%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 11:53:04 AM UTC 2026
% Result : Theorem 11.49s 2.66s
% Output : Refutation 13.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 30
% Syntax : Number of formulae : 178 ( 93 unt; 0 def)
% Number of atoms : 294 ( 59 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 202 ( 86 ~; 81 |; 4 &)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 229 ( 228 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f3,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f8,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adjunction) ).
fof(f9,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_strict_equiv) ).
fof(f12,axiom,
( axiom_4
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f19,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m1) ).
fof(f20,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m2) ).
fof(f22,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m4) ).
fof(f23,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/sandbox2/benchmark/theBenchmark.p',axiom_m5) ).
fof(f24,axiom,
( axiom_m6
<=> ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m6) ).
fof(f27,axiom,
( axiom_m9
<=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m9) ).
fof(f29,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_possibly) ).
fof(f31,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f32,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f33,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f36,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f38,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f39,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f40,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f41,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f42,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f43,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f45,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f46,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m5) ).
fof(f47,axiom,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
fof(f49,axiom,
axiom_m9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(f51,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f52,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f55,conjecture,
axiom_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_4) ).
fof(f56,negated_conjecture,
~ axiom_4,
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f57,plain,
~ axiom_4,
inference(flattening,[],[f56]) ).
fof(f58,plain,
( axiom_m9
=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(unused_predicate_definition_removal,[],[f27]) ).
fof(f59,plain,
( axiom_m6
=> ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f60,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,[],[f23]) ).
fof(f61,plain,
( axiom_m4
=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f63,plain,
( axiom_m2
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f64,plain,
( axiom_m1
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f66,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
=> axiom_4 ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f67,plain,
( substitution_strict_equiv
=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f68,plain,
( adjunction
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f69,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,[],[f7]) ).
fof(f76,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f1]) ).
fof(f77,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f3]) ).
fof(f79,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,[],[f69]) ).
fof(f80,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ modus_ponens_strict_implies ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(ennf_transformation,[],[f68]) ).
fof(f82,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) )
| ~ substitution_strict_equiv ),
inference(ennf_transformation,[],[f67]) ).
fof(f84,plain,
( axiom_4
| ? [X0] : ~ is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f86,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(ennf_transformation,[],[f64]) ).
fof(f87,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(ennf_transformation,[],[f63]) ).
fof(f89,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(ennf_transformation,[],[f61]) ).
fof(f90,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,[],[f60]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ axiom_m6 ),
inference(ennf_transformation,[],[f59]) ).
fof(f92,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| ~ axiom_m9 ),
inference(ennf_transformation,[],[f58]) ).
fof(f93,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f29]) ).
fof(f94,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f31]) ).
fof(f95,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f32]) ).
fof(f96,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily(sK0),necessarily(necessarily(sK0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f84]) ).
fof(f97,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f76]) ).
fof(f98,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f77]) ).
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(cnf_transformation,[],[f80]) ).
fof(f101,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ adjunction ),
inference(cnf_transformation,[],[f82]) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[],[f83]) ).
fof(f103,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily(sK0),necessarily(necessarily(sK0)))) ),
inference(cnf_transformation,[],[f96]) ).
fof(f105,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[],[f86]) ).
fof(f106,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[],[f87]) ).
fof(f108,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[],[f89]) ).
fof(f109,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,[],[f90]) ).
fof(f110,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ axiom_m6 ),
inference(cnf_transformation,[],[f91]) ).
fof(f111,plain,
! [X0] :
( is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| ~ axiom_m9 ),
inference(cnf_transformation,[],[f92]) ).
fof(f112,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f93]) ).
fof(f113,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f94]) ).
fof(f114,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f95]) ).
fof(f115,plain,
op_possibly,
inference(cnf_transformation,[],[f33]) ).
fof(f117,plain,
op_strict_implies,
inference(cnf_transformation,[],[f36]) ).
fof(f119,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f38]) ).
