%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN059+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 : n016.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 02:06:36 PM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 103 ( 19 unt; 14 def)
% Number of atoms : 314 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 344 ( 133 ~; 146 |; 40 &)
% ( 16 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 15 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 60 ( 0 sgn 48 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] : big_f(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29_1) ).
fof(f2,axiom,
? [X0] : big_g(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29_2) ).
fof(f3,conjecture,
( ( ! [X0] :
( big_f(X0)
=> big_h(X0) )
& ! [X1] :
( big_g(X1)
=> big_j(X1) ) )
<=> ! [X2,X3] :
( ( big_f(X2)
& big_g(X3) )
=> ( big_h(X2)
& big_j(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29) ).
fof(f4,negated_conjecture,
~ ( ( ! [X0] :
( big_f(X0)
=> big_h(X0) )
& ! [X1] :
( big_g(X1)
=> big_j(X1) ) )
<=> ! [X2,X3] :
( ( big_f(X2)
& big_g(X3) )
=> ( big_h(X2)
& big_j(X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
( ( ! [X0] :
( big_h(X0)
| ~ big_f(X0) )
& ! [X1] :
( big_j(X1)
| ~ big_g(X1) ) )
<~> ! [X2,X3] :
( ( big_h(X2)
& big_j(X3) )
| ~ big_f(X2)
| ~ big_g(X3) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ! [X0] :
( big_h(X0)
| ~ big_f(X0) )
& ! [X1] :
( big_j(X1)
| ~ big_g(X1) ) )
<~> ! [X2,X3] :
( ( big_h(X2)
& big_j(X3) )
| ~ big_f(X2)
| ~ big_g(X3) ) ),
inference(flattening,[],[f5]) ).
fof(f7,definition,
( sP0
<=> ( ! [X0] :
( big_h(X0)
| ~ big_f(X0) )
& ! [X1] :
( big_j(X1)
| ~ big_g(X1) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f8,plain,
( sP0
<~> ! [X2,X3] :
( ( big_h(X2)
& big_j(X3) )
| ~ big_f(X2)
| ~ big_g(X3) ) ),
inference(definition_folding,[],[f6,f7]) ).
fof(f9,plain,
big_f(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f1]) ).
fof(f10,plain,
big_g(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f2]) ).
fof(f11,plain,
( ( sP0
| ? [X0] :
( ~ big_h(X0)
& big_f(X0) )
| ? [X1] :
( ~ big_j(X1)
& big_g(X1) ) )
& ( ( ! [X0] :
( big_h(X0)
| ~ big_f(X0) )
& ! [X1] :
( big_j(X1)
| ~ big_g(X1) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f12,plain,
( ( sP0
| ? [X0] :
( ~ big_h(X0)
& big_f(X0) )
| ? [X1] :
( ~ big_j(X1)
& big_g(X1) ) )
& ( ( ! [X0] :
( big_h(X0)
| ~ big_f(X0) )
& ! [X1] :
( big_j(X1)
| ~ big_g(X1) ) )
| ~ sP0 ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
( ( sP0
| ? [X0] :
( ~ big_h(X0)
& big_f(X0) )
| ? [X1] :
( ~ big_j(X1)
& big_g(X1) ) )
& ( ( ! [X2] :
( big_h(X2)
| ~ big_f(X2) )
& ! [X3] :
( big_j(X3)
| ~ big_g(X3) ) )
| ~ sP0 ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
( ( sP0
| ( ~ big_h(sK3)
& big_f(sK3) )
| ( ~ big_j(sK4)
& big_g(sK4) ) )
& ( ( ! [X2] :
( big_h(X2)
| ~ big_f(X2) )
& ! [X3] :
( big_j(X3)
| ~ big_g(X3) ) )
| ~ sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f13]) ).
fof(f15,plain,
( ( ? [X2,X3] :
( ( ~ big_h(X2)
| ~ big_j(X3) )
& big_f(X2)
& big_g(X3) )
| ~ sP0 )
& ( ! [X2,X3] :
( ( big_h(X2)
& big_j(X3) )
| ~ big_f(X2)
| ~ big_g(X3) )
| sP0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f16,plain,
( ( ? [X0,X1] :
( ( ~ big_h(X0)
| ~ big_j(X1) )
& big_f(X0)
& big_g(X1) )
| ~ sP0 )
& ( ! [X2,X3] :
( ( big_h(X2)
& big_j(X3) )
| ~ big_f(X2)
| ~ big_g(X3) )
| sP0 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
( ( ( ( ~ big_h(sK5)
| ~ big_j(sK6) )
& big_f(sK5)
& big_g(sK6) )
| ~ sP0 )
& ( ! [X2,X3] :
( ( big_h(X2)
& big_j(X3) )
| ~ big_f(X2)
| ~ big_g(X3) )
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f16]) ).
