%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 7 unt; 6 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 130 ( 51 ~; 61 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 27 ( 0 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2128) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<=> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<~> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f6,plain,
! [X2,X3,X0,X1] :
( big_p(X3)
| ~ big_p(X2)
| big_p(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,plain,
! [X2] :
( ~ big_p(sK2)
| ~ big_p(X2)
| ~ big_p(sK3)
| ~ big_p(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f11,plain,
! [X3,X1] :
( big_p(X3)
| big_p(sK1)
| big_p(X1)
| big_p(sK0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f14,definition,
( spl4_1
<=> ! [X0] : big_p(X0) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f15,plain,
( ! [X0] : big_p(X0)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f17,definition,
( spl4_2
<=> big_p(sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f19,plain,
( ~ big_p(sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f21,definition,
( spl4_3
<=> ! [X2] : ~ big_p(X2) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f22,plain,
( ! [X2] : ~ big_p(X2)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,plain,
( spl4_3
| spl4_1
| spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f6,f14,f21,f14,f21]) ).
fof(f26,definition,
( spl4_4
<=> big_p(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f28,plain,
( big_p(sK1)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f30,definition,
( spl4_5
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f32,plain,
( ~ big_p(sK2)
| spl4_5 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f36,definition,
( spl4_6
<=> big_p(sK0) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f37,plain,
( ~ big_p(sK0)
| spl4_6 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f38,plain,
( big_p(sK0)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,plain,
( ~ spl4_6
| ~ spl4_2
| spl4_3
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f10,f30,f21,f17,f36]) ).
fof(f41,plain,
( spl4_6
| spl4_1
| spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f11,f14,f26,f14,f36]) ).
fof(f43,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f28,f22]) ).
fof(f44,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f38,f22]) ).
fof(f46,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f47,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f15,f22]) ).
fof(f48,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f47]) ).
fof(f49,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f19,f15]) ).
fof(f50,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f49]) ).
fof(f53,plain,
( $false
| ~ spl4_1
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f37,f15]) ).
fof(f54,plain,
( ~ spl4_1
| spl4_6 ),
inference(avatar_contradiction_clause,[],[f53]) ).
fof(f55,plain,
( $false
| ~ spl4_1
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f32,f15]) ).
fof(f56,plain,
( ~ spl4_1
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f55]) ).
cnf(s3,plain,
( spl4_1
| spl4_3
| spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f24]) ).
cnf(s4,plain,
( spl4_1
| spl4_3 ),
inference(rat,[],[s3]) ).
cnf(s8,plain,
( ~ spl4_2
| spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f40]) ).
cnf(s9,plain,
( spl4_1
| spl4_1
| spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f41]) ).
cnf(s10,plain,
( spl4_1
| spl4_4
| spl4_6 ),
inference(rat,[],[s9]) ).
cnf(s12,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s13,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f46]) ).
cnf(s14,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s15,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s17,plain,
( ~ spl4_1
| spl4_6 ),
inference(sat_conversion,[],[f54]) ).
cnf(s18,plain,
( ~ spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s19,plain,
spl4_1,
inference(rat,[],[s10,s12,s13,s4]) ).
cnf(s20,plain,
spl4_5,
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
spl4_6,
inference(rat,[],[s17,s19]) ).
cnf(s23,plain,
spl4_2,
inference(rat,[],[s15,s19]) ).
cnf(s24,plain,
~ spl4_3,
inference(rat,[],[s14,s19]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s8,s21,s20,s24,s23]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n013.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 15:50:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.09/0.26 % (1294537)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (1294543)% WARNING: option uhcvi not known.
% 0.09/0.26 % (1294543)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1206896624:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (1294543) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1294537-1294543"...
% 0.09/0.26 % (1294543)...printing done.
% 0.09/0.26 % (1294543)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (1294543)------------------------------
% 0.09/0.26 % (1294543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (1294543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (1294543)CaDiCaL version: 2.1.3
% 0.09/0.26 % (1294543)Termination reason: Refutation
% 0.09/0.26 % (1294543)Time elapsed: 0.001 s
% 0.09/0.26 % (1294543)Peak memory usage: 12 MB
% 0.09/0.26 % (1294543)Instructions burned: 1 (million)
% 0.09/0.26 % (1294537)Success in time 0.033 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------