fof(f120,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[],[f39]) ).
fof(f121,plain,
substitution_strict_equiv,
inference(cnf_transformation,[],[f40]) ).
fof(f122,plain,
adjunction,
inference(cnf_transformation,[],[f41]) ).
fof(f123,plain,
axiom_m1,
inference(cnf_transformation,[],[f42]) ).
fof(f124,plain,
axiom_m2,
inference(cnf_transformation,[],[f43]) ).
fof(f126,plain,
axiom_m4,
inference(cnf_transformation,[],[f45]) ).
fof(f127,plain,
axiom_m5,
inference(cnf_transformation,[],[f46]) ).
fof(f128,plain,
axiom_m6,
inference(cnf_transformation,[],[f47]) ).
fof(f130,plain,
axiom_m9,
inference(cnf_transformation,[],[f49]) ).
fof(f131,plain,
op_or,
inference(cnf_transformation,[],[f51]) ).
fof(f132,plain,
op_implies_and,
inference(cnf_transformation,[],[f52]) ).
fof(f134,plain,
~ axiom_4,
inference(cnf_transformation,[],[f57]) ).
fof(f135,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f114,f119]) ).
fof(f136,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f113,f117]) ).
fof(f137,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(forward_subsumption_resolution,[],[f112,f115]) ).
fof(f138,plain,
! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))),
inference(forward_subsumption_resolution,[],[f111,f130]) ).
fof(f139,plain,
! [X0] : is_a_theorem(strict_implies(X0,possibly(X0))),
inference(forward_subsumption_resolution,[],[f110,f128]) ).
fof(f140,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,[],[f109,f127]) ).
fof(f141,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[],[f108,f126]) ).
fof(f143,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f106,f124]) ).
fof(f144,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f105,f123]) ).
fof(f146,plain,
~ is_a_theorem(implies(necessarily(sK0),necessarily(necessarily(sK0)))),
inference(forward_subsumption_resolution,[],[f103,f134]) ).
fof(f147,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f102,f121]) ).
fof(f148,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f101,f122]) ).
fof(f149,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f100,f120]) ).
fof(f151,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f98,f132]) ).
fof(f152,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f97,f131]) ).
fof(f153,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f152,f151]) ).
fof(f157,plain,
! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)),
inference(superposition,[],[f136,f153]) ).
fof(f169,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,[],[f148,f135]) ).
fof(f175,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(and(X0,X0),X0))
| is_a_theorem(strict_equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f169,f141]) ).
fof(f176,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,[],[f169,f144]) ).
fof(f177,plain,
! [X0,X1] : is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f176,f144]) ).
fof(f178,plain,
! [X0] : is_a_theorem(strict_equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f175,f143]) ).
fof(f185,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,[],[f140,f149]) ).
fof(f187,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,[],[f185,f148]) ).
fof(f217,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f147,f178]) ).
fof(f218,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(resolution,[],[f147,f177]) ).
fof(f221,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f151,f217]) ).
fof(f230,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(superposition,[],[f141,f217]) ).
fof(f239,plain,
! [X0] : not(not(X0)) = or(X0,X0),
inference(forward_demodulation,[],[f221,f153]) ).
fof(f261,plain,
! [X0,X1] : implies(X1,X0) = not(and(not(X0),X1)),
inference(superposition,[],[f151,f218]) ).
fof(f292,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f151,f261]) ).
fof(f297,plain,
! [X0,X1] : implies(not(X0),X1) = or(X1,X0),
inference(forward_demodulation,[],[f292,f153]) ).
fof(f303,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_demodulation,[],[f297,f153]) ).
fof(f306,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X1),X0),
inference(superposition,[],[f157,f303]) ).
fof(f307,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),X0),
inference(forward_demodulation,[],[f306,f157]) ).
fof(f314,plain,
! [X0,X1] : strict_implies(not(X1),necessarily(not(X0))) = strict_implies(possibly(X0),X1),
inference(superposition,[],[f307,f137]) ).