fof(f18,plain,
big_f(sK1),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
big_g(sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X3] :
( big_j(X3)
| ~ big_g(X3)
| ~ sP0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X2] :
( big_h(X2)
| ~ big_f(X2)
| ~ sP0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( sP0
| big_f(sK3)
| big_g(sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( sP0
| big_f(sK3)
| ~ big_j(sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
( sP0
| ~ big_h(sK3)
| big_g(sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
( sP0
| ~ big_h(sK3)
| ~ big_j(sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X3] :
( big_j(X3)
| ~ big_f(X2)
| ~ big_g(X3)
| sP0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X2,X3] :
( big_h(X2)
| ~ big_f(X2)
| ~ big_g(X3)
| sP0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
( big_g(sK6)
| ~ sP0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
( big_f(sK5)
| ~ sP0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
( ~ big_h(sK5)
| ~ big_j(sK6)
| ~ sP0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,definition,
( spl7_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f36,definition,
( spl7_2
<=> ! [X2] : ~ big_f(X2) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f37,plain,
( ! [X2] : ~ big_f(X2)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,definition,
( spl7_3
<=> ! [X3] :
( big_j(X3)
| ~ big_g(X3) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f40,plain,
( ! [X3] :
( ~ big_g(X3)
| big_j(X3) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( spl7_1
| spl7_2
| spl7_3 ),
inference(avatar_split_clause,[],[f26,f39,f36,f32]) ).
fof(f43,definition,
( spl7_4
<=> ! [X3] : ~ big_g(X3) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
fof(f44,plain,
( ! [X3] : ~ big_g(X3)
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,definition,
( spl7_5
<=> ! [X2] :
( big_h(X2)
| ~ big_f(X2) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f47,plain,
( ! [X2] :
( ~ big_f(X2)
| big_h(X2) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl7_1
| spl7_4
| spl7_5 ),
inference(avatar_split_clause,[],[f27,f46,f43,f32]) ).
fof(f50,definition,
( spl7_6
<=> big_g(sK6) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f52,plain,
( big_g(sK6)
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( ~ spl7_1
| spl7_6 ),
inference(avatar_split_clause,[],[f28,f50,f32]) ).
fof(f55,definition,
( spl7_7
<=> big_f(sK5) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
fof(f57,plain,
( big_f(sK5)
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
( ~ spl7_1
| spl7_7 ),
inference(avatar_split_clause,[],[f29,f55,f32]) ).
fof(f60,definition,
( spl7_8
<=> big_j(sK6) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
fof(f64,definition,
( spl7_9
<=> big_h(sK5) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
fof(f67,plain,
( ~ spl7_1
| ~ spl7_8
| ~ spl7_9 ),
inference(avatar_split_clause,[],[f30,f64,f60,f32]) ).
fof(f68,plain,
( ~ spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f20,f39,f32]) ).
fof(f69,plain,
( ~ spl7_1
| spl7_5 ),
inference(avatar_split_clause,[],[f21,f46,f32]) ).
fof(f71,definition,
( spl7_10
<=> big_g(sK4) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
fof(f73,plain,
( big_g(sK4)
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl7_11
<=> big_f(sK3) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
fof(f77,plain,
( big_f(sK3)
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,plain,
( spl7_10
| spl7_11
| spl7_1 ),
inference(avatar_split_clause,[],[f22,f32,f75,f71]) ).
fof(f80,definition,
( spl7_12
<=> big_j(sK4) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
fof(f83,plain,
( ~ spl7_12
| spl7_11
| spl7_1 ),
inference(avatar_split_clause,[],[f23,f32,f75,f80]) ).
fof(f85,definition,
( spl7_13
<=> big_h(sK3) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
fof(f88,plain,
( spl7_10
| ~ spl7_13
| spl7_1 ),
inference(avatar_split_clause,[],[f24,f32,f85,f71]) ).
fof(f89,plain,
( ~ spl7_12
| ~ spl7_13
| spl7_1 ),
inference(avatar_split_clause,[],[f25,f32,f85,f80]) ).
fof(f90,plain,
( $false
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f18,f37]) ).
fof(f91,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f92,plain,
( $false
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f19,f44]) ).
fof(f93,plain,
~ spl7_4,
inference(avatar_contradiction_clause,[],[f92]) ).
fof(f96,plain,
( big_j(sK4)
| ~ spl7_3
| ~ spl7_10 ),
inference(resolution,[],[f73,f40]) ).
fof(f97,plain,
( spl7_12
| ~ spl7_3
| ~ spl7_10 ),
inference(avatar_split_clause,[],[f96,f71,f39,f80]) ).
