%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL555+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 : n012.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 11:52:56 AM UTC 2026
% Result : Theorem 4.17s 1.31s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 26
% Syntax : Number of formulae : 166 ( 72 unt; 2 def)
% Number of atoms : 298 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 240 ( 108 ~; 100 |; 4 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 253 ( 0 sgn 251 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
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(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(f77,conjecture,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f78,negated_conjecture,
~ and_1,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f79,plain,
~ and_1,
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,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
=> and_1 ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f95,plain,
( and_1
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f88]) ).
fof(f96,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f97,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f99,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(f100,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ modus_ponens_strict_implies ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(ennf_transformation,[],[f86]) ).
fof(f102,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) )
| ~ substitution_strict_equiv ),
inference(ennf_transformation,[],[f85]) ).
fof(f104,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(ennf_transformation,[],[f84]) ).
fof(f105,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(ennf_transformation,[],[f83]) ).
fof(f107,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(ennf_transformation,[],[f81]) ).
fof(f108,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(f110,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f57]) ).
fof(f111,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f58]) ).
fof(f112,plain,
( and_1
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f95]) ).
fof(f114,plain,
( and_1
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f115,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f96]) ).
fof(f116,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f97]) ).
fof(f118,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,[],[f100]) ).
fof(f119,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ adjunction ),
inference(cnf_transformation,[],[f102]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[],[f103]) ).
fof(f121,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[],[f104]) ).
fof(f122,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[],[f105]) ).
fof(f124,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[],[f107]) ).
fof(f125,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,[],[f108]) ).
fof(f127,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f110]) ).
fof(f128,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f111]) ).
fof(f131,plain,
op_strict_implies,
inference(cnf_transformation,[],[f62]) ).
fof(f133,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f64]) ).
fof(f134,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[],[f65]) ).
fof(f135,plain,
substitution_strict_equiv,
inference(cnf_transformation,[],[f66]) ).
fof(f136,plain,
adjunction,
inference(cnf_transformation,[],[f67]) ).
fof(f137,plain,
axiom_m1,
inference(cnf_transformation,[],[f68]) ).
fof(f138,plain,
axiom_m2,
inference(cnf_transformation,[],[f69]) ).
fof(f140,plain,
axiom_m4,
inference(cnf_transformation,[],[f71]) ).
fof(f141,plain,
axiom_m5,
inference(cnf_transformation,[],[f72]) ).
fof(f142,plain,
op_or,
inference(cnf_transformation,[],[f73]) ).
fof(f143,plain,
op_implies_and,
inference(cnf_transformation,[],[f74]) ).
fof(f146,plain,
~ and_1,
inference(cnf_transformation,[],[f79]) ).
fof(f147,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f128,f133]) ).
fof(f148,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f127,f131]) ).
fof(f150,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,[],[f125,f141]) ).
fof(f151,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[],[f124,f140]) ).
fof(f153,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f122,f138]) ).
fof(f154,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f121,f137]) ).
fof(f155,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f120,f135]) ).
fof(f156,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f119,f136]) ).
fof(f157,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f118,f134]) ).
fof(f159,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f116,f143]) ).
fof(f160,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f115,f142]) ).
fof(f161,plain,
~ is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(forward_subsumption_resolution,[],[f114,f146]) ).
fof(f163,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f160,f159]) ).
fof(f170,plain,
! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)),
inference(superposition,[],[f148,f163]) ).
fof(f184,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,[],[f156,f147]) ).
fof(f193,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X0,X1)))
| is_a_theorem(strict_equiv(X0,and(X0,X1))) ),
inference(resolution,[],[f184,f153]) ).
fof(f194,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,[],[f184,f154]) ).
fof(f196,plain,
! [X0,X1] : is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f194,f154]) ).
fof(f209,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,[],[f150,f157]) ).
fof(f211,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,[],[f209,f156]) ).
fof(f213,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,and(X1,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f211,f151]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,X2)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f211,f153]) ).
fof(f218,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f214,f151]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(X2,and(X1,X1))) ),
inference(resolution,[],[f213,f211]) ).
fof(f241,plain,
! [X0] : is_a_theorem(strict_equiv(X0,and(X0,X0))),
inference(resolution,[],[f193,f151]) ).
fof(f289,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(resolution,[],[f155,f196]) ).
fof(f291,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f155,f241]) ).
fof(f337,plain,
! [X0,X1] : implies(X1,X0) = not(and(not(X0),X1)),
inference(superposition,[],[f159,f289]) ).
fof(f394,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f159,f337]) ).
fof(f397,plain,
! [X0,X1] : implies(not(X0),X1) = or(X1,X0),
inference(forward_demodulation,[],[f394,f163]) ).