fof(f332,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,[],[f169,f307]) ).
fof(f335,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,[],[f187,f307]) ).
fof(f340,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(not(X1))))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f335,f230]) ).
fof(f349,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
inference(resolution,[],[f340,f230]) ).
fof(f360,plain,
! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0)),
inference(resolution,[],[f349,f340]) ).
fof(f392,plain,
! [X0] : strict_implies(not(X0),X0) = necessarily(not(not(X0))),
inference(superposition,[],[f157,f239]) ).
fof(f410,plain,
! [X0] : possibly(not(X0)) = not(strict_implies(not(X0),X0)),
inference(superposition,[],[f137,f392]) ).
fof(f880,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,[],[f360,f332]) ).
fof(f903,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))),
inference(forward_subsumption_resolution,[],[f880,f349]) ).
fof(f904,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f903,f147]) ).
fof(f913,plain,
! [X0] : possibly(not(X0)) = not(not(possibly(not(X0)))),
inference(superposition,[],[f904,f410]) ).
fof(f924,plain,
! [X0] : not(necessarily(not(X0))) = possibly(not(not(X0))),
inference(superposition,[],[f137,f904]) ).
fof(f927,plain,
! [X0,X1] : not(and(not(X0),X1)) = implies(X1,not(not(X0))),
inference(superposition,[],[f261,f904]) ).
fof(f930,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),not(not(X0))),
inference(superposition,[],[f307,f904]) ).
fof(f936,plain,
! [X0,X1] : strict_implies(not(X0),necessarily(not(X1))) = strict_implies(possibly(X1),not(not(X0))),
inference(superposition,[],[f314,f904]) ).
fof(f954,plain,
! [X0,X1] : strict_implies(possibly(X1),X0) = strict_implies(possibly(X1),not(not(X0))),
inference(forward_demodulation,[],[f936,f314]) ).
fof(f961,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f927,f261]) ).
fof(f964,plain,
! [X0] : possibly(X0) = possibly(not(not(X0))),
inference(forward_demodulation,[],[f924,f137]) ).
fof(f1020,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,not(not(X1))),
inference(superposition,[],[f136,f961]) ).
fof(f1023,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,not(not(X1))),
inference(forward_demodulation,[],[f1020,f136]) ).
fof(f1054,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,[],[f169,f1023]) ).
fof(f1253,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),possibly(X0))),
inference(superposition,[],[f139,f964]) ).
fof(f1281,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(possibly(X0),not(not(X0))))
| is_a_theorem(strict_equiv(possibly(X0),not(not(X0)))) ),
inference(resolution,[],[f1253,f169]) ).
fof(f1301,plain,
! [X0] :
( is_a_theorem(strict_equiv(possibly(X0),not(not(X0))))
| ~ is_a_theorem(strict_implies(possibly(X0),X0)) ),
inference(forward_demodulation,[],[f1281,f954]) ).
fof(f1712,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f1054,f349]) ).
fof(f1749,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f1712,f230]) ).
fof(f1758,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f1749,f147]) ).
fof(f1777,plain,
! [X0] : not(possibly(X0)) = necessarily(not(X0)),
inference(superposition,[],[f1758,f137]) ).
fof(f1799,plain,
! [X0] : possibly(not(X0)) = not(necessarily(X0)),
inference(superposition,[],[f137,f1758]) ).
fof(f1833,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(not(X1),not(X0)),
inference(superposition,[],[f930,f1758]) ).
fof(f1871,plain,
! [X0] : is_a_theorem(strict_implies(not(X0),not(necessarily(X0)))),
inference(superposition,[],[f139,f1799]) ).
fof(f1882,plain,
! [X0] :
( is_a_theorem(strict_equiv(not(necessarily(X0)),not(not(not(X0)))))
| ~ is_a_theorem(strict_implies(not(necessarily(X0)),not(X0))) ),
inference(superposition,[],[f1301,f1799]) ).
