%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN056+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 : n014.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 02:06:35 PM UTC 2026
% Result : Theorem 0.25s 0.35s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 103 ( 12 unt; 12 def)
% Number of atoms : 268 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 304 ( 139 ~; 127 |; 14 &)
% ( 18 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 13 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 58 ( 0 sgn 48 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ? [X0] : big_p(X0)
<=> ? [X1] : big_q(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_1) ).
fof(f2,axiom,
! [X0,X1] :
( ( big_p(X0)
& big_q(X1) )
=> ( big_r(X0)
<=> big_s(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_2) ).
fof(f3,conjecture,
( ! [X0] :
( big_p(X0)
=> big_r(X0) )
<=> ! [X1] :
( big_q(X1)
=> big_s(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26) ).
fof(f4,negated_conjecture,
~ ( ! [X0] :
( big_p(X0)
=> big_r(X0) )
<=> ! [X1] :
( big_q(X1)
=> big_s(X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( big_r(X0)
<=> big_s(X1) )
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f6,plain,
! [X0,X1] :
( ( big_r(X0)
<=> big_s(X1) )
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
( ! [X0] :
( big_r(X0)
| ~ big_p(X0) )
<~> ! [X1] :
( big_s(X1)
| ~ big_q(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f8,plain,
( ( ? [X0] : big_p(X0)
| ! [X1] : ~ big_q(X1) )
& ( ? [X1] : big_q(X1)
| ! [X0] : ~ big_p(X0) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f9,plain,
( ( ? [X0] : big_p(X0)
| ! [X1] : ~ big_q(X1) )
& ( ? [X2] : big_q(X2)
| ! [X3] : ~ big_p(X3) ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( big_p(sK0)
| ! [X1] : ~ big_q(X1) )
& ( big_q(sK1)
| ! [X3] : ~ big_p(X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( ( big_r(X0)
| ~ big_s(X1) )
& ( big_s(X1)
| ~ big_r(X0) ) )
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(nnf_transformation,[],[f6]) ).
fof(f12,plain,
( ( ? [X1] :
( ~ big_s(X1)
& big_q(X1) )
| ? [X0] :
( ~ big_r(X0)
& big_p(X0) ) )
& ( ! [X1] :
( big_s(X1)
| ~ big_q(X1) )
| ! [X0] :
( big_r(X0)
| ~ big_p(X0) ) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f13,plain,
( ( ? [X0] :
( ~ big_s(X0)
& big_q(X0) )
| ? [X1] :
( ~ big_r(X1)
& big_p(X1) ) )
& ( ! [X2] :
( big_s(X2)
| ~ big_q(X2) )
| ! [X3] :
( big_r(X3)
| ~ big_p(X3) ) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
( ( ( ~ big_s(sK2)
& big_q(sK2) )
| ( ~ big_r(sK3)
& big_p(sK3) ) )
& ( ! [X2] :
( big_s(X2)
| ~ big_q(X2) )
| ! [X3] :
( big_r(X3)
| ~ big_p(X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13]) ).
fof(f15,plain,
! [X3] :
( big_q(sK1)
| ~ big_p(X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X1] :
( big_p(sK0)
| ~ big_q(X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X0,X1] :
( big_s(X1)
| ~ big_r(X0)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( big_r(X0)
| ~ big_s(X1)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X2,X3] :
( big_s(X2)
| ~ big_q(X2)
| big_r(X3)
| ~ big_p(X3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
( big_q(sK2)
| big_p(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
( big_q(sK2)
| ~ big_r(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( ~ big_s(sK2)
| big_p(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( ~ big_s(sK2)
| ~ big_r(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,definition,
( spl4_1
<=> ! [X3] :
( big_r(X3)
| ~ big_p(X3) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f26,plain,
( ! [X3] :
( ~ big_p(X3)
| big_r(X3) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,definition,
( spl4_2
<=> ! [X2] :
( big_s(X2)
| ~ big_q(X2) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f29,plain,
( ! [X2] :
( ~ big_q(X2)
| big_s(X2) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f19,f28,f25]) ).