fof(f98,plain,
( big_h(sK3)
| ~ spl7_5
| ~ spl7_11 ),
inference(resolution,[],[f77,f47]) ).
fof(f99,plain,
( spl7_13
| ~ spl7_5
| ~ spl7_11 ),
inference(avatar_split_clause,[],[f98,f75,f46,f85]) ).
fof(f100,plain,
( big_j(sK6)
| ~ spl7_3
| ~ spl7_6 ),
inference(resolution,[],[f52,f40]) ).
fof(f101,plain,
( spl7_8
| ~ spl7_3
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f100,f50,f39,f60]) ).
fof(f102,plain,
( big_h(sK5)
| ~ spl7_5
| ~ spl7_7 ),
inference(resolution,[],[f57,f47]) ).
fof(f103,plain,
( spl7_9
| ~ spl7_5
| ~ spl7_7 ),
inference(avatar_split_clause,[],[f102,f55,f46,f64]) ).
cnf(s1,plain,
( spl7_1
| spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( spl7_1
| spl7_4
| spl7_5 ),
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
( ~ spl7_1
| spl7_6 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( ~ spl7_1
| spl7_7 ),
inference(sat_conversion,[],[f58]) ).
cnf(s5,plain,
( ~ spl7_1
| ~ spl7_8
| ~ spl7_9 ),
inference(sat_conversion,[],[f67]) ).
cnf(s6,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f68]) ).
cnf(s7,plain,
( ~ spl7_1
| spl7_5 ),
inference(sat_conversion,[],[f69]) ).
cnf(s8,plain,
( spl7_1
| spl7_10
| spl7_11 ),
inference(sat_conversion,[],[f78]) ).
cnf(s9,plain,
( spl7_1
| spl7_11
| ~ spl7_12 ),
inference(sat_conversion,[],[f83]) ).
cnf(s10,plain,
( spl7_1
| spl7_10
| ~ spl7_13 ),
inference(sat_conversion,[],[f88]) ).
cnf(s11,plain,
( spl7_1
| ~ spl7_12
| ~ spl7_13 ),
inference(sat_conversion,[],[f89]) ).
cnf(s12,plain,
~ spl7_2,
inference(sat_conversion,[],[f91]) ).
cnf(s13,plain,
~ spl7_4,
inference(sat_conversion,[],[f93]) ).
cnf(s14,plain,
( ~ spl7_3
| ~ spl7_10
| spl7_12 ),
inference(sat_conversion,[],[f97]) ).
cnf(s15,plain,
( ~ spl7_5
| ~ spl7_11
| spl7_13 ),
inference(sat_conversion,[],[f99]) ).
cnf(s16,plain,
( ~ spl7_3
| ~ spl7_6
| spl7_8 ),
inference(sat_conversion,[],[f101]) ).
cnf(s17,plain,
( ~ spl7_5
| ~ spl7_7
| spl7_9 ),
inference(sat_conversion,[],[f103]) ).
cnf(s18,plain,
( spl7_1
| spl7_5 ),
inference(rat,[],[s2,s13]) ).
cnf(s19,plain,
( spl7_1
| spl7_3 ),
inference(rat,[],[s1,s12]) ).
cnf(s20,plain,
( spl7_10
| spl7_1 ),
inference(rat,[],[s15,s8,s10,s18]) ).
cnf(s21,plain,
spl7_1,
inference(rat,[],[s15,s9,s11,s14,s20,s19,s18]) ).
cnf(s22,plain,
spl7_5,
inference(rat,[],[s7,s21]) ).
cnf(s23,plain,
spl7_3,
inference(rat,[],[s6,s21]) ).
cnf(s24,plain,
spl7_7,
inference(rat,[],[s4,s21]) ).
cnf(s25,plain,
spl7_6,
inference(rat,[],[s3,s21]) ).
cnf(s26,plain,
spl7_9,
inference(rat,[],[s17,s22,s24]) ).
cnf(s27,plain,
spl7_8,
inference(rat,[],[s16,s23,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s5,s21,s26,s27]) ).
fof(f104,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN059+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:32:04 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.28 % (3709282)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (3709290)dis+10_1_sil=32000:sp=arity:random_seed=2998654016:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (3709290) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3709282-3709290"...
% 0.21/0.28 % (3709290)...printing done.
% 0.21/0.28 % (3709290)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3709290)------------------------------
% 0.21/0.28 % (3709290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3709290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3709290)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3709290)Termination reason: Refutation
% 0.21/0.28 % (3709290)Time elapsed: 0.001 s
% 0.21/0.28 % (3709290)Peak memory usage: 12 MB
% 0.21/0.28 % (3709290)Instructions burned: 2 (million)
% 0.21/0.28 % (3709282)Success in time 0.038 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------