%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC213+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 : n002.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 01:05:07 PM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 15 unt; 3 def)
% Number of atoms : 194 ( 61 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 235 ( 84 ~; 71 |; 61 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 38 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ equalelemsP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssList(X8)
& app(cons(X6,nil),X8) = X2 ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X5
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) ) )
| neq(X0,nil)
| ( 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
| ~ neq(X1,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ equalelemsP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssList(X8)
& app(cons(X6,nil),X8) = X2 ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X5
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) ) )
| neq(X0,nil)
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& equalelemsP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != X2 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X5
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 ) ) )
& ssList(X5) )
& ssList(X4) )
& ~ neq(X0,nil)
& ( 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
& neq(X1,nil)
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& equalelemsP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != X2 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X5
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 ) ) )
& ssList(X5) )
& ssList(X4) )
& ~ neq(X0,nil)
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& neq(sK54,nil)
& sK56 = app(app(sK57,sK55),sK58)
& equalelemsP(sK55)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK57
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != sK55 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != sK58
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK55 ) ) )
& ssList(sK58)
& ssList(sK57)
& ~ neq(sK53,nil)
& ( 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(X4,sK57),skolemize(X5,sK58)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil = sK56
| nil != sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
~ neq(sK53,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f508,f510]) ).
fof(f512,plain,
~ neq(sK55,nil),
inference(definition_unfolding,[],[f501,f509]) ).
fof(f550,definition,
( spl59_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f551,plain,
( nil = sK55
| ~ spl59_1 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f554,definition,
( spl59_2
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f556,plain,
( nil = sK56
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f557,plain,
( ~ spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f500,f554,f550]) ).
fof(f559,definition,
( spl59_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f560,plain,
( ssList(nil)
| ~ spl59_3 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f592,plain,
spl59_3,
inference(avatar_split_clause,[],[f389,f559]) ).
fof(f1046,plain,
( nil = sK55
| ~ ssList(nil)
| ~ ssList(sK55) ),
inference(resolution,[],[f387,f512]) ).
fof(f1055,plain,
( nil = sK55
| ~ ssList(sK55)
| ~ spl59_3 ),
inference(forward_subsumption_resolution,[],[f1046,f560]) ).
fof(f1056,plain,
( nil = sK55
| ~ spl59_3 ),
inference(forward_subsumption_resolution,[],[f1055,f498]) ).
fof(f1057,plain,
( spl59_1
| ~ spl59_3 ),
inference(avatar_split_clause,[],[f1056,f559,f550]) ).
fof(f1061,plain,
( ~ neq(nil,nil)
| ~ spl59_1 ),
inference(superposition,[],[f512,f551]) ).
fof(f1096,plain,
( neq(nil,nil)
| ~ spl59_2 ),
inference(superposition,[],[f511,f556]) ).
fof(f1195,plain,
( $false
| ~ spl59_1
| ~ spl59_2 ),
inference(forward_subsumption_resolution,[],[f1096,f1061]) ).
fof(f1196,plain,
( ~ spl59_1
| ~ spl59_2 ),
inference(avatar_contradiction_clause,[],[f1195]) ).
cnf(s1,plain,
( ~ spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f557]) ).
cnf(s10,plain,
spl59_3,
inference(sat_conversion,[],[f592]) ).
cnf(s41,plain,
( spl59_1
| ~ spl59_3 ),
inference(sat_conversion,[],[f1057]) ).
cnf(s55,plain,
( ~ spl59_1
| ~ spl59_2 ),
inference(sat_conversion,[],[f1196]) ).
cnf(s56,plain,
spl59_1,
inference(rat,[],[s41,s10]) ).
cnf(s57,plain,
~ spl59_2,
inference(rat,[],[s55,s56]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s1,s57,s56]) ).
fof(f1197,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC213+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 08:34:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.28 % (212430)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (212438)dis+10_1_sil=32000:sp=arity:random_seed=1585933011:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (212436)% WARNING: option uhcvi not known.
% 0.20/0.28 % (212435)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=130760946_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (212436)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1758175992:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (212437)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=569330345:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (212439)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2483286723:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (212440)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=157611749:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (212441)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=83074725:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (212438) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-212430-212438"...
% 0.20/0.28 % (212438)...printing done.
% 0.20/0.28 % (212438)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (212438)------------------------------
% 0.20/0.28 % (212438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (212438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (212438)CaDiCaL version: 2.1.3
% 0.20/0.28 % (212438)Termination reason: Refutation
% 0.20/0.28 % (212438)Time elapsed: 0.010 s
% 0.20/0.28 % (212438)Peak memory usage: 13 MB
% 0.20/0.28 % (212438)Instructions burned: 27 (million)
% 0.20/0.28 % (212430)Success in time 0.043 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------