fof(f402,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_demodulation,[],[f397,f163]) ).
fof(f405,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X1),X0),
inference(superposition,[],[f170,f402]) ).
fof(f406,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),X0),
inference(forward_demodulation,[],[f405,f170]) ).
fof(f411,plain,
! [X2,X0,X1] : strict_implies(implies(X0,X1),X2) = strict_implies(not(X2),and(not(X1),X0)),
inference(superposition,[],[f406,f337]) ).
fof(f430,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(and(X0,X0)),X1))
| ~ is_a_theorem(strict_implies(not(X1),X0)) ),
inference(superposition,[],[f213,f406]) ).
fof(f437,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,[],[f184,f406]) ).
fof(f440,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,[],[f211,f406]) ).
fof(f441,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(X0,X2))
| is_a_theorem(strict_implies(not(X1),and(X2,X2))) ),
inference(superposition,[],[f236,f406]) ).
fof(f442,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(X0,X2)) ),
inference(forward_demodulation,[],[f441,f291]) ).
fof(f443,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X0))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f430,f291]) ).
fof(f448,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(not(X1))))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f440,f218]) ).
fof(f459,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
inference(resolution,[],[f443,f218]) ).
fof(f489,plain,
! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0)),
inference(resolution,[],[f448,f459]) ).
fof(f579,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(strict_implies(not(X2),not(X1))) ),
inference(superposition,[],[f214,f411]) ).
fof(f631,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(not(not(X0))),X1))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(resolution,[],[f489,f442]) ).
fof(f632,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,[],[f489,f437]) ).
fof(f652,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))),
inference(forward_subsumption_resolution,[],[f632,f459]) ).
fof(f653,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f652,f155]) ).
fof(f671,plain,
! [X0,X1] : not(and(not(X0),X1)) = implies(X1,not(not(X0))),
inference(superposition,[],[f337,f653]) ).
fof(f673,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),not(not(X0))),
inference(superposition,[],[f406,f653]) ).
fof(f690,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f671,f337]) ).
fof(f729,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,not(not(X1))),
inference(superposition,[],[f148,f690]) ).
fof(f732,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,not(not(X1))),
inference(forward_demodulation,[],[f729,f148]) ).
fof(f754,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,[],[f184,f732]) ).
fof(f813,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f754,f459]) ).
fof(f832,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f813,f218]) ).
fof(f836,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f832,f155]) ).
fof(f860,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X0,X1)),
inference(superposition,[],[f337,f836]) ).
fof(f862,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(not(X1),not(X0)),
inference(superposition,[],[f406,f836]) ).
fof(f1052,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(and(X0,X1)),X2))
| is_a_theorem(strict_implies(not(X2),not(not(X0)))) ),
inference(superposition,[],[f579,f860]) ).
fof(f1056,plain,
! [X0,X1] : strict_implies(X1,not(X0)) = necessarily(not(and(X0,X1))),
inference(superposition,[],[f148,f860]) ).
fof(f1062,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(and(X0,X1)),X2))
| is_a_theorem(strict_implies(not(X0),X2)) ),
inference(forward_demodulation,[],[f1052,f673]) ).
fof(f1070,plain,
! [X0] : necessarily(not(X0)) = strict_implies(X0,not(X0)),
inference(superposition,[],[f1056,f291]) ).
fof(f1142,plain,
! [X0] : necessarily(X0) = strict_implies(not(X0),X0),
inference(superposition,[],[f1070,f836]) ).
fof(f2888,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(strict_implies(not(X0),X2)) ),
inference(superposition,[],[f1062,f159]) ).
fof(f2930,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(X0),implies(X0,X1))),
inference(resolution,[],[f2888,f218]) ).
fof(f2968,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,implies(X1,X2)))
| ~ is_a_theorem(strict_implies(X0,not(X1))) ),
inference(resolution,[],[f2930,f211]) ).
fof(f3233,plain,
! [X0,X1] :
( is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),not(X0))) ),
inference(superposition,[],[f2968,f1142]) ).
fof(f3238,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),not(X0))) ),
inference(forward_demodulation,[],[f3233,f148]) ).
fof(f3258,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f3238,f862]) ).
fof(f3534,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(not(X0),implies(X1,X2)))
| ~ is_a_theorem(strict_implies(not(not(not(X0))),not(X1))) ),
inference(resolution,[],[f631,f2968]) ).
fof(f3580,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X1,not(not(X0))))
| is_a_theorem(strict_implies(not(X0),implies(X1,X2))) ),
inference(forward_demodulation,[],[f3534,f862]) ).
fof(f3590,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(not(X0),implies(X1,X2)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(forward_demodulation,[],[f3580,f732]) ).