fof(f1885,plain,
! [X0] :
( is_a_theorem(strict_equiv(not(necessarily(X0)),not(X0)))
| ~ is_a_theorem(strict_implies(not(necessarily(X0)),not(X0))) ),
inference(forward_demodulation,[],[f1882,f904]) ).
fof(f1892,plain,
! [X0] : is_a_theorem(strict_implies(necessarily(X0),X0)),
inference(forward_demodulation,[],[f1871,f1833]) ).
fof(f1899,plain,
! [X0] :
( is_a_theorem(strict_equiv(not(necessarily(X0)),not(X0)))
| ~ is_a_theorem(strict_implies(X0,necessarily(X0))) ),
inference(forward_demodulation,[],[f1885,f1833]) ).
fof(f1908,plain,
! [X0,X1] : is_a_theorem(strict_implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f1892,f136]) ).
fof(f2411,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1908,f149]) ).
fof(f2452,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f2411,f230]) ).
fof(f2629,plain,
! [X0,X1] : strict_equiv(not(X0),not(X1)) = and(strict_implies(not(X0),not(X1)),strict_implies(X0,X1)),
inference(superposition,[],[f135,f1833]) ).
fof(f2645,plain,
! [X0,X1] : and(strict_implies(X1,X0),strict_implies(X0,X1)) = strict_equiv(not(X0),not(X1)),
inference(forward_demodulation,[],[f2629,f1833]) ).
fof(f2677,plain,
! [X0,X1] : strict_equiv(X1,X0) = strict_equiv(not(X0),not(X1)),
inference(forward_demodulation,[],[f2645,f135]) ).
fof(f12628,plain,
! [X0] :
( is_a_theorem(strict_equiv(not(necessarily(not(possibly(not(X0))))),possibly(not(X0))))
| ~ is_a_theorem(strict_implies(not(possibly(not(X0))),necessarily(not(possibly(not(X0)))))) ),
inference(superposition,[],[f1899,f913]) ).
fof(f12659,plain,
! [X0] :
( is_a_theorem(strict_equiv(not(necessarily(not(not(necessarily(X0))))),not(necessarily(X0))))
| ~ is_a_theorem(strict_implies(not(possibly(not(X0))),necessarily(not(possibly(not(X0)))))) ),
inference(forward_demodulation,[],[f12628,f1799]) ).
fof(f12683,plain,
! [X0] :
( is_a_theorem(strict_equiv(necessarily(X0),necessarily(not(not(necessarily(X0))))))
| ~ is_a_theorem(strict_implies(not(possibly(not(X0))),necessarily(not(possibly(not(X0)))))) ),
inference(forward_demodulation,[],[f12659,f2677]) ).
fof(f12701,plain,
! [X0] :
( is_a_theorem(strict_equiv(necessarily(X0),not(possibly(not(necessarily(X0))))))
| ~ is_a_theorem(strict_implies(not(possibly(not(X0))),necessarily(not(possibly(not(X0)))))) ),
inference(forward_demodulation,[],[f12683,f1777]) ).
fof(f12713,plain,
! [X0] :
( is_a_theorem(strict_equiv(necessarily(X0),not(not(necessarily(necessarily(X0))))))
| ~ is_a_theorem(strict_implies(not(possibly(not(X0))),necessarily(not(possibly(not(X0)))))) ),
inference(forward_demodulation,[],[f12701,f1799]) ).
fof(f12718,plain,
! [X0] :
( is_a_theorem(strict_equiv(necessarily(X0),necessarily(necessarily(X0))))
| ~ is_a_theorem(strict_implies(not(possibly(not(X0))),necessarily(not(possibly(not(X0)))))) ),
inference(forward_demodulation,[],[f12713,f1758]) ).
