%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC254+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 : n019.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 01:05:16 PM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 12 unt; 4 def)
% Number of atoms : 144 ( 24 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 156 ( 57 ~; 52 |; 28 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 18 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( cons(X4,nil) != X2
| app(X5,cons(X4,nil)) != X3 ) ) )
| singletonP(X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( cons(X4,nil) != X2
| app(X5,cons(X4,nil)) != X3 ) ) )
| singletonP(X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ? [X4] :
( ? [X5] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ~ singletonP(X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& 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] :
( cons(X4,nil) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
& ~ singletonP(X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f416,plain,
( ~ neq(sK50,nil)
| sK49 = cons(sK51,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
( ~ neq(sK50,nil)
| ~ singletonP(sK47) ),
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f432,plain,
( ~ neq(sK50,nil)
| ~ singletonP(sK49) ),
inference(definition_unfolding,[],[f421,f424]) ).
fof(f433,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f420,f425]) ).
fof(f441,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f234]) ).
fof(f472,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(consistent_polarity_flipping,[],[f441]) ).
fof(f564,plain,
( ~ neq(sK50,nil)
| ~ ssItem(sK51) ),
inference(consistent_polarity_flipping,[],[f417]) ).
fof(f577,definition,
( spl53_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f587,definition,
( spl53_4
<=> sK49 = cons(sK51,nil) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f589,plain,
( sK49 = cons(sK51,nil)
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f593,plain,
( spl53_4
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f416,f577,f587]) ).
fof(f595,definition,
( spl53_5
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f597,plain,
( ~ ssItem(sK51)
| spl53_5 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f598,plain,
( ~ spl53_5
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f564,f577,f595]) ).
fof(f601,definition,
( spl53_6
<=> singletonP(sK49) ),
introduced(definition,[new_symbols(definition,[spl53_6])],[avatar_definition]) ).
fof(f603,plain,
( ~ singletonP(sK49)
| spl53_6 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f605,plain,
spl53_2,
inference(avatar_split_clause,[],[f433,f577]) ).
fof(f606,plain,
( ~ spl53_6
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f432,f577,f601]) ).
fof(f852,plain,
( singletonP(sK49)
| ssItem(sK51)
| ~ ssList(sK49)
| ~ spl53_4 ),
inference(superposition,[],[f472,f589]) ).
fof(f854,plain,
( ssItem(sK51)
| ~ ssList(sK49)
| ~ spl53_4
| spl53_6 ),
inference(forward_subsumption_resolution,[],[f852,f603]) ).
fof(f855,plain,
( ~ ssList(sK49)
| ~ spl53_4
| spl53_5
| spl53_6 ),
inference(forward_subsumption_resolution,[],[f854,f597]) ).
fof(f856,plain,
( $false
| ~ spl53_4
| spl53_5
| spl53_6 ),
inference(forward_subsumption_resolution,[],[f855,f426]) ).
fof(f857,plain,
( ~ spl53_4
| spl53_5
| spl53_6 ),
inference(avatar_contradiction_clause,[],[f856]) ).
cnf(s6,plain,
( ~ spl53_2
| spl53_4 ),
inference(sat_conversion,[],[f593]) ).
cnf(s7,plain,
( ~ spl53_2
| ~ spl53_5 ),
inference(sat_conversion,[],[f598]) ).
cnf(s10,plain,
spl53_2,
inference(sat_conversion,[],[f605]) ).
cnf(s11,plain,
( ~ spl53_2
| ~ spl53_6 ),
inference(sat_conversion,[],[f606]) ).
cnf(s25,plain,
( ~ spl53_4
| spl53_5
| spl53_6 ),
inference(sat_conversion,[],[f857]) ).
cnf(s30,plain,
~ spl53_6,
inference(rat,[],[s11,s10]) ).
cnf(s31,plain,
~ spl53_5,
inference(rat,[],[s7,s10]) ).
cnf(s32,plain,
~ spl53_4,
inference(rat,[],[s25,s30,s31]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s6,s32,s10]) ).
fof(f858,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 08:42:48 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
% 0.20/0.30 % (3858707)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (3858715)dis+10_1_sil=32000:sp=arity:random_seed=1738844898:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (3858713)% WARNING: option uhcvi not known.
% 0.20/0.30 % (3858712)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3677206950_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (3858713)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3526741867:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (3858714)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1013250506:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (3858717)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=411502795:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (3858716)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1992414830:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (3858718)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4164669695:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (3858713) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3858707-3858713"...
% 0.20/0.30 % TRYING [1]
% 0.20/0.30 % (3858713)...printing done.
% 0.20/0.30 % TRYING [2]
% 0.20/0.30 % (3858713)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (3858713)------------------------------
% 0.20/0.30 % (3858713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3858713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3858713)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3858713)Termination reason: Refutation
% 0.20/0.30 % (3858713)Time elapsed: 0.014 s
% 0.20/0.30 % (3858713)Peak memory usage: 13 MB
% 0.20/0.30 % (3858713)Instructions burned: 21 (million)
% 0.20/0.30 % (3858707)Success in time 0.057 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------