%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN373+1 : TPTP v9.3.1. Released v2.0.0.
% 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 02:07:30 PM UTC 2026
% Result : Theorem 0.18s 0.29s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 8 unt; 6 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 139 ( 56 ~; 55 |; 12 &)
% ( 9 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 23 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
( big_p(X0)
=> big_q(X0) )
<=> ( ! [X0] : big_p(X0)
=> ? [X0] : big_q(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2124) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( big_p(X0)
=> big_q(X0) )
<=> ( ! [X0] : big_p(X0)
=> ? [X0] : big_q(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
( big_p(X0)
=> big_q(X0) )
<=> ( ! [X1] : big_p(X1)
=> ? [X2] : big_q(X2) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
( big_q(X0)
| ~ big_p(X0) )
<~> ( ? [X2] : big_q(X2)
| ? [X1] : ~ big_p(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ( ! [X2] : ~ big_q(X2)
& ! [X1] : big_p(X1) )
| ! [X0] :
( ~ big_q(X0)
& big_p(X0) ) )
& ( ? [X2] : big_q(X2)
| ? [X1] : ~ big_p(X1)
| ? [X0] :
( big_q(X0)
| ~ big_p(X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ( ! [X2] : ~ big_q(X2)
& ! [X1] : big_p(X1) )
| ! [X0] :
( ~ big_q(X0)
& big_p(X0) ) )
& ( ? [X2] : big_q(X2)
| ? [X1] : ~ big_p(X1)
| ? [X0] :
( big_q(X0)
| ~ big_p(X0) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
( ( ( ! [X0] : ~ big_q(X0)
& ! [X1] : big_p(X1) )
| ! [X2] :
( ~ big_q(X2)
& big_p(X2) ) )
& ( ? [X3] : big_q(X3)
| ? [X4] : ~ big_p(X4)
| ? [X5] :
( big_q(X5)
| ~ big_p(X5) ) ) ),
inference(rectify,[],[f6]) ).
fof(f8,plain,
( ( ( ! [X0] : ~ big_q(X0)
& ! [X1] : big_p(X1) )
| ! [X2] :
( ~ big_q(X2)
& big_p(X2) ) )
& ( big_q(sK0)
| ~ big_p(sK1)
| big_q(sK2)
| ~ big_p(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f7]) ).
fof(f9,plain,
( big_q(sK0)
| ~ big_p(sK1)
| big_q(sK2)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f10,plain,
! [X2,X1] :
( big_p(X1)
| big_p(X2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
! [X2,X0] :
( ~ big_q(X0)
| ~ big_q(X2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f15,definition,
( spl3_1
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f17,plain,
( ~ big_p(sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f19,definition,
( spl3_2
<=> big_q(sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f21,plain,
( big_q(sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,definition,
( spl3_3
<=> big_p(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f25,plain,
( ~ big_p(sK1)
| spl3_3 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f27,definition,
( spl3_4
<=> big_q(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f29,plain,
( big_q(sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f30,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f9,f27,f23,f19,f15]) ).
fof(f32,definition,
( spl3_5
<=> ! [X2] : big_p(X2) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f33,plain,
( ! [X2] : big_p(X2)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f34,plain,
( spl3_5
| spl3_5 ),
inference(avatar_split_clause,[],[f10,f32,f32]) ).
fof(f36,definition,
( spl3_6
<=> ! [X2] : ~ big_q(X2) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f37,plain,
( ! [X2] : ~ big_q(X2)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,plain,
( spl3_6
| spl3_6 ),
inference(avatar_split_clause,[],[f13,f36,f36]) ).
fof(f41,plain,
( $false
| spl3_1
| ~ spl3_5 ),
inference(resolution,[],[f33,f17]) ).
fof(f42,plain,
( spl3_1
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f41]) ).
fof(f43,plain,
( $false
| spl3_3
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f25,f33]) ).
fof(f44,plain,
( spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
( $false
| ~ spl3_4
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f29,f37]) ).
fof(f46,plain,
( ~ spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f47,plain,
( $false
| ~ spl3_2
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f21,f37]) ).
fof(f48,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f47]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s2,plain,
( spl3_5
| spl3_5 ),
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
spl3_5,
inference(rat,[],[s2]) ).
cnf(s6,plain,
( spl3_6
| spl3_6 ),
inference(sat_conversion,[],[f40]) ).
cnf(s7,plain,
spl3_6,
inference(rat,[],[s6]) ).
cnf(s8,plain,
( spl3_1
| ~ spl3_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s9,plain,
( spl3_3
| ~ spl3_5 ),
inference(sat_conversion,[],[f44]) ).
cnf(s10,plain,
( ~ spl3_4
| ~ spl3_6 ),
inference(sat_conversion,[],[f46]) ).
cnf(s11,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(sat_conversion,[],[f48]) ).
cnf(s12,plain,
~ spl3_2,
inference(rat,[],[s11,s7]) ).
cnf(s13,plain,
~ spl3_4,
inference(rat,[],[s10,s7]) ).
cnf(s14,plain,
spl3_3,
inference(rat,[],[s9,s3]) ).
cnf(s15,plain,
spl3_1,
inference(rat,[],[s8,s3]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s13,s14,s12,s15]) ).
fof(f49,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN373+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 % Computer : n019.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Mon Sep 28 15:49:19 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.26 Running first-order model finding
% 0.08/0.26 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
% 0.18/0.29 % (4115075)Will run a generic schedule for satisfiability detection.
% 0.18/0.29 % (4115085)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3928404265:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.29 % (4115085) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4115075-4115085"...
% 0.18/0.29 % (4115085)...printing done.
% 0.18/0.29 % (4115081)% WARNING: option uhcvi not known.
% 0.18/0.29 % (4115085)Refutation found. Thanks to Tanya!
% 0.18/0.29 % SZS status Theorem for theBenchmark
% 0.18/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.29 % (4115085)------------------------------
% 0.18/0.29 % (4115085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (4115085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (4115085)CaDiCaL version: 2.1.3
% 0.18/0.29 % (4115085)Termination reason: Refutation
% 0.18/0.29 % (4115085)Time elapsed: 0.001 s
% 0.18/0.29 % (4115085)Peak memory usage: 12 MB
% 0.18/0.29 % (4115085)Instructions burned: 1 (million)
% 0.18/0.29 % (4115075)Success in time 0.027 s
% 0.18/0.29 % Vampire exiting
%------------------------------------------------------------------------------