fof(f12722,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(possibly(possibly(not(X0))),possibly(not(X0))))
| is_a_theorem(strict_equiv(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(forward_demodulation,[],[f12718,f314]) ).
fof(f12726,plain,
! [X0] : is_a_theorem(strict_equiv(necessarily(X0),necessarily(necessarily(X0)))),
inference(forward_subsumption_resolution,[],[f12722,f138]) ).
fof(f12729,plain,
! [X0] : necessarily(X0) = necessarily(necessarily(X0)),
inference(resolution,[],[f12726,f147]) ).
fof(f12750,plain,
~ is_a_theorem(implies(necessarily(sK0),necessarily(sK0))),
inference(superposition,[],[f146,f12729]) ).
fof(f12847,plain,
$false,
inference(forward_subsumption_resolution,[],[f12750,f2452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n015.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 16:06:01 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.10/2.53 % (1819546)Detected formulas, will run a generic FOF schedule.
% 11.10/2.53 % (1819555)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=129959169:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.10/2.53 % (1819555)Refutation not found, incomplete strategy
% 11.10/2.53 % (1819555)------------------------------
% 11.10/2.53 % (1819555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.10/2.53 % (1819555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.10/2.53 % (1819555)CaDiCaL version: 2.1.3
% 11.10/2.53 % (1819555)Termination reason: Refutation not found, incomplete strategy
% 11.10/2.53 % (1819555)Time elapsed: 0.0000 s
% 11.10/2.53 % (1819555)Peak memory usage: 87 MB
% 11.10/2.53 % (1819554)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2728732203:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.10/2.53 % (1819553)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=1493886928:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.10/2.53 % (1819552)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=2421707195:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.10/2.53 % (1819551)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=2145751993:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.10/2.53 % (1819554)Refutation not found, incomplete strategy
% 11.10/2.53 % (1819554)------------------------------
% 11.10/2.53 % (1819554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.10/2.53 % (1819554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.10/2.53 % (1819554)CaDiCaL version: 2.1.3
% 11.10/2.53 % (1819554)Termination reason: Refutation not found, incomplete strategy
% 11.10/2.53 % (1819554)Time elapsed: 0.001 s
% 11.10/2.53 % (1819554)Peak memory usage: 87 MB
% 11.10/2.53 % (1819556)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2776865287:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.10/2.53 % (1819557)dis-21_1_sil=8000:lcm=predicate:random_seed=204000619: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)
% 11.10/2.53 % (1819557)Refutation not found, incomplete strategy
% 11.10/2.53 % (1819557)------------------------------
% 11.10/2.53 % (1819557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.10/2.53 % (1819557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.10/2.53 % (1819557)CaDiCaL version: 2.1.3
% 11.10/2.53 % (1819557)Termination reason: Refutation not found, incomplete strategy
% 11.10/2.53 % (1819557)Time elapsed: 0.002 s
% 11.10/2.53 % (1819557)Peak memory usage: 88 MB
% 11.10/2.53 % (1819557)Instructions burned: 1 (million)
% 11.10/2.53 % (1819555)------------------------------
% 11.10/2.53 % (1819555)------------------------------
% 11.10/2.53 % (1819556)Instruction limit reached!
