%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL550+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:52:55 AM UTC 2026
% Result : Theorem 13.04s 3.08s
% Output : Refutation 15.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 30
% Syntax : Number of formulae : 171 ( 79 unt; 2 def)
% Number of atoms : 309 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 233 ( 95 ~; 91 |; 12 &)
% ( 11 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 227 ( 0 sgn 223 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f33,axiom,
( modus_ponens_strict_implies
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f34,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adjunction) ).
fof(f35,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
fof(f45,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
fof(f46,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2) ).
fof(f48,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
fof(f49,axiom,
( axiom_m5
<=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m5) ).
fof(f57,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f58,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f62,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f64,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f65,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f66,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f67,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f68,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f69,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f71,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f72,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m5) ).
fof(f73,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f74,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f75,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f76,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f77,conjecture,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f78,negated_conjecture,
~ modus_ponens,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f79,plain,
~ modus_ponens,
inference(flattening,[],[f78]) ).
fof(f80,plain,
( axiom_m5
=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(unused_predicate_definition_removal,[],[f49]) ).
fof(f81,plain,
( axiom_m4
=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f48]) ).
fof(f83,plain,
( axiom_m2
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f84,plain,
( axiom_m1
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
fof(f85,plain,
( substitution_strict_equiv
=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f86,plain,
( adjunction
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f87,plain,
( modus_ponens_strict_implies
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f88,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f89,plain,
( ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) )
=> modus_ponens ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f94,plain,
( modus_ponens
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) ) ),
inference(ennf_transformation,[],[f89]) ).
fof(f95,plain,
( modus_ponens
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f88]) ).
fof(f97,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f98,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f99,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f100,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ modus_ponens_strict_implies ),
inference(ennf_transformation,[],[f87]) ).
fof(f101,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ modus_ponens_strict_implies ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(ennf_transformation,[],[f86]) ).
fof(f103,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) )
| ~ substitution_strict_equiv ),
inference(ennf_transformation,[],[f85]) ).
fof(f105,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(ennf_transformation,[],[f84]) ).
fof(f106,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(ennf_transformation,[],[f83]) ).
fof(f108,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(ennf_transformation,[],[f81]) ).
fof(f109,plain,
( ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(ennf_transformation,[],[f80]) ).
fof(f111,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f57]) ).
fof(f112,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f58]) ).
fof(f113,plain,
( modus_ponens
| ( ~ is_a_theorem(sK1)
& is_a_theorem(sK0)
& is_a_theorem(implies(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f95]) ).
fof(f114,plain,
( modus_ponens
| is_a_theorem(implies(sK0,sK1)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f115,plain,
( modus_ponens
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f116,plain,
( modus_ponens
| ~ is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f117,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f96]) ).
fof(f118,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f97]) ).
fof(f119,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f98]) ).
fof(f120,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f99]) ).
fof(f121,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f101]) ).
fof(f122,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ adjunction ),
inference(cnf_transformation,[],[f103]) ).
fof(f123,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[],[f104]) ).
fof(f124,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f125,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[],[f106]) ).
fof(f127,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[],[f108]) ).
fof(f128,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(cnf_transformation,[],[f109]) ).
fof(f130,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f111]) ).
fof(f131,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f112]) ).
fof(f134,plain,
op_strict_implies,
inference(cnf_transformation,[],[f62]) ).
fof(f136,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f64]) ).
fof(f137,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[],[f65]) ).
fof(f138,plain,
substitution_strict_equiv,
inference(cnf_transformation,[],[f66]) ).
fof(f139,plain,
adjunction,
inference(cnf_transformation,[],[f67]) ).
fof(f140,plain,
axiom_m1,
inference(cnf_transformation,[],[f68]) ).
fof(f141,plain,
axiom_m2,
inference(cnf_transformation,[],[f69]) ).
fof(f143,plain,
axiom_m4,
inference(cnf_transformation,[],[f71]) ).
fof(f144,plain,
axiom_m5,
inference(cnf_transformation,[],[f72]) ).
fof(f145,plain,
op_or,
inference(cnf_transformation,[],[f73]) ).
