%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL566+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 : n011.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 3.43s 1.61s
% Output : Refutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 28
% Syntax : Number of formulae : 141 ( 72 unt; 0 def)
% Number of atoms : 241 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 171 ( 71 ~; 67 |; 4 &)
% ( 9 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 189 ( 188 !; 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(f11,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
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(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(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_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f56,negated_conjecture,
~ axiom_M,
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f57,plain,
~ axiom_M,
inference(flattening,[],[f56]) ).
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),X0))
=> axiom_M ),
inference(unused_predicate_definition_removal,[],[f11]) ).
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_M
| ? [X0] : ~ is_a_theorem(implies(necessarily(X0),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(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_M
| ~ is_a_theorem(implies(necessarily(sK0),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_M
| ~ is_a_theorem(implies(necessarily(sK0),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(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(f131,plain,
op_or,
inference(cnf_transformation,[],[f51]) ).
fof(f132,plain,
op_implies_and,
inference(cnf_transformation,[],[f52]) ).
fof(f134,plain,
~ axiom_M,
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(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),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(f164,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(f170,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(and(X0,X0),X0))
| is_a_theorem(strict_equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f164,f141]) ).
fof(f171,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,[],[f164,f144]) ).
fof(f172,plain,
! [X0,X1] : is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f171,f144]) ).
fof(f173,plain,
! [X0] : is_a_theorem(strict_equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f170,f143]) ).
fof(f180,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(f182,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,[],[f180,f148]) ).
fof(f220,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f147,f173]) ).
fof(f221,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(resolution,[],[f147,f172]) ).
fof(f233,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(superposition,[],[f141,f220]) ).
fof(f264,plain,
! [X0,X1] : implies(X1,X0) = not(and(not(X0),X1)),
inference(superposition,[],[f151,f221]) ).
fof(f295,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f151,f264]) ).
fof(f300,plain,
! [X0,X1] : implies(not(X0),X1) = or(X1,X0),
inference(forward_demodulation,[],[f295,f153]) ).
fof(f306,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_demodulation,[],[f300,f153]) ).
fof(f309,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X1),X0),
inference(superposition,[],[f157,f306]) ).
fof(f310,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),X0),
inference(forward_demodulation,[],[f309,f157]) ).
fof(f339,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,[],[f164,f310]) ).
fof(f342,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,[],[f182,f310]) ).
fof(f347,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(not(X1))))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f342,f233]) ).
fof(f356,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
inference(resolution,[],[f347,f233]) ).
fof(f367,plain,
! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0)),
inference(resolution,[],[f356,f347]) ).
fof(f869,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,[],[f367,f339]) ).
fof(f892,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))),
inference(forward_subsumption_resolution,[],[f869,f356]) ).
fof(f893,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f892,f147]) ).
fof(f916,plain,
! [X0,X1] : not(and(not(X0),X1)) = implies(X1,not(not(X0))),
inference(superposition,[],[f264,f893]) ).
fof(f919,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),not(not(X0))),
inference(superposition,[],[f310,f893]) ).
fof(f948,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f916,f264]) ).
fof(f1005,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,not(not(X1))),
inference(superposition,[],[f136,f948]) ).
fof(f1008,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,not(not(X1))),
inference(forward_demodulation,[],[f1005,f136]) ).
fof(f1038,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,[],[f164,f1008]) ).
fof(f1670,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f1038,f356]) ).
fof(f1708,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f1670,f233]) ).
fof(f1717,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f1708,f147]) ).
fof(f1757,plain,
! [X0] : possibly(not(X0)) = not(necessarily(X0)),
inference(superposition,[],[f137,f1717]) ).
fof(f1789,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(not(X1),not(X0)),
inference(superposition,[],[f919,f1717]) ).
fof(f1828,plain,
! [X0] : is_a_theorem(strict_implies(not(X0),not(necessarily(X0)))),
inference(superposition,[],[f139,f1757]) ).
fof(f1845,plain,
! [X0] : is_a_theorem(strict_implies(necessarily(X0),X0)),
inference(forward_demodulation,[],[f1828,f1789]) ).
fof(f1859,plain,
! [X0,X1] : is_a_theorem(strict_implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f1845,f136]) ).
fof(f2219,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1859,f149]) ).
fof(f2276,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(resolution,[],[f2219,f1845]) ).
fof(f2337,plain,
$false,
inference(resolution,[],[f2276,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL566+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n011.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 16:02:16 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.43/1.60 % (2589463)Detected formulas, will run a generic FOF schedule.
% 3.43/1.60 % (2589468)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=4069571066:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.43/1.60 % (2589474)dis-21_1_sil=8000:lcm=predicate:random_seed=1424270080: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)
% 3.43/1.60 % (2589469)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=4287303695:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.43/1.60 % (2589472)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1987537477:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.43/1.60 % (2589470)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=755430157:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.43/1.60 % (2589471)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1719893780:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.43/1.60 % (2589473)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1465531179:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.43/1.60 % (2589472)Refutation not found, incomplete strategy
% 3.43/1.60 % (2589472)------------------------------
% 3.43/1.60 % (2589472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.60 % (2589472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.60 % (2589471)Refutation not found, incomplete strategy
% 3.43/1.60 % (2589471)------------------------------
% 3.43/1.60 % (2589471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.60 % (2589472)CaDiCaL version: 2.1.3
% 3.43/1.60 % (2589472)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.60 % (2589472)Time elapsed: 0.001 s
% 3.43/1.60 % (2589472)Peak memory usage: 87 MB
% 3.43/1.60 % (2589471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.60 % (2589471)CaDiCaL version: 2.1.3
% 3.43/1.60 % (2589471)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.60 % (2589471)Time elapsed: 0.001 s
% 3.43/1.60 % (2589471)Peak memory usage: 87 MB
% 3.43/1.60 % (2589474)Refutation not found, incomplete strategy
% 3.43/1.60 % (2589474)------------------------------
% 3.43/1.60 % (2589474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.60 % (2589474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.60 % (2589474)CaDiCaL version: 2.1.3
% 3.43/1.60 % (2589474)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.60 % (2589474)Time elapsed: 0.002 s
% 3.43/1.60 % (2589474)Peak memory usage: 88 MB
% 3.43/1.60 % (2589474)Instructions burned: 1 (million)
% 3.43/1.60 % (2589473)Instruction limit reached!