% 11.10/2.53 % (1819556)------------------------------
% 11.10/2.53 % (1819556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.10/2.53 % (1819556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.10/2.53 % (1819556)CaDiCaL version: 2.1.3
% 11.10/2.53 % (1819556)Termination reason: Instruction limit
% 11.10/2.53 % (1819556)Termination phase: Saturation
% 11.10/2.53 % (1819556)Time elapsed: 0.091 s
% 11.10/2.53 % (1819556)Peak memory usage: 90 MB
% 11.10/2.53 % (1819556)Instructions burned: 140 (million)
% 11.10/2.53 % (1819566)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3297045855:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.10/2.53 % (1819566)Refutation not found, incomplete strategy
% 11.10/2.53 % (1819566)------------------------------
% 11.10/2.53 % (1819566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.10/2.53 % (1819566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.10/2.53 % (1819566)CaDiCaL version: 2.1.3
% 11.10/2.53 % (1819566)Termination reason: Refutation not found, incomplete strategy
% 11.10/2.53 % (1819566)Time elapsed: 0.0000 s
% 11.10/2.53 % (1819566)Peak memory usage: 87 MB
% 11.10/2.53 % (1819554)------------------------------
% 11.10/2.53 % (1819554)------------------------------
% 11.49/2.66 % (1819557)------------------------------
% 11.49/2.66 % (1819557)------------------------------
% 11.49/2.66 % (1819565)lrs+10_1_sil=8000:sp=occurrence:random_seed=1150724201:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.49/2.66 % (1819565)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819565)------------------------------
% 11.49/2.66 % (1819565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819565)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819565)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819565)Time elapsed: 0.001 s
% 11.49/2.66 % (1819565)Peak memory usage: 87 MB
% 11.49/2.66 % (1819566)------------------------------
% 11.49/2.66 % (1819566)------------------------------
% 11.49/2.66 % (1819568)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1332092911:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 11.49/2.66 % (1819568)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819568)------------------------------
% 11.49/2.66 % (1819568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819568)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819568)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819568)Time elapsed: 0.001 s
% 11.49/2.66 % (1819568)Peak memory usage: 87 MB
% 11.49/2.66 % (1819569)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=2338176214:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 11.49/2.66 % (1819571)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3408433560:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 11.49/2.66 % (1819571)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819571)------------------------------
% 11.49/2.66 % (1819571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819571)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819571)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819571)Time elapsed: 0.0000 s
% 11.49/2.66 % (1819571)Peak memory usage: 87 MB
% 11.49/2.66 % (1819565)------------------------------
% 11.49/2.66 % (1819565)------------------------------
% 11.49/2.66 % (1819553)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819553)------------------------------
% 11.49/2.66 % (1819553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819553)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819553)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819553)Time elapsed: 0.557 s
% 11.49/2.66 % (1819553)Peak memory usage: 124 MB
% 11.49/2.66 % (1819553)Instructions burned: 824 (million)
% 11.49/2.66 % (1819569)Instruction limit reached!
% 11.49/2.66 % (1819569)------------------------------
% 11.49/2.66 % (1819569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819569)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819569)Termination reason: Instruction limit
% 11.49/2.66 % (1819569)Termination phase: Saturation
% 11.49/2.66 % (1819569)Time elapsed: 0.149 s
% 11.49/2.66 % (1819569)Peak memory usage: 92 MB
% 11.49/2.66 % (1819569)Instructions burned: 248 (million)
% 11.49/2.66 % (1819568)------------------------------
% 11.49/2.66 % (1819568)------------------------------
% 11.49/2.66 % (1819571)------------------------------
% 11.49/2.66 % (1819571)------------------------------
% 11.49/2.66 % (1819575)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=563557647:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 11.49/2.66 % (1819576)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3473355896:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 11.49/2.66 % (1819576)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819576)------------------------------
% 11.49/2.66 % (1819576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819576)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819576)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819576)Time elapsed: 0.001 s
% 11.49/2.66 % (1819576)Peak memory usage: 88 MB
% 11.49/2.66 % (1819578)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2834856554:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.49/2.66 % (1819578)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819578)------------------------------
% 11.49/2.66 % (1819578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819578)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819578)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819578)Time elapsed: 0.001 s
% 11.49/2.66 % (1819578)Peak memory usage: 88 MB
% 11.49/2.66 % (1819578)Instructions burned: 1 (million)
% 11.49/2.66 % (1819553)------------------------------
% 11.49/2.66 % (1819553)------------------------------
% 11.49/2.66 % (1819577)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1337038568:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 11.49/2.66 % (1819577)Instruction limit reached!