fof(f146,plain,
op_implies_and,
inference(cnf_transformation,[],[f74]) ).
fof(f147,plain,
op_equiv,
inference(cnf_transformation,[],[f75]) ).
fof(f148,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f76]) ).
fof(f149,plain,
~ modus_ponens,
inference(cnf_transformation,[],[f79]) ).
fof(f150,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f131,f136]) ).
fof(f151,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f130,f134]) ).
fof(f153,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))),
inference(forward_subsumption_resolution,[],[f128,f144]) ).
fof(f154,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[],[f127,f143]) ).
fof(f156,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f125,f141]) ).
fof(f157,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f124,f140]) ).
fof(f158,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f123,f138]) ).
fof(f159,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f122,f139]) ).
fof(f160,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f121,f137]) ).
fof(f161,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f120,f147]) ).
fof(f162,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f119,f146]) ).
fof(f163,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f118,f145]) ).
fof(f164,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f117,f148]) ).
fof(f165,plain,
is_a_theorem(implies(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f114,f149]) ).
fof(f166,plain,
is_a_theorem(sK0),
inference(forward_subsumption_resolution,[],[f115,f149]) ).
fof(f167,plain,
~ is_a_theorem(sK1),
inference(forward_subsumption_resolution,[],[f116,f149]) ).
fof(f168,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f163,f162]) ).
fof(f173,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f159,f161]) ).
fof(f175,plain,
( ~ is_a_theorem(implies(sK1,sK0))
| is_a_theorem(equiv(sK1,sK0)) ),
inference(resolution,[],[f173,f165]) ).
fof(f177,definition,
( spl2_1
<=> is_a_theorem(equiv(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f179,plain,
( is_a_theorem(equiv(sK1,sK0))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f181,definition,
( spl2_2
<=> is_a_theorem(implies(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f183,plain,
( ~ is_a_theorem(implies(sK1,sK0))
| spl2_2 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f175,f181,f177]) ).
fof(f189,plain,
! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)),
inference(superposition,[],[f151,f168]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2)))
| is_a_theorem(strict_implies(X0,X2)) ),
inference(resolution,[],[f153,f160]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X0,X2))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f190,f159]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,X2)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f191,f156]) ).
fof(f194,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,and(X1,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f191,f154]) ).
fof(f196,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f192,f154]) ).
fof(f233,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f159,f150]) ).
fof(f240,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X0,X1)))
| is_a_theorem(strict_equiv(X0,and(X0,X1))) ),
inference(resolution,[],[f233,f156]) ).
fof(f242,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))) ),
inference(resolution,[],[f233,f157]) ).
fof(f250,plain,
! [X0,X1] : is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f242,f157]) ).
fof(f274,plain,
! [X0] : is_a_theorem(strict_equiv(X0,and(X0,X0))),
inference(resolution,[],[f240,f154]) ).
fof(f283,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(resolution,[],[f158,f250]) ).
fof(f284,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f158,f274]) ).
fof(f351,plain,
! [X0,X1] : implies(X1,X0) = not(and(not(X0),X1)),
inference(superposition,[],[f162,f283]) ).
fof(f373,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f162,f351]) ).
fof(f376,plain,
! [X0,X1] : implies(not(X0),X1) = or(X1,X0),
inference(forward_demodulation,[],[f373,f168]) ).
fof(f381,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_demodulation,[],[f376,f168]) ).
fof(f384,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X1),X0),
inference(superposition,[],[f189,f381]) ).
fof(f385,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),X0),
inference(forward_demodulation,[],[f384,f189]) ).
fof(f412,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(X2,not(X1)))
| is_a_theorem(strict_implies(X2,X0)) ),
inference(superposition,[],[f191,f385]) ).
fof(f413,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(X0,not(X1)))
| is_a_theorem(strict_equiv(X0,not(X1))) ),
inference(superposition,[],[f233,f385]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(and(X0,X1)),X2))
| is_a_theorem(strict_implies(not(X2),X0)) ),
inference(superposition,[],[f192,f385]) ).