% 3.43/1.60 % (2589473)------------------------------
% 3.43/1.60 % (2589473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.60 % (2589473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.61 % (2589473)CaDiCaL version: 2.1.3
% 3.43/1.61 % (2589473)Termination reason: Instruction limit
% 3.43/1.61 % (2589473)Termination phase: Saturation
% 3.43/1.61 % (2589473)Time elapsed: 0.092 s
% 3.43/1.61 % (2589473)Peak memory usage: 90 MB
% 3.43/1.61 % (2589473)Instructions burned: 140 (million)
% 3.43/1.61 % (2589482)lrs+10_1_sil=8000:sp=occurrence:random_seed=847018256:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.43/1.61 % (2589482)Refutation not found, incomplete strategy
% 3.43/1.61 % (2589482)------------------------------
% 3.43/1.61 % (2589482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.61 % (2589482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.61 % (2589482)CaDiCaL version: 2.1.3
% 3.43/1.61 % (2589482)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.61 % (2589482)Time elapsed: 0.001 s
% 3.43/1.61 % (2589482)Peak memory usage: 87 MB
% 3.43/1.61 % (2589474)------------------------------
% 3.43/1.61 % (2589474)------------------------------
% 3.43/1.61 % (2589472)------------------------------
% 3.43/1.61 % (2589472)------------------------------
% 3.43/1.61 % (2589471)------------------------------
% 3.43/1.61 % (2589471)------------------------------
% 3.43/1.61 % (2589485)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1511694638:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.43/1.61 % (2589486)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=3056299048:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.43/1.61 % (2589484)lrs+10_1_sil=32000:urr=on:br=off:random_seed=865073326:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.43/1.61 % (2589485)Refutation not found, incomplete strategy
% 3.43/1.61 % (2589485)------------------------------
% 3.43/1.61 % (2589485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.61 % (2589485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.61 % (2589485)CaDiCaL version: 2.1.3
% 3.43/1.61 % (2589485)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.61 % (2589485)Time elapsed: 0.001 s
% 3.43/1.61 % (2589485)Peak memory usage: 87 MB
% 3.43/1.61 % (2589484)Refutation not found, incomplete strategy
% 3.43/1.61 % (2589484)------------------------------
% 3.43/1.61 % (2589484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.61 % (2589484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.61 % (2589484)CaDiCaL version: 2.1.3
% 3.43/1.61 % (2589484)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.61 % (2589484)Time elapsed: 0.001 s
% 3.43/1.61 % (2589484)Peak memory usage: 87 MB
% 3.43/1.61 % (2589468)First to succeed.
% 3.43/1.61 % (2589468)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2589463"
% 3.43/1.61 % (2589482)------------------------------
% 3.43/1.61 % (2589482)------------------------------
% 3.43/1.61 % (2589486)Instruction limit reached!
% 3.43/1.61 % (2589486)------------------------------
% 3.43/1.61 % (2589486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.61 % (2589486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.61 % (2589486)CaDiCaL version: 2.1.3
% 3.43/1.61 % (2589486)Termination reason: Instruction limit
% 3.43/1.61 % (2589486)Termination phase: Saturation
% 3.43/1.61 % (2589486)Time elapsed: 0.148 s
% 3.43/1.61 % (2589486)Peak memory usage: 92 MB
% 3.43/1.61 % (2589486)Instructions burned: 249 (million)
% 3.43/1.61 % (2589470)Refutation not found, incomplete strategy
% 3.43/1.61 % (2589470)------------------------------
% 3.43/1.61 % (2589470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.61 % (2589470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.61 % (2589470)CaDiCaL version: 2.1.3
% 3.43/1.61 % (2589470)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.61 % (2589470)Time elapsed: 0.559 s
% 3.43/1.61 % (2589470)Peak memory usage: 127 MB
% 3.43/1.61 % (2589470)Instructions burned: 829 (million)
% 3.43/1.61 % (2589468)Refutation found. Thanks to Tanya!
% 3.43/1.61 % SZS status Theorem for theBenchmark
% 3.43/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 5.94/1.80 % (2589468)------------------------------
% 5.94/1.80 % (2589468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.80 % (2589468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.80 % (2589468)CaDiCaL version: 2.1.3
% 5.94/1.80 % (2589468)Termination reason: Refutation
% 5.94/1.80 % (2589468)Time elapsed: 0.476 s
% 5.94/1.80 % (2589468)Peak memory usage: 131 MB
% 5.94/1.80 % (2589468)Instructions burned: 1236 (million)
% 5.94/1.80 % (2589468)------------------------------
% 5.94/1.80 % (2589468)------------------------------
% 5.94/1.80 % (2589463)Success in time 0.747 s
% 5.94/1.80 % Vampire exiting
%------------------------------------------------------------------------------