%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL549+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:55 AM UTC 2026
% Result : Theorem 13.64s 3.05s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 42
% Syntax : Number of formulae : 295 ( 159 unt; 0 def)
% Number of atoms : 458 ( 99 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 285 ( 122 ~; 117 |; 2 &)
% ( 17 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 22 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 440 ( 439 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,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(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f54,axiom,
( axiom_K
<=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_K) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f56,axiom,
( axiom_4
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f57,axiom,
( axiom_B
<=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_B) ).
fof(f72,axiom,
( axiom_m10
<=> ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m10) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_possibly) ).
fof(f75,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(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f79,axiom,
axiom_K,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_K) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_4) ).
fof(f82,axiom,
axiom_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_B) ).
fof(f83,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f84,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).
fof(f90,negated_conjecture,
~ axiom_m10,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ axiom_m10,
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_m10 ),
inference(unused_predicate_definition_removal,[],[f72]) ).
fof(f93,plain,
( axiom_B
=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f94,plain,
( axiom_4
=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f95,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f96,plain,
( axiom_K
=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f97,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f98,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f99,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f101,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f104,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f105,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f107,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f108,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f109,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f110,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f111,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f112,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f117,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f111]) ).
fof(f120,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f110]) ).
fof(f121,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f109]) ).
fof(f122,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f108]) ).
fof(f123,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f107]) ).
fof(f125,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f105]) ).
fof(f126,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f129,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f101]) ).
fof(f131,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f99]) ).
fof(f132,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f98]) ).
fof(f133,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f134,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f136,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f97]) ).
fof(f137,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(ennf_transformation,[],[f96]) ).
fof(f138,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f95]) ).
fof(f139,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(ennf_transformation,[],[f94]) ).
fof(f140,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(ennf_transformation,[],[f93]) ).
fof(f141,plain,
( axiom_m10
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f92]) ).
fof(f142,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f143,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f145,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f141]) ).
fof(f146,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f147,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f119]) ).
fof(f148,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f120]) ).
fof(f149,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f121]) ).
fof(f150,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f122]) ).
fof(f151,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f123]) ).
fof(f153,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f154,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f126]) ).
fof(f157,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f129]) ).
fof(f159,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f160,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f132]) ).
fof(f161,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f133]) ).
fof(f162,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f134]) ).
fof(f165,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f167,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f168,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f169,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f170,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f171,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f173,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f174,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f177,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f179,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f180,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f181,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f182,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f136]) ).
fof(f183,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(cnf_transformation,[],[f137]) ).
fof(f184,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f138]) ).
fof(f185,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[],[f139]) ).
fof(f186,plain,
! [X0] :
( is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(cnf_transformation,[],[f140]) ).
fof(f187,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(cnf_transformation,[],[f145]) ).
fof(f188,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f142]) ).
fof(f189,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f143]) ).
fof(f192,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f193,plain,
axiom_K,
inference(cnf_transformation,[],[f79]) ).
fof(f194,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f195,plain,
axiom_4,
inference(cnf_transformation,[],[f81]) ).
fof(f196,plain,
axiom_B,
inference(cnf_transformation,[],[f82]) ).
fof(f197,plain,
op_possibly,
inference(cnf_transformation,[],[f83]) ).
fof(f198,plain,
op_or,
inference(cnf_transformation,[],[f84]) ).
fof(f199,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f202,plain,
~ axiom_m10,
inference(cnf_transformation,[],[f91]) ).
fof(f204,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f189,f199]) ).
fof(f205,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(forward_subsumption_resolution,[],[f188,f197]) ).
fof(f206,plain,
~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(forward_subsumption_resolution,[],[f187,f202]) ).
fof(f207,plain,
! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))),
inference(forward_subsumption_resolution,[],[f186,f196]) ).
fof(f208,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(forward_subsumption_resolution,[],[f185,f195]) ).
fof(f209,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f184,f194]) ).
fof(f210,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))),
inference(forward_subsumption_resolution,[],[f183,f193]) ).
fof(f211,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f182,f192]) ).
fof(f213,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f162,f165]) ).
fof(f214,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f161,f198]) ).
fof(f215,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[],[f160,f180]) ).
fof(f216,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f159,f179]) ).
fof(f218,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(forward_subsumption_resolution,[],[f157,f177]) ).
fof(f221,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_subsumption_resolution,[],[f154,f174]) ).
fof(f222,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[],[f153,f173]) ).
fof(f224,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f151,f171]) ).
fof(f225,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f150,f170]) ).
fof(f226,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f149,f169]) ).
fof(f227,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f148,f168]) ).
fof(f228,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f147,f181]) ).
fof(f229,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f146,f167]) ).
fof(f230,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))),
inference(forward_demodulation,[],[f210,f204]) ).
fof(f231,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f214,f213]) ).
fof(f232,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f211,f204]) ).
fof(f233,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f209,f229]) ).
fof(f234,plain,
! [X0] : is_a_theorem(strict_implies(necessarily(X0),X0)),
inference(resolution,[],[f209,f232]) ).
fof(f236,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f225,f229]) ).
fof(f239,plain,
! [X0] : is_a_theorem(strict_implies(X0,necessarily(possibly(X0)))),
inference(resolution,[],[f207,f232]) ).
fof(f243,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f224,f229]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f243,f229]) ).
fof(f248,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f246,f209]) ).