fof(f3608,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X0))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(resolution,[],[f3590,f3258]) ).
fof(f3640,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f3608,f1142]) ).
fof(f3811,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f3640,f862]) ).
fof(f3857,definition,
( spl2_8
<=> ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f3858,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f3857]) ).
fof(f3864,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1)
| is_a_theorem(X0) ),
inference(resolution,[],[f3811,f157]) ).
fof(f3929,definition,
( spl2_9
<=> ! [X1] : ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f3930,plain,
( ! [X1] : ~ is_a_theorem(X1)
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f3929]) ).
fof(f3952,plain,
( spl2_9
| spl2_8 ),
inference(avatar_split_clause,[],[f3864,f3857,f3929]) ).
fof(f3957,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_8 ),
inference(superposition,[],[f3858,f148]) ).
fof(f3974,plain,
( $false
| ~ spl2_9 ),
inference(resolution,[],[f3930,f218]) ).
fof(f4030,plain,
~ spl2_9,
inference(avatar_contradiction_clause,[],[f3974]) ).
fof(f4043,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_8 ),
inference(resolution,[],[f3957,f153]) ).
fof(f4117,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f4043,f161]) ).
fof(f4126,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f4117]) ).
cnf(s15,plain,
( spl2_8
| spl2_9 ),
inference(sat_conversion,[],[f3952]) ).
cnf(s38,plain,
~ spl2_9,
inference(sat_conversion,[],[f4030]) ).
cnf(s39,plain,
~ spl2_8,
inference(sat_conversion,[],[f4126]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s15,s38,s39]) ).
fof(f4131,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL555+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 16:00:19 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 4.17/1.31 % (2548114)Detected formulas, will run a generic FOF schedule.
% 4.17/1.31 % (2548121)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=3693701735:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.17/1.31 % (2548124)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=406589086:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.17/1.31 % (2548122)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1479531774:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.17/1.31 % (2548123)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2188345635:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.17/1.31 % (2548125)dis-21_1_sil=8000:lcm=predicate:random_seed=3961885084: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)
% 4.17/1.31 % (2548120)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=1492678691:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.17/1.31 % (2548119)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=499014728:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.17/1.31 % (2548123)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548123)------------------------------
% 4.17/1.31 % (2548123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548123)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548122)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548122)------------------------------
% 4.17/1.31 % (2548122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548123)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548123)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548123)Peak memory usage: 86 MB
% 4.17/1.31 % (2548122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548122)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548122)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548122)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548122)Peak memory usage: 87 MB
% 4.17/1.31 % (2548125)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548125)------------------------------
% 4.17/1.31 % (2548125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548125)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548125)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548125)Time elapsed: 0.001 s
% 4.17/1.31 % (2548125)Peak memory usage: 88 MB
% 4.17/1.31 % (2548125)Instructions burned: 1 (million)
% 4.17/1.31 % (2548124)Instruction limit reached!
% 4.17/1.31 % (2548124)------------------------------
% 4.17/1.31 % (2548124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548124)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548124)Termination reason: Instruction limit
% 4.17/1.31 % (2548124)Termination phase: Saturation
% 4.17/1.31 % (2548124)Time elapsed: 0.060 s
% 4.17/1.31 % (2548124)Peak memory usage: 90 MB
% 4.17/1.31 % (2548124)Instructions burned: 140 (million)
% 4.17/1.31 % (2548125)------------------------------
% 4.17/1.31 % (2548125)------------------------------
% 4.17/1.31 % (2548123)------------------------------
% 4.17/1.31 % (2548123)------------------------------
% 4.17/1.31 % (2548122)------------------------------
% 4.17/1.31 % (2548122)------------------------------
% 4.17/1.31 % (2548133)lrs+10_1_sil=8000:sp=occurrence:random_seed=2962188141:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.17/1.31 % (2548133)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548133)------------------------------
% 4.17/1.31 % (2548133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548133)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548133)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548133)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548133)Peak memory usage: 87 MB
% 4.17/1.31 % (2548135)lrs+1011_1_sil=32000:sp=occurrence:random_seed=294527128:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.17/1.31 % (2548134)lrs+10_1_sil=32000:urr=on:br=off:random_seed=463606952:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.17/1.31 % (2548136)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=1855391197:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.17/1.31 % (2548135)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548135)------------------------------
% 4.17/1.31 % (2548135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548135)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548135)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548135)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548135)Peak memory usage: 87 MB
% 4.17/1.31 % (2548134)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548134)------------------------------
% 4.17/1.31 % (2548134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548134)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548134)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548134)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548134)Peak memory usage: 87 MB
% 4.17/1.31 % (2548121)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548121)------------------------------
% 4.17/1.31 % (2548121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548121)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548121)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548121)Time elapsed: 0.316 s
% 4.17/1.31 % (2548121)Peak memory usage: 125 MB
% 4.17/1.31 % (2548121)Instructions burned: 829 (million)
% 4.17/1.31 % (2548133)------------------------------
% 4.17/1.31 % (2548133)------------------------------
% 4.17/1.31 % (2548136)Instruction limit reached!
