%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 11:59:35 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 11 unt; 2 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 41 ~; 23 |; 12 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 11 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( p201(X1)
& p101(X1) ) )
| ~ ( p201(X0)
& p101(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( p201(X1)
& p101(X1) ) )
| ~ ( p201(X0)
& p101(X0) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( p201(X1)
& p101(X1) ) )
| ~ ( p201(X0)
& p101(X0) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ~ p201(X1)
| ~ p101(X1) )
& p201(X0)
& p101(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ~ p201(X1)
| ~ p101(X1) )
& p201(X0)
& p101(X0) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
( ! [X1] :
( ~ r1(sK0,X1)
| ~ p201(X1)
| ~ p101(X1) )
& p201(sK0)
& p101(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
fof(f8,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f9,plain,
p101(sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
p201(sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X1] :
( ~ r1(sK0,X1)
| ~ p201(X1)
| ~ p101(X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0] : ~ r1(X0,X0),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f13,plain,
! [X1] :
( r1(sK0,X1)
| ~ p201(X1)
| ~ p101(X1) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f14,plain,
( ~ p201(sK0)
| ~ p101(sK0) ),
inference(resolution,[],[f12,f13]) ).
fof(f16,definition,
( spl1_1
<=> p101(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f18,plain,
( ~ p101(sK0)
| spl1_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f20,definition,
( spl1_2
<=> p201(sK0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f22,plain,
( ~ p201(sK0)
| spl1_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f14,f20,f16]) ).
fof(f24,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f18,f9]) ).
fof(f25,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f24]) ).
fof(f26,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f22,f10]) ).
fof(f27,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f26]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
spl1_1,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
spl1_2,
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f28,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 : Sun Sep 27 16:27:15 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
% 0.10/0.45 % (2226861)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2226872)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1103462996:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2226872) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2226861-2226872"...
% 0.10/0.45 % (2226872)...printing done.
% 0.10/0.45 % (2226872)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2226872)------------------------------
% 0.10/0.45 % (2226872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2226872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2226872)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2226872)Termination reason: Refutation
% 0.10/0.45 % (2226872)Time elapsed: 0.001 s
% 0.10/0.45 % (2226872)Peak memory usage: 12 MB
% 0.10/0.45 % (2226861)Success in time 0.026 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------