fof(f32,definition,
( spl4_3
<=> big_p(sK3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f34,plain,
( big_p(sK3)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f36,definition,
( spl4_4
<=> big_q(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f38,plain,
( big_q(sK2)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f20,f36,f32]) ).
fof(f41,definition,
( spl4_5
<=> big_r(sK3) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f43,plain,
( ~ big_r(sK3)
| spl4_5 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
( ~ spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f21,f36,f41]) ).
fof(f46,definition,
( spl4_6
<=> big_s(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f48,plain,
( ~ big_s(sK2)
| spl4_6 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,plain,
( spl4_3
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f22,f46,f32]) ).
fof(f50,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f23,f46,f41]) ).
fof(f52,definition,
( spl4_7
<=> ! [X0] :
( ~ big_r(X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f53,plain,
( ! [X0] :
( ~ big_r(X0)
| ~ big_p(X0) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f54,plain,
( spl4_7
| spl4_2 ),
inference(avatar_split_clause,[],[f17,f28,f52]) ).
fof(f56,definition,
( spl4_8
<=> ! [X1] :
( ~ big_s(X1)
| ~ big_q(X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f57,plain,
( ! [X1] :
( ~ big_s(X1)
| ~ big_q(X1) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( spl4_8
| spl4_1 ),
inference(avatar_split_clause,[],[f18,f25,f56]) ).
fof(f60,definition,
( spl4_9
<=> ! [X3] : ~ big_p(X3) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f61,plain,
( ! [X3] : ~ big_p(X3)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,definition,
( spl4_10
<=> big_q(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f65,plain,
( big_q(sK1)
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,plain,
( spl4_9
| spl4_10 ),
inference(avatar_split_clause,[],[f15,f63,f60]) ).
fof(f68,definition,
( spl4_11
<=> ! [X1] : ~ big_q(X1) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f69,plain,
( ! [X1] : ~ big_q(X1)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl4_12
<=> big_p(sK0) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
fof(f73,plain,
( big_p(sK0)
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl4_11
| spl4_12 ),
inference(avatar_split_clause,[],[f16,f71,f68]) ).
fof(f75,plain,
( $false
| ~ spl4_3
| ~ spl4_9 ),
inference(resolution,[],[f61,f34]) ).
fof(f76,plain,
( ~ spl4_3
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f75]) ).
fof(f78,plain,
( $false
| ~ spl4_10
| ~ spl4_11 ),
inference(resolution,[],[f69,f65]) ).
fof(f79,plain,
( ~ spl4_10
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f78]) ).
fof(f80,plain,
( ! [X1] : ~ big_q(X1)
| ~ spl4_2
| ~ spl4_8 ),
inference(forward_subsumption_resolution,[],[f57,f29]) ).
fof(f81,plain,
( spl4_11
| ~ spl4_2
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f80,f56,f28,f68]) ).
fof(f82,plain,
( big_r(sK3)
| ~ spl4_1
| ~ spl4_3 ),
inference(resolution,[],[f26,f34]) ).
fof(f84,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f82,f43]) ).
fof(f85,plain,
( ~ spl4_1
| ~ spl4_3
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f84]) ).
fof(f86,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl4_1
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f53,f26]) ).
fof(f87,plain,
( spl4_9
| ~ spl4_1
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f86,f52,f25,f60]) ).
fof(f88,plain,
( $false
| ~ spl4_9
| ~ spl4_12 ),
inference(resolution,[],[f61,f73]) ).
fof(f89,plain,
( ~ spl4_9
| ~ spl4_12 ),
inference(avatar_contradiction_clause,[],[f88]) ).
fof(f90,plain,
( $false
| ~ spl4_4
| ~ spl4_11 ),
inference(resolution,[],[f69,f38]) ).
fof(f91,plain,
( ~ spl4_4
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f92,plain,
( big_s(sK2)
| ~ spl4_2
| ~ spl4_4 ),
inference(resolution,[],[f29,f38]) ).
fof(f93,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| spl4_6 ),
inference(forward_subsumption_resolution,[],[f92,f48]) ).