% 4.17/1.31 % (2548136)------------------------------
% 4.17/1.31 % (2548136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548136)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548136)Termination reason: Instruction limit
% 4.17/1.31 % (2548136)Termination phase: Saturation
% 4.17/1.31 % (2548136)Time elapsed: 0.080 s
% 4.17/1.31 % (2548136)Peak memory usage: 92 MB
% 4.17/1.31 % (2548136)Instructions burned: 250 (million)
% 4.17/1.31 % (2548141)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=212870383:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.17/1.31 % (2548141)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548141)------------------------------
% 4.17/1.31 % (2548141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548141)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548141)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548141)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548141)Peak memory usage: 87 MB
% 4.17/1.31 % (2548134)------------------------------
% 4.17/1.31 % (2548134)------------------------------
% 4.17/1.31 % (2548135)------------------------------
% 4.17/1.31 % (2548135)------------------------------
% 4.17/1.31 % (2548142)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=786001564:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.17/1.31 % (2548121)------------------------------
% 4.17/1.31 % (2548121)------------------------------
% 4.17/1.31 % (2548119)First to succeed.
% 4.17/1.31 % (2548119)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2548114"
% 4.17/1.31 % (2548145)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2072154476:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.17/1.31 % (2548144)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1450778511:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.17/1.31 % (2548144)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548144)------------------------------
% 4.17/1.31 % (2548144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548144)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548144)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548144)Time elapsed: 0.001 s
% 4.17/1.31 % (2548144)Peak memory usage: 88 MB
% 4.17/1.31 % (2548147)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2987309173:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 4.17/1.31 % (2548147)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548147)------------------------------
% 4.17/1.31 % (2548147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548147)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548147)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548147)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548147)Peak memory usage: 87 MB
% 4.17/1.31 % (2548145)Instruction limit reached!
% 4.17/1.31 % (2548145)------------------------------
% 4.17/1.31 % (2548145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548145)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548145)Termination reason: Instruction limit
% 4.17/1.31 % (2548145)Termination phase: Saturation
% 4.17/1.31 % (2548145)Time elapsed: 0.037 s
% 4.17/1.31 % (2548145)Peak memory usage: 88 MB
% 4.17/1.31 % (2548145)Instructions burned: 129 (million)
% 4.17/1.31 % (2548141)------------------------------
% 4.17/1.31 % (2548141)------------------------------
% 4.17/1.31 % (2548152)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2051234630:i=437:sd=1:aac=none:ss=included_2993 on theBenchmark for (2993ds/437Mi)
% 4.17/1.31 % (2548151)lrs+10_1_sil=8000:sp=occurrence:random_seed=823715186:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 4.17/1.31 % (2548151)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548151)------------------------------
% 4.17/1.31 % (2548151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548151)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548151)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548151)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548151)Peak memory usage: 87 MB
% 4.17/1.31 % (2548152)Refutation not found, incomplete strategy
% 4.17/1.31 % (2548152)------------------------------
% 4.17/1.31 % (2548152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.31 % (2548152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.31 % (2548152)CaDiCaL version: 2.1.3
% 4.17/1.31 % (2548152)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.31 % (2548152)Time elapsed: 0.0000 s
% 4.17/1.31 % (2548152)Peak memory usage: 87 MB
% 4.17/1.31 % (2548119)Refutation found. Thanks to Tanya!
% 4.17/1.31 % SZS status Theorem for theBenchmark
% 4.17/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 5.74/1.41 % (2548119)------------------------------
% 5.74/1.41 % (2548119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.41 % (2548119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.41 % (2548119)CaDiCaL version: 2.1.3
% 5.74/1.41 % (2548119)Termination reason: Refutation
% 5.74/1.41 % (2548119)Time elapsed: 0.517 s
% 5.74/1.41 % (2548119)Peak memory usage: 131 MB
% 5.74/1.41 % (2548119)Instructions burned: 1379 (million)
% 5.74/1.41 % (2548119)------------------------------
% 5.74/1.41 % (2548119)------------------------------
% 5.74/1.41 % (2548114)Success in time 0.79 s
% 5.74/1.41 % Vampire exiting
%------------------------------------------------------------------------------