fof(f416,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(and(X0,X0)),X1))
| ~ is_a_theorem(strict_implies(not(X1),X0)) ),
inference(superposition,[],[f194,f385]) ).
fof(f417,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X0))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f416,f284]) ).
fof(f421,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(not(X1))))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f412,f196]) ).
fof(f432,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
inference(resolution,[],[f417,f196]) ).
fof(f459,plain,
! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0)),
inference(resolution,[],[f421,f432]) ).
fof(f502,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(strict_implies(not(X2),X0)) ),
inference(superposition,[],[f415,f162]) ).
fof(f512,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(implies(X0,X1)),X0)),
inference(resolution,[],[f502,f196]) ).
fof(f527,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(X0),implies(X0,X1))),
inference(superposition,[],[f512,f385]) ).
fof(f554,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(not(not(not(X0))),not(X0)))
| is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))) ),
inference(resolution,[],[f459,f413]) ).
fof(f569,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))),
inference(forward_subsumption_resolution,[],[f554,f432]) ).
fof(f570,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f569,f158]) ).
fof(f587,plain,
! [X0,X1] : not(and(not(X0),X1)) = implies(X1,not(not(X0))),
inference(superposition,[],[f351,f570]) ).
fof(f600,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f587,f351]) ).
fof(f629,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,not(not(X1))),
inference(superposition,[],[f151,f600]) ).
fof(f643,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,not(not(X1))),
inference(forward_demodulation,[],[f629,f151]) ).
fof(f664,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(not(X1)),X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_equiv(not(not(X1)),X0)) ),
inference(superposition,[],[f233,f643]) ).
fof(f825,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f664,f432]) ).
fof(f846,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f825,f196]) ).
fof(f851,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f846,f158]) ).
fof(f875,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X0,X1)),
inference(superposition,[],[f351,f851]) ).
fof(f885,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,implies(not(X0),X1))),
inference(superposition,[],[f527,f851]) ).
fof(f896,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f885,f168]) ).
fof(f1152,plain,
! [X0,X1] : not(and(X0,not(X1))) = or(X1,not(X0)),
inference(superposition,[],[f168,f875]) ).
fof(f1153,plain,
! [X0,X1] : implies(X0,X1) = or(X1,not(X0)),
inference(forward_demodulation,[],[f1152,f162]) ).
fof(f1174,plain,
! [X0,X1] : is_a_theorem(strict_implies(X1,implies(X0,X1))),
inference(superposition,[],[f896,f1153]) ).
fof(f1194,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1174,f160]) ).
fof(f3007,plain,
( ~ is_a_theorem(sK0)
| spl2_2 ),
inference(resolution,[],[f1194,f183]) ).
fof(f3012,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f3007,f166]) ).
fof(f3013,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f3012]) ).
fof(f3016,plain,
( sK0 = sK1
| ~ spl2_1 ),
inference(resolution,[],[f179,f164]) ).
fof(f3019,plain,
( ~ is_a_theorem(sK0)
| ~ spl2_1 ),
inference(superposition,[],[f167,f3016]) ).
fof(f3021,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f3019,f166]) ).
fof(f3022,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f3021]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f184]) ).
cnf(s40,plain,
spl2_2,
inference(sat_conversion,[],[f3013]) ).
cnf(s41,plain,
~ spl2_1,
inference(sat_conversion,[],[f3022]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s1,s40,s41]) ).
fof(f3024,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL550+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 16:05:46 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.04/3.08 % (3751621)Detected formulas, will run a generic FOF schedule.
