%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC027+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 : 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 01:04:21 PM UTC 2026
% Result : Theorem 0.31s 0.46s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 7 unt; 2 def)
% Number of atoms : 200 ( 78 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 224 ( 78 ~; 82 |; 49 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 22 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
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
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( sK55 = cons(sK57,nil)
& memberP(sK56,sK57)
& ! [X5] :
( ~ ssItem(X5)
| sK57 = X5
| ~ memberP(sK56,X5)
| ~ leq(sK57,X5) )
& ssItem(sK57) )
| ( nil = sK56
& nil = sK55 ) )
& ( ( nil = sK54
& nil != sK53 )
| ( nil = sK53
& nil != sK54 ) )
& 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(X4,sK57)],[f222]) ).
fof(f390,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil != sK53
| nil != sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK54
| nil = sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( ssItem(sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( ssItem(sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
( memberP(sK56,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
( sK55 = cons(sK57,nil)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
( nil = sK56
| nil = sK55 ),
inference(definition_unfolding,[],[f503,f513,f512]) ).
fof(f517,plain,
( nil != sK55
| nil != sK56 ),
inference(definition_unfolding,[],[f500,f512,f513]) ).
fof(f555,definition,
( spl58_1
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f556,plain,
( nil = sK56
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f557,plain,
( nil != sK56
| spl58_1 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f559,definition,
( spl58_2
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f560,plain,
( nil = sK55
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f561,plain,
( nil != sK55
| spl58_2 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f562,plain,
( ~ spl58_1
| ~ spl58_2 ),
inference(avatar_split_clause,[],[f517,f559,f555]) ).
fof(f610,plain,
( ssItem(sK57)
| spl58_2 ),
inference(forward_subsumption_resolution,[],[f504,f561]) ).
fof(f611,plain,
( memberP(sK56,sK57)
| spl58_2 ),
inference(forward_subsumption_resolution,[],[f508,f561]) ).
fof(f612,plain,
( nil = sK56
| spl58_2 ),
inference(forward_subsumption_resolution,[],[f514,f561]) ).
fof(f613,plain,
( spl58_1
| spl58_2 ),
inference(avatar_split_clause,[],[f612,f559,f555]) ).
fof(f614,plain,
( memberP(nil,sK57)
| ~ spl58_1
| spl58_2 ),
inference(superposition,[],[f611,f556]) ).
fof(f618,plain,
( ~ ssItem(sK57)
| ~ spl58_1
| spl58_2 ),
inference(resolution,[],[f614,f419]) ).
fof(f619,plain,
( $false
| ~ spl58_1
| spl58_2 ),
inference(forward_subsumption_resolution,[],[f618,f610]) ).
fof(f620,plain,
( ~ spl58_1
| spl58_2 ),
inference(avatar_contradiction_clause,[],[f619]) ).
fof(f621,plain,
( ssList(nil)
| ~ spl58_2 ),
inference(superposition,[],[f498,f560]) ).
fof(f622,plain,
( ssItem(sK57)
| spl58_1 ),
inference(forward_subsumption_resolution,[],[f505,f557]) ).
fof(f624,plain,
( sK55 = cons(sK57,nil)
| spl58_1 ),
inference(forward_subsumption_resolution,[],[f511,f557]) ).
fof(f625,plain,
( nil = cons(sK57,nil)
| spl58_1
| ~ spl58_2 ),
inference(forward_demodulation,[],[f624,f560]) ).
fof(f630,plain,
( nil != nil
| ~ ssItem(sK57)
| ~ ssList(nil)
| spl58_1
| ~ spl58_2 ),
inference(superposition,[],[f390,f625]) ).
fof(f643,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| spl58_1
| ~ spl58_2 ),
inference(trivial_inequality_removal,[],[f630]) ).
fof(f647,plain,
( ~ ssList(nil)
| spl58_1
| ~ spl58_2 ),
inference(forward_subsumption_resolution,[],[f643,f622]) ).
fof(f652,plain,
( $false
| spl58_1
| ~ spl58_2 ),
inference(forward_subsumption_resolution,[],[f647,f621]) ).
fof(f653,plain,
( spl58_1
| ~ spl58_2 ),
inference(avatar_contradiction_clause,[],[f652]) ).
cnf(s213,plain,
( ~ spl58_1
| ~ spl58_2 ),
inference(sat_conversion,[],[f562]) ).
cnf(s289,plain,
( spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f613]) ).
cnf(s297,plain,
( ~ spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f620]) ).
cnf(s324,plain,
( spl58_1
| ~ spl58_2 ),
inference(sat_conversion,[],[f653]) ).
cnf(s327,plain,
spl58_1,
inference(rat,[],[s289,s324]) ).
cnf(s328,plain,
spl58_2,
inference(rat,[],[s297,s327]) ).
cnf(s329,plain,
$false,
inference(rat,[],[s213,s328,s327]) ).
fof(f654,plain,
$false,
inference(avatar_sat_refutation,[],[s329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC027+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 07:30:45 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.31/0.46 % (2862330)Will run a generic schedule for satisfiability detection.
% 0.31/0.46 % (2862337)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2296692726:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.31/0.46 % (2862336)% WARNING: option uhcvi not known.
% 0.31/0.46 % (2862337) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2862330-2862337"...
% 0.31/0.46 % (2862337)...printing done.
% 0.31/0.46 % (2862335)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=977297992_2999 on theBenchmark for (2999ds/0Mi)
% 0.31/0.46 % (2862336)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1072280386:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.31/0.46 % (2862339)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=313126067:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.31/0.46 % (2862338)dis+10_1_sil=32000:sp=arity:random_seed=532616771:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.31/0.46 % (2862340)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1582919822:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.46 % (2862341)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=900037733:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.31/0.46 % (2862337)Refutation found. Thanks to Tanya!
% 0.31/0.46 % SZS status Theorem for theBenchmark
% 0.31/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.46 % (2862337)------------------------------
% 0.31/0.46 % (2862337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.46 % (2862337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.46 % (2862337)CaDiCaL version: 2.1.3
% 0.31/0.46 % (2862337)Termination reason: Refutation
% 0.31/0.46 % (2862337)Time elapsed: 0.006 s
% 0.31/0.46 % (2862337)Peak memory usage: 13 MB
% 0.31/0.46 % (2862337)Instructions burned: 15 (million)
% 0.31/0.46 % (2862330)Success in time 0.038 s
% 0.31/0.46 % Vampire exiting
%------------------------------------------------------------------------------