fof(f94,plain,
( ~ spl4_2
| ~ spl4_4
| spl4_6 ),
inference(avatar_contradiction_clause,[],[f93]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f30]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f44]) ).
cnf(s4,plain,
( spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s5,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f50]) ).
cnf(s6,plain,
( spl4_2
| spl4_7 ),
inference(sat_conversion,[],[f54]) ).
cnf(s7,plain,
( spl4_1
| spl4_8 ),
inference(sat_conversion,[],[f58]) ).
cnf(s8,plain,
( spl4_9
| spl4_10 ),
inference(sat_conversion,[],[f66]) ).
cnf(s9,plain,
( spl4_11
| spl4_12 ),
inference(sat_conversion,[],[f74]) ).
cnf(s10,plain,
( ~ spl4_3
| ~ spl4_9 ),
inference(sat_conversion,[],[f76]) ).
cnf(s11,plain,
( ~ spl4_10
| ~ spl4_11 ),
inference(sat_conversion,[],[f79]) ).
cnf(s12,plain,
( ~ spl4_2
| ~ spl4_8
| spl4_11 ),
inference(sat_conversion,[],[f81]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f85]) ).
cnf(s14,plain,
( ~ spl4_1
| ~ spl4_7
| spl4_9 ),
inference(sat_conversion,[],[f87]) ).
cnf(s15,plain,
( ~ spl4_9
| ~ spl4_12 ),
inference(sat_conversion,[],[f89]) ).
cnf(s16,plain,
( ~ spl4_4
| ~ spl4_11 ),
inference(sat_conversion,[],[f91]) ).
cnf(s17,plain,
( ~ spl4_2
| ~ spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f94]) ).
cnf(s18,plain,
~ spl4_11,
inference(rat,[],[s10,s8,s2,s11,s16]) ).
cnf(s19,plain,
spl4_12,
inference(rat,[],[s9,s18]) ).
cnf(s20,plain,
~ spl4_9,
inference(rat,[],[s15,s19]) ).
cnf(s22,plain,
spl4_1,
inference(rat,[],[s12,s1,s7,s18]) ).
cnf(s23,plain,
~ spl4_7,
inference(rat,[],[s14,s20,s22]) ).
cnf(s24,plain,
spl4_2,
inference(rat,[],[s6,s23]) ).
cnf(s26,plain,
~ spl4_5,
inference(rat,[],[s17,s3,s5,s24]) ).
cnf(s27,plain,
~ spl4_3,
inference(rat,[],[s13,s22,s26]) ).
cnf(s28,plain,
~ spl4_6,
inference(rat,[],[s4,s27]) ).
cnf(s29,plain,
spl4_4,
inference(rat,[],[s2,s27]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s17,s24,s28,s29]) ).
fof(f95,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 % Computer : n014.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Mon Sep 28 15:26:45 UTC 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.32 Running first-order model finding
% 0.25/0.32 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
% 0.25/0.35 % (1852283)Will run a generic schedule for satisfiability detection.
% 0.25/0.35 % (1852291)dis+10_1_sil=32000:sp=arity:random_seed=3174015583:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.25/0.35 % (1852291) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1852283-1852291"...
% 0.25/0.35 % (1852291)...printing done.
% 0.25/0.35 % (1852291)Refutation found. Thanks to Tanya!
% 0.25/0.35 % SZS status Theorem for theBenchmark
% 0.25/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.35 % (1852291)------------------------------
% 0.25/0.35 % (1852291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (1852291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (1852291)CaDiCaL version: 2.1.3
% 0.25/0.35 % (1852291)Termination reason: Refutation
% 0.25/0.35 % (1852291)Time elapsed: 0.003 s
% 0.25/0.35 % (1852291)Peak memory usage: 12 MB
% 0.25/0.35 % (1852291)Instructions burned: 2 (million)
% 0.25/0.35 % (1852283)Success in time 0.025 s
% 0.25/0.35 % Vampire exiting
%------------------------------------------------------------------------------