nil = sK56
& nil = sK55 ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6)),skolemize(X8,sK58)],[f222]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ssItem(sK58)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( sK55 = cons(sK58,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ssItem(sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| memberP(X5,sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
nil != sK53,
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f516,plain,
nil != sK55,
inference(definition_unfolding,[],[f513,f514]) ).
fof(f517,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X5,sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f512,f514]) ).
fof(f521,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f508,f514]) ).
fof(f559,definition,
( spl59_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f563,definition,
( spl59_2
<=> ssItem(sK58) ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f565,plain,
( ssItem(sK58)
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f566,plain,
( spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f500,f563,f559]) ).
fof(f584,definition,
( spl59_6
<=> sK55 = cons(sK58,nil) ),
introduced(definition,[new_symbols(definition,[spl59_6])],[avatar_definition]) ).
fof(f586,plain,
( sK55 = cons(sK58,nil)
| ~ spl59_6 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f587,plain,
( spl59_1
| spl59_6 ),
inference(avatar_split_clause,[],[f506,f584,f559]) ).
fof(f589,plain,
~ spl59_1,
inference(avatar_split_clause,[],[f516,f559]) ).
fof(f591,definition,
( spl59_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl59_7])],[avatar_definition]) ).
fof(f592,plain,
( ssList(nil)
| ~ spl59_7 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f624,plain,
spl59_7,
inference(avatar_split_clause,[],[f389,f591]) ).
fof(f625,plain,
( ! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK58)
| ssItem(sK57(sK58,X0,X1)) )
| ~ spl59_6 ),
inference(superposition,[],[f521,f586]) ).
fof(f626,plain,
( ! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssItem(sK57(sK58,X0,X1)) )
| ~ spl59_2
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f625,f565]) ).
fof(f627,plain,
( ! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK58)
| memberP(X0,sK57(sK58,X0,X1)) )
| ~ spl59_6 ),
inference(superposition,[],[f517,f586]) ).
fof(f628,plain,
( ! [X0,X1] :
( sK55 != app(app(X0,sK55),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,sK57(sK58,X0,X1)) )
| ~ spl59_2
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f627,f565]) ).
fof(f865,plain,
sK55 = app(nil,sK55),
inference(resolution,[],[f403,f498]) ).
fof(f870,plain,
( ! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(nil,sK57(sK58,nil,X0)) )
| ~ spl59_2
| ~ spl59_6 ),
inference(superposition,[],[f628,f865]) ).
fof(f871,plain,
( ! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ssItem(sK57(sK58,nil,X0)) )
| ~ spl59_2
| ~ spl59_6 ),
inference(superposition,[],[f626,f865]) ).
fof(f872,plain,
( ! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(X0)
| ssItem(sK57(sK58,nil,X0)) )
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f871,f592]) ).
fof(f873,plain,
( ! [X0] :
( sK55 != app(sK55,X0)
| ~ ssList(X0)
| memberP(nil,sK57(sK58,nil,X0)) )
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f870,f592]) ).
fof(f898,plain,
sK55 = app(sK55,nil),
inference(resolution,[],[f482,f498]) ).
fof(f911,plain,
( sK55 != sK55
| ~ ssList(nil)
| ssItem(sK57(sK58,nil,nil))
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(superposition,[],[f872,f898]) ).
fof(f912,plain,
( ~ ssList(nil)
| ssItem(sK57(sK58,nil,nil))
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(trivial_inequality_removal,[],[f911]) ).
fof(f913,plain,
( ssItem(sK57(sK58,nil,nil))
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f912,f592]) ).
fof(f919,plain,
( sK55 != sK55
| ~ ssList(nil)
| memberP(nil,sK57(sK58,nil,nil))
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(superposition,[],[f873,f898]) ).
fof(f920,plain,
( ~ ssList(nil)
| memberP(nil,sK57(sK58,nil,nil))
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(trivial_inequality_removal,[],[f919]) ).
fof(f921,plain,
( memberP(nil,sK57(sK58,nil,nil))
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f920,f592]) ).
fof(f933,plain,
( ~ ssItem(sK57(sK58,nil,nil))
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(resolution,[],[f921,f419]) ).
fof(f934,plain,
( $false
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f933,f913]) ).
fof(f935,plain,
( ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(avatar_contradiction_clause,[],[f934]) ).
cnf(s1,plain,
( spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f566]) ).
cnf(s7,plain,
( spl59_1
| spl59_6 ),
inference(sat_conversion,[],[f587]) ).
cnf(s9,plain,
~ spl59_1,
inference(sat_conversion,[],[f589]) ).
cnf(s18,plain,
spl59_7,
inference(sat_conversion,[],[f624]) ).
cnf(s35,plain,
( ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(sat_conversion,[],[f935]) ).
cnf(s40,plain,
spl59_6,
inference(rat,[],[s7,s9]) ).
cnf(s41,plain,
~ spl59_2,
inference(rat,[],[s35,s18,s40]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s1,s41,s9]) ).
fof(f936,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC219+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 08:32:55 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.19/0.27 % (2099837)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (2099845)dis+10_1_sil=32000:sp=arity:random_seed=284507803:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (2099843)% WARNING: option uhcvi not known.
% 0.19/0.27 % (2099845) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2099837-2099845"...
% 0.19/0.27 % (2099842)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=829265001_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (2099843)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1233373372:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (2099844)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1040359767:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (2099846)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=110032099:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (2099847)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3942563665:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (2099848)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3674894216:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (2099845)...printing done.
% 0.19/0.27 % (2099845)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (2099845)------------------------------
% 0.19/0.28 % (2099845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2099845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2099845)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2099845)Termination reason: Refutation
% 0.19/0.28 % (2099845)Time elapsed: 0.008 s
% 0.19/0.28 % (2099845)Peak memory usage: 13 MB
% 0.19/0.28 % (2099845)Instructions burned: 22 (million)
% 0.19/0.28 % (2099837)Success in time 0.042 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------