%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC094+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 : n006.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 01:04:38 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 20 unt; 4 def)
% Number of atoms : 163 ( 50 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 172 ( 63 ~; 67 |; 29 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 34 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| X3 != X2
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X0
& app(X4,X6) = X1 ) ) ) ) ) ) ) ),
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
| X3 != X2
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X0
& app(X4,X6) = X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& X2 = X3
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1 ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& X2 = X3
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1 ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& sK55 = sK56
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != sK53
| app(X4,X6) != sK54 ) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f403,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK53
| app(X4,X6) != sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
sK55 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK53 = sK56,
inference(definition_unfolding,[],[f502,f501]) ).
fof(f505,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK56
| app(X4,X6) != sK56 ),
inference(definition_unfolding,[],[f500,f504,f503]) ).
fof(f508,plain,
ssList(sK56),
inference(definition_unfolding,[],[f496,f504]) ).
fof(f624,plain,
~ ssList(nil),
inference(consistent_polarity_flipping,[],[f389]) ).
fof(f638,plain,
! [X0] :
( ssList(X0)
| app(nil,X0) = X0 ),
inference(consistent_polarity_flipping,[],[f403]) ).
fof(f728,plain,
! [X6,X4,X5] :
( app(X4,X6) != sK56
| ssList(X5)
| ssList(X6)
| app(app(X4,X5),X6) != sK56
| ssList(X4) ),
inference(consistent_polarity_flipping,[],[f505]) ).
fof(f732,plain,
~ ssList(sK56),
inference(consistent_polarity_flipping,[],[f508]) ).
fof(f741,definition,
( spl57_1
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f742,plain,
( ~ ssList(nil)
| spl57_1 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f769,plain,
~ spl57_1,
inference(avatar_split_clause,[],[f624,f741]) ).
fof(f813,plain,
sK56 = app(nil,sK56),
inference(resolution,[],[f638,f732]) ).
fof(f814,plain,
( nil = app(nil,nil)
| spl57_1 ),
inference(resolution,[],[f638,f742]) ).
fof(f815,plain,
! [X0] :
( sK56 != sK56
| ssList(X0)
| ssList(sK56)
| sK56 != app(app(nil,X0),sK56)
| ssList(nil) ),
inference(superposition,[],[f728,f813]) ).
fof(f816,plain,
! [X0] :
( ssList(X0)
| ssList(sK56)
| sK56 != app(app(nil,X0),sK56)
| ssList(nil) ),
inference(trivial_inequality_removal,[],[f815]) ).
fof(f818,definition,
( spl57_7
<=> ssList(sK56) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f820,plain,
( ssList(sK56)
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f822,definition,
( spl57_8
<=> ! [X0] :
( ssList(X0)
| sK56 != app(app(nil,X0),sK56) ) ),
introduced(definition,[new_symbols(definition,[spl57_8])],[avatar_definition]) ).
fof(f823,plain,
( ! [X0] :
( sK56 != app(app(nil,X0),sK56)
| ssList(X0) )
| ~ spl57_8 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f824,plain,
( spl57_1
| spl57_7
| spl57_8 ),
inference(avatar_split_clause,[],[f816,f822,f818,f741]) ).
fof(f831,plain,
( sK56 != app(nil,sK56)
| ssList(nil)
| spl57_1
| ~ spl57_8 ),
inference(superposition,[],[f823,f814]) ).
fof(f843,definition,
( spl57_12
<=> sK56 = app(nil,sK56) ),
introduced(definition,[new_symbols(definition,[spl57_12])],[avatar_definition]) ).
fof(f845,plain,
( sK56 != app(nil,sK56)
| spl57_12 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f846,plain,
( spl57_1
| ~ spl57_12
| spl57_1
| ~ spl57_8 ),
inference(avatar_split_clause,[],[f831,f822,f741,f843,f741]) ).
fof(f847,plain,
( sK56 != sK56
| spl57_12 ),
inference(superposition,[],[f845,f813]) ).
fof(f848,plain,
( $false
| spl57_12 ),
inference(trivial_inequality_removal,[],[f847]) ).
fof(f849,plain,
spl57_12,
inference(avatar_contradiction_clause,[],[f848]) ).
fof(f850,plain,
( $false
| ~ spl57_7 ),
inference(resolution,[],[f820,f732]) ).
fof(f851,plain,
~ spl57_7,
inference(avatar_contradiction_clause,[],[f850]) ).
cnf(s8,plain,
~ spl57_1,
inference(sat_conversion,[],[f769]) ).
cnf(s9,plain,
( spl57_1
| spl57_7
| spl57_8 ),
inference(sat_conversion,[],[f824]) ).
cnf(s13,plain,
( spl57_1
| spl57_1
| ~ spl57_8
| ~ spl57_12 ),
inference(sat_conversion,[],[f846]) ).
cnf(s14,plain,
( spl57_1
| ~ spl57_8
| ~ spl57_12 ),
inference(rat,[],[s13]) ).
cnf(s15,plain,
spl57_12,
inference(sat_conversion,[],[f849]) ).
cnf(s16,plain,
~ spl57_7,
inference(sat_conversion,[],[f851]) ).
cnf(s17,plain,
( spl57_1
| ~ spl57_8 ),
inference(rat,[],[s14,s15]) ).
cnf(s19,plain,
( spl57_1
| spl57_8 ),
inference(rat,[],[s9,s16]) ).
cnf(s20,plain,
~ spl57_8,
inference(rat,[],[s17,s8]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s19,s20,s8]) ).
fof(f852,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC094+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 07:51:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (3808694)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (3808705)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2630128216:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (3808705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3808694-3808705"...
% 0.11/0.45 % (3808699)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1237170924_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (3808703)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4171365192:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (3808701)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1498781271:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (3808702)dis+10_1_sil=32000:sp=arity:random_seed=4227379440:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (3808704)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1342102209:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (3808705)...printing done.
% 0.11/0.45 % (3808700)% WARNING: option uhcvi not known.
% 0.11/0.45 % (3808705)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (3808705)------------------------------
% 0.11/0.45 % (3808705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (3808705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (3808705)CaDiCaL version: 2.1.3
% 0.11/0.45 % (3808705)Termination reason: Refutation
% 0.11/0.45 % (3808705)Time elapsed: 0.006 s
% 0.11/0.45 % (3808705)Peak memory usage: 12 MB
% 0.11/0.45 % (3808705)Instructions burned: 17 (million)
% 0.11/0.45 % (3808694)Success in time 0.036 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------