% 13.04/3.08 % (3751631)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2101929112:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.04/3.08 % (3751631)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751631)------------------------------
% 13.04/3.08 % (3751631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751631)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751631)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751631)Time elapsed: 0.001 s
% 13.04/3.08 % (3751631)Peak memory usage: 87 MB
% 13.04/3.08 % (3751630)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1660192319:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.04/3.08 % (3751630)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751630)------------------------------
% 13.04/3.08 % (3751630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751630)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751630)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751630)Time elapsed: 0.002 s
% 13.04/3.08 % (3751630)Peak memory usage: 87 MB
% 13.04/3.08 % (3751633)dis-21_1_sil=8000:lcm=predicate:random_seed=18902685:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 13.04/3.08 % (3751628)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3442102625:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.04/3.08 % (3751627)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2928025127:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.04/3.08 % (3751629)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4270220138:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.04/3.08 % (3751633)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751633)------------------------------
% 13.04/3.08 % (3751633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751633)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751633)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751633)Time elapsed: 0.003 s
% 13.04/3.08 % (3751633)Peak memory usage: 88 MB
% 13.04/3.08 % (3751633)Instructions burned: 1 (million)
% 13.04/3.08 % (3751632)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1695158630:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.04/3.08 % (3751632)Instruction limit reached!
% 13.04/3.08 % (3751632)------------------------------
% 13.04/3.08 % (3751632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751632)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751632)Termination reason: Instruction limit
% 13.04/3.08 % (3751632)Termination phase: Saturation
% 13.04/3.08 % (3751632)Time elapsed: 0.147 s
% 13.04/3.08 % (3751632)Peak memory usage: 90 MB
% 13.04/3.08 % (3751632)Instructions burned: 139 (million)
% 13.04/3.08 % (3751631)------------------------------
% 13.04/3.08 % (3751631)------------------------------
% 13.04/3.08 % (3751630)------------------------------
% 13.04/3.08 % (3751630)------------------------------
% 13.04/3.08 % (3751633)------------------------------
% 13.04/3.08 % (3751633)------------------------------
% 13.04/3.08 % (3751643)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3781705659:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 13.04/3.08 % (3751643)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751643)------------------------------
% 13.04/3.08 % (3751643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751643)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751643)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751643)Time elapsed: 0.001 s
% 13.04/3.08 % (3751643)Peak memory usage: 88 MB
% 13.04/3.08 % (3751643)Instructions burned: 1 (million)
% 13.04/3.08 % (3751642)lrs+10_1_sil=8000:sp=occurrence:random_seed=1148185879:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 13.04/3.08 % (3751642)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751642)------------------------------
% 13.04/3.08 % (3751642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751642)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751642)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751642)Time elapsed: 0.002 s
% 13.04/3.08 % (3751642)Peak memory usage: 88 MB
% 13.04/3.08 % (3751643)------------------------------
% 13.04/3.08 % (3751643)------------------------------
% 13.04/3.08 % (3751645)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1547984168:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 13.04/3.08 % (3751645)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751645)------------------------------
% 13.04/3.08 % (3751645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751645)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751645)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751645)Time elapsed: 0.002 s
% 13.04/3.08 % (3751645)Peak memory usage: 88 MB
% 13.04/3.08 % (3751646)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2047253457:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 13.04/3.08 % (3751642)------------------------------
% 13.04/3.08 % (3751642)------------------------------
% 13.04/3.08 % (3751648)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2584268985:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2990 on theBenchmark for (2990ds/294Mi)
% 13.04/3.08 % (3751648)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751648)------------------------------
% 13.04/3.08 % (3751648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751648)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751648)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751648)Time elapsed: 0.001 s
% 13.04/3.08 % (3751648)Peak memory usage: 87 MB
% 13.04/3.08 % (3751646)Instruction limit reached!
% 13.04/3.08 % (3751646)------------------------------
% 13.04/3.08 % (3751646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751646)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751646)Termination reason: Instruction limit
% 13.04/3.08 % (3751646)Termination phase: Saturation
% 13.04/3.08 % (3751646)Time elapsed: 0.232 s
% 13.04/3.08 % (3751646)Peak memory usage: 92 MB
% 13.04/3.08 % (3751646)Instructions burned: 248 (million)
% 13.04/3.08 % (3751645)------------------------------
% 13.04/3.08 % (3751645)------------------------------
% 13.04/3.08 % (3751629)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751629)------------------------------
% 13.04/3.08 % (3751629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751629)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751629)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751629)Time elapsed: 0.985 s
% 13.04/3.08 % (3751629)Peak memory usage: 128 MB
% 13.04/3.08 % (3751629)Instructions burned: 897 (million)
% 13.04/3.08 % (3751648)------------------------------
% 13.04/3.08 % (3751648)------------------------------
% 13.04/3.08 % (3751652)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2471776587:i=2350_2988 on theBenchmark for (2988ds/2350Mi)
% 13.04/3.08 % (3751654)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2420775135:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 13.04/3.08 % (3751654)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751654)------------------------------
% 13.04/3.08 % (3751654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751654)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751654)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751654)Time elapsed: 0.003 s
% 13.04/3.08 % (3751654)Peak memory usage: 88 MB
% 13.04/3.08 % (3751655)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2230709853:i=127:av=off:fsr=off:sup=off_2987 on theBenchmark for (2987ds/127Mi)
% 13.04/3.08 % (3751655)Instruction limit reached!
