%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN374+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 : n011.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 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 7 unt; 7 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 153 ( 62 ~; 72 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2125) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<~> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X2,X3,X1] :
( big_p(X3)
| ~ big_p(X2)
| ~ big_p(X1)
| big_p(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X2,X3,X1] :
( big_p(X3)
| ~ big_p(X2)
| big_p(X1)
| ~ big_p(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,plain,
! [X2,X0] :
( ~ big_p(sK3)
| ~ big_p(X2)
| ~ big_p(sK1(X0))
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f11,plain,
! [X3,X0] :
( big_p(X3)
| big_p(sK2)
| big_p(sK1(X0))
| big_p(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f14,definition,
( spl4_1
<=> big_p(sK0) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f18,definition,
( spl4_2
<=> ! [X1] : ~ big_p(X1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f19,plain,
( ! [X1] : ~ big_p(X1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f21,definition,
( spl4_3
<=> ! [X3] : big_p(X3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f22,plain,
( ! [X3] : big_p(X3)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( spl4_1
| spl4_2
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f5,f21,f18,f18,f14]) ).
fof(f24,plain,
( ~ spl4_1
| spl4_3
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f6,f21,f18,f21,f14]) ).
fof(f26,definition,
( spl4_4
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f28,plain,
( big_p(sK2)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f30,definition,
( spl4_5
<=> big_p(sK3) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f31,plain,
( big_p(sK3)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f32,plain,
( ~ big_p(sK3)
| spl4_5 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f36,definition,
( spl4_6
<=> ! [X0] :
( big_p(sK1(X0))
| big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f37,plain,
( ! [X0] :
( big_p(sK1(X0))
| big_p(X0) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl4_7
<=> ! [X0] :
( ~ big_p(sK1(X0))
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f41,plain,
( ! [X0] :
( ~ big_p(sK1(X0))
| ~ big_p(X0) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( spl4_7
| spl4_2
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f10,f30,f18,f40]) ).
fof(f43,plain,
( spl4_6
| spl4_4
| spl4_3 ),
inference(avatar_split_clause,[],[f11,f21,f26,f36]) ).
fof(f45,plain,
( $false
| ~ spl4_3
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f32,f22]) ).
fof(f46,plain,
( ~ spl4_3
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f47,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl4_3
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f41,f22]) ).
fof(f48,plain,
( $false
| ~ spl4_3
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f47,f22]) ).
fof(f49,plain,
( ~ spl4_3
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f48]) ).
fof(f50,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f28,f19]) ).
fof(f51,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f31,f19]) ).
fof(f53,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f52]) ).
fof(f54,plain,
( ! [X0] : big_p(X0)
| ~ spl4_2
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f37,f19]) ).
fof(f55,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f54,f19]) ).
fof(f56,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f55]) ).
cnf(s1,plain,
( spl4_2
| spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl4_3
| spl4_2
| ~ spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f24]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(rat,[],[s3]) ).
cnf(s8,plain,
( spl4_2
| ~ spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f42]) ).
cnf(s9,plain,
( spl4_3
| spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f43]) ).
cnf(s11,plain,
( ~ spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s12,plain,
( ~ spl4_3
| ~ spl4_7 ),
inference(sat_conversion,[],[f49]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s14,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f53]) ).
cnf(s15,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f56]) ).
cnf(s16,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s8,s11,s12,s2]) ).
cnf(s17,plain,
~ spl4_2,
inference(rat,[],[s9,s11,s13,s14,s15]) ).
cnf(s18,plain,
spl4_1,
inference(rat,[],[s16,s17]) ).
cnf(s19,plain,
spl4_3,
inference(rat,[],[s4,s17,s18]) ).
cnf(s20,plain,
~ spl4_7,
inference(rat,[],[s12,s19]) ).
cnf(s21,plain,
spl4_5,
inference(rat,[],[s11,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s8,s17,s20,s21]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN374+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:50:32 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.27 % (3492502)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3492511)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1853582103:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (3492511) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3492502-3492511"...
% 0.19/0.27 % (3492511)...printing done.
% 0.19/0.27 % (3492508)% WARNING: option uhcvi not known.
% 0.19/0.27 % (3492511)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (3492511)------------------------------
% 0.19/0.27 % (3492511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3492511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3492511)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3492511)Termination reason: Refutation
% 0.19/0.27 % (3492511)Time elapsed: 0.001 s
% 0.19/0.27 % (3492511)Peak memory usage: 12 MB
% 0.19/0.27 % (3492511)Instructions burned: 1 (million)
% 0.19/0.27 % (3492502)Success in time 0.038 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------