%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 02:07:31 PM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 11 unt; 3 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 34 ~; 21 |; 13 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 37 ( 0 sgn 22 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( big_p(X1)
<=> big_p(X0) )
=> ( ! [X0] : big_p(X0)
| ! [X0] : ~ big_p(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2127) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( big_p(X1)
<=> big_p(X0) )
=> ( ! [X0] : big_p(X0)
| ! [X0] : ~ big_p(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
! [X1] :
( big_p(X1)
<=> big_p(X0) )
=> ( ! [X2] : big_p(X2)
| ! [X3] : ~ big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X2] : ~ big_p(X2)
& ? [X3] : big_p(X3)
& ? [X0] :
! [X1] :
( big_p(X1)
<=> big_p(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X2] : ~ big_p(X2)
& ? [X3] : big_p(X3)
& ? [X0] :
! [X1] :
( big_p(X1)
<=> big_p(X0) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ? [X2] : ~ big_p(X2)
& ? [X3] : big_p(X3)
& ? [X0] :
! [X1] :
( ( big_p(X1)
| ~ big_p(X0) )
& ( big_p(X0)
| ~ big_p(X1) ) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f7,plain,
( ? [X0] : ~ big_p(X0)
& ? [X1] : big_p(X1)
& ? [X2] :
! [X3] :
( ( big_p(X3)
| ~ big_p(X2) )
& ( big_p(X2)
| ~ big_p(X3) ) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
( ~ big_p(sK0)
& big_p(sK1)
& ! [X3] :
( ( big_p(X3)
| ~ big_p(sK2) )
& ( big_p(sK2)
| ~ big_p(X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
fof(f9,plain,
! [X3] :
( big_p(sK2)
| ~ big_p(X3) ),
inference(cnf_transformation,[],[f8]) ).
fof(f10,plain,
! [X3] :
( big_p(X3)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f11,plain,
big_p(sK1),
inference(cnf_transformation,[],[f8]) ).
fof(f12,plain,
~ big_p(sK0),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
big_p(sK0),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f14,plain,
~ big_p(sK1),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f15,plain,
! [X3] :
( ~ big_p(X3)
| big_p(sK2) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f16,plain,
! [X3] :
( ~ big_p(sK2)
| big_p(X3) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f18,definition,
( spl3_1
<=> ! [X3] : big_p(X3) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f19,plain,
( ! [X3] : big_p(X3)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f21,definition,
( spl3_2
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f24,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f16,f21,f18]) ).
fof(f26,definition,
( spl3_3
<=> ! [X3] : ~ big_p(X3) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f27,plain,
( ! [X3] : ~ big_p(X3)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f28,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f15,f26,f21]) ).
fof(f29,plain,
( $false
| ~ spl3_3 ),
inference(resolution,[],[f27,f13]) ).
fof(f30,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f31,plain,
( $false
| ~ spl3_1 ),
inference(resolution,[],[f19,f14]) ).
fof(f32,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f31]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl3_3,
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
spl3_2,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s4]) ).
fof(f33,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n020.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 15:51:49 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 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
% 0.06/0.24 % (267040)Will run a generic schedule for satisfiability detection.
% 0.06/0.24 % (267051)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3081294374:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.24 % (267051) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-267040-267051"...
% 0.06/0.24 % (267051)...printing done.
% 0.06/0.24 % (267051)Refutation found. Thanks to Tanya!
% 0.06/0.24 % SZS status Theorem for theBenchmark
% 0.06/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.24 % (267051)------------------------------
% 0.06/0.24 % (267051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.24 % (267051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.24 % (267051)CaDiCaL version: 2.1.3
% 0.06/0.24 % (267051)Termination reason: Refutation
% 0.06/0.24 % (267051)Time elapsed: 0.001 s
% 0.06/0.24 % (267051)Peak memory usage: 12 MB
% 0.06/0.24 % (267051)Instructions burned: 1 (million)
% 0.06/0.24 % (267040)Success in time 0.032 s
% 0.06/0.24 % Vampire exiting
%------------------------------------------------------------------------------