% 13.04/3.08 % (3751655)------------------------------
% 13.04/3.08 % (3751655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751655)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751655)Termination reason: Instruction limit
% 13.04/3.08 % (3751655)Termination phase: Saturation
% 13.04/3.08 % (3751655)Time elapsed: 0.097 s
% 13.04/3.08 % (3751655)Peak memory usage: 89 MB
% 13.04/3.08 % (3751655)Instructions burned: 128 (million)
% 13.04/3.08 % (3751627)First to succeed.
% 13.04/3.08 % (3751627)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3751621"
% 13.04/3.08 % (3751658)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=51041518:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2985 on theBenchmark for (2985ds/114Mi)
% 13.04/3.08 % (3751629)------------------------------
% 13.04/3.08 % (3751629)------------------------------
% 13.04/3.08 % (3751658)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751658)------------------------------
% 13.04/3.08 % (3751658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751658)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751658)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751658)Time elapsed: 0.001 s
% 13.04/3.08 % (3751658)Peak memory usage: 88 MB
% 13.04/3.08 % (3751658)Instructions burned: 1 (million)
% 13.04/3.08 % (3751665)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=999483094:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 13.04/3.08 % (3751665)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751665)------------------------------
% 13.04/3.08 % (3751665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751665)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751665)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751665)Time elapsed: 0.002 s
% 13.04/3.08 % (3751665)Peak memory usage: 88 MB
% 13.04/3.08 % (3751662)lrs+10_1_sil=8000:sp=occurrence:random_seed=2115867061:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2983 on theBenchmark for (2983ds/907Mi)
% 13.04/3.08 % (3751662)Refutation not found, incomplete strategy
% 13.04/3.08 % (3751662)------------------------------
% 13.04/3.08 % (3751662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.04/3.08 % (3751662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/3.08 % (3751662)CaDiCaL version: 2.1.3
% 13.04/3.08 % (3751662)Termination reason: Refutation not found, incomplete strategy
% 13.04/3.08 % (3751662)Time elapsed: 0.002 s
% 13.04/3.08 % (3751662)Peak memory usage: 88 MB
% 13.04/3.08 % (3751658)------------------------------
% 13.04/3.08 % (3751658)------------------------------
% 13.04/3.08 % (3751654)------------------------------
% 13.04/3.08 % (3751654)------------------------------
% 13.04/3.08 % (3751627)Refutation found. Thanks to Tanya!
% 13.04/3.08 % SZS status Theorem for theBenchmark
% 13.04/3.08 % SZS output start Proof for theBenchmark
% See solution above
% 15.52/3.28 % (3751627)------------------------------
% 15.52/3.28 % (3751627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.52/3.28 % (3751627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.52/3.28 % (3751627)CaDiCaL version: 2.1.3
% 15.52/3.28 % (3751627)Termination reason: Refutation
% 15.52/3.28 % (3751627)Time elapsed: 1.377 s
% 15.52/3.28 % (3751627)Peak memory usage: 130 MB
% 15.52/3.28 % (3751627)Instructions burned: 1235 (million)
% 15.52/3.28 % (3751627)------------------------------
% 15.52/3.28 % (3751627)------------------------------
% 15.52/3.28 % (3751621)Success in time 2.104 s
% 15.52/3.28 % Vampire exiting
%------------------------------------------------------------------------------