% 11.49/2.66 % (1819577)------------------------------
% 11.49/2.66 % (1819577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819577)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819577)Termination reason: Instruction limit
% 11.49/2.66 % (1819577)Termination phase: Saturation
% 11.49/2.66 % (1819577)Time elapsed: 0.071 s
% 11.49/2.66 % (1819577)Peak memory usage: 88 MB
% 11.49/2.66 % (1819577)Instructions burned: 128 (million)
% 11.49/2.66 % (1819578)------------------------------
% 11.49/2.66 % (1819578)------------------------------
% 11.49/2.66 % (1819582)lrs+10_1_sil=8000:sp=occurrence:random_seed=3174586148:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 11.49/2.66 % (1819576)------------------------------
% 11.49/2.66 % (1819576)------------------------------
% 11.49/2.66 % (1819585)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2670662218:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 11.49/2.66 % (1819584)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3409739987:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 11.49/2.66 % (1819584)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819584)------------------------------
% 11.49/2.66 % (1819584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819584)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819584)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819584)Time elapsed: 0.001 s
% 11.49/2.66 % (1819584)Peak memory usage: 88 MB
% 11.49/2.66 % (1819587)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2162219932:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 11.49/2.66 % (1819587)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819587)------------------------------
% 11.49/2.66 % (1819587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819587)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819587)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819587)Time elapsed: 0.001 s
% 11.49/2.66 % (1819587)Peak memory usage: 89 MB
% 11.49/2.66 % (1819584)------------------------------
% 11.49/2.66 % (1819584)------------------------------
% 11.49/2.66 % (1819551)First to succeed.
% 11.49/2.66 % (1819551)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1819546"
% 11.49/2.66 % (1819587)------------------------------
% 11.49/2.66 % (1819587)------------------------------
% 11.49/2.66 % (1819591)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=981923474:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 11.49/2.66 % (1819591)Refutation not found, incomplete strategy
% 11.49/2.66 % (1819591)------------------------------
% 11.49/2.66 % (1819591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819591)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819591)Termination reason: Refutation not found, incomplete strategy
% 11.49/2.66 % (1819591)Time elapsed: 0.001 s
% 11.49/2.66 % (1819591)Peak memory usage: 88 MB
% 11.49/2.66 % (1819582)Instruction limit reached!
% 11.49/2.66 % (1819582)------------------------------
% 11.49/2.66 % (1819582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.49/2.66 % (1819582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.49/2.66 % (1819582)CaDiCaL version: 2.1.3
% 11.49/2.66 % (1819582)Termination reason: Instruction limit
% 11.49/2.66 % (1819582)Termination phase: Saturation
% 11.49/2.66 % (1819582)Time elapsed: 0.511 s
% 11.49/2.66 % (1819582)Peak memory usage: 101 MB
% 11.49/2.66 % (1819582)Instructions burned: 907 (million)
% 11.49/2.66 % (1819592)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3210960738:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 11.49/2.66 % (1819551)Refutation found. Thanks to Tanya!
% 11.49/2.66 % SZS status Theorem for theBenchmark
% 11.49/2.66 % SZS output start Proof for theBenchmark
% See solution above
% 13.06/2.86 % (1819551)------------------------------
% 13.06/2.86 % (1819551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.06/2.86 % (1819551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.06/2.86 % (1819551)CaDiCaL version: 2.1.3
% 13.06/2.86 % (1819551)Termination reason: Refutation
% 13.06/2.86 % (1819551)Time elapsed: 1.340 s
% 13.06/2.86 % (1819551)Peak memory usage: 137 MB
% 13.06/2.86 % (1819551)Instructions burned: 2033 (million)
% 13.06/2.86 % (1819551)------------------------------
% 13.06/2.86 % (1819551)------------------------------
% 13.06/2.86 % (1819546)Success in time 1.767 s
% 13.06/2.86 % Vampire exiting
%------------------------------------------------------------------------------