fof(f253,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f226,f236]) ).
fof(f255,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f226,f229]) ).
fof(f259,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f253,f232]) ).
fof(f264,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(superposition,[],[f231,f205]) ).
fof(f295,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f221,f236]) ).
fof(f297,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f221,f229]) ).
fof(f310,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f233,f204]) ).
fof(f315,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f227,f229]) ).
fof(f327,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f315,f231]) ).
fof(f337,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f215,f229]) ).
fof(f342,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f337,f229]) ).
fof(f347,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X0,X1))))
| is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))) ),
inference(resolution,[],[f342,f225]) ).
fof(f353,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| is_a_theorem(equiv(equiv(X0,X1),implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f342,f337]) ).
fof(f357,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X0,X1),X1))
| is_a_theorem(equiv(and(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f342,f297]) ).
fof(f358,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f342,f295]) ).
fof(f361,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f358,f222]) ).
fof(f362,plain,
! [X0,X1] :
( is_a_theorem(equiv(and(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f357,f222]) ).
fof(f364,plain,
! [X0,X1] :
( is_a_theorem(equiv(equiv(X0,X1),implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f353,f216]) ).
fof(f367,plain,
! [X0,X1] : is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))),
inference(forward_subsumption_resolution,[],[f347,f226]) ).
fof(f371,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f361,f228]) ).
fof(f372,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f213,f371]) ).
fof(f377,plain,
! [X0] : or(X0,X0) = not(not(X0)),
inference(forward_demodulation,[],[f372,f231]) ).
fof(f379,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| equiv(X0,X1) = implies(X1,X0) ),
inference(resolution,[],[f364,f228]) ).
fof(f381,plain,
! [X0] : implies(X0,necessarily(X0)) = equiv(necessarily(X0),X0),
inference(resolution,[],[f379,f209]) ).
fof(f391,plain,
! [X0,X1] : equiv(X0,implies(X1,X0)) = implies(implies(X1,X0),X0),
inference(resolution,[],[f379,f226]) ).
fof(f395,plain,
! [X0] : implies(necessarily(possibly(X0)),X0) = equiv(X0,necessarily(possibly(X0))),
inference(resolution,[],[f379,f207]) ).
fof(f407,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,necessarily(X0)))
| necessarily(X0) = X0 ),
inference(superposition,[],[f228,f381]) ).
fof(f408,plain,
! [X0] : necessarily(X0) = necessarily(necessarily(X0)),
inference(resolution,[],[f407,f208]) ).
fof(f430,plain,
! [X0] :
( ~ is_a_theorem(implies(necessarily(possibly(X0)),X0))
| necessarily(possibly(X0)) = X0 ),
inference(superposition,[],[f228,f395]) ).
fof(f446,plain,
! [X0] :
( ~ is_a_theorem(X0)
| necessarily(possibly(X0)) = X0 ),
inference(resolution,[],[f255,f430]) ).
fof(f480,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| and(X0,X1) = X1 ),
inference(resolution,[],[f362,f228]) ).
fof(f483,plain,
! [X0,X1] : and(implies(necessarily(X0),X0),X1) = X1,
inference(resolution,[],[f480,f209]) ).
fof(f492,plain,
! [X0,X1] : and(implies(X0,X0),X1) = X1,
inference(resolution,[],[f480,f253]) ).
fof(f505,plain,
! [X0,X1] : and(strict_implies(necessarily(X0),X0),X1) = X1,
inference(resolution,[],[f480,f234]) ).
fof(f506,plain,
! [X0,X1] : and(strict_implies(X0,X0),X1) = X1,
inference(resolution,[],[f480,f259]) ).
fof(f517,plain,
! [X0,X1] : not(not(X0)) = implies(implies(X1,X1),X0),
inference(superposition,[],[f213,f492]) ).
fof(f520,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X1),implies(X0,X0))),
inference(superposition,[],[f221,f492]) ).
fof(f536,plain,
! [X0,X1] : strict_implies(implies(X1,X1),X0) = necessarily(not(not(X0))),
inference(superposition,[],[f204,f517]) ).
fof(f637,plain,
! [X0,X1] : not(not(X0)) = implies(strict_implies(X1,X1),X0),
inference(superposition,[],[f213,f506]) ).
fof(f712,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),implies(X1,X1)))
| is_a_theorem(equiv(implies(X0,X0),implies(X1,X1))) ),
inference(resolution,[],[f520,f342]) ).
fof(f734,plain,
! [X0,X1] : is_a_theorem(equiv(implies(X0,X0),implies(X1,X1))),
inference(forward_subsumption_resolution,[],[f712,f520]) ).
fof(f738,plain,
! [X0,X1] : implies(X0,X0) = implies(X1,X1),
inference(resolution,[],[f734,f228]) ).
fof(f813,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X0))),
inference(superposition,[],[f226,f738]) ).
fof(f832,plain,
! [X0,X1] : implies(X0,X0) = or(X1,not(X1)),
inference(superposition,[],[f231,f738]) ).
fof(f833,plain,
! [X0,X1] : implies(X0,X0) = not(not(strict_implies(X1,X1))),
inference(superposition,[],[f637,f738]) ).
fof(f902,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[],[f813,f231]) ).
fof(f930,plain,
! [X0,X1] : strict_implies(X1,X1) = necessarily(or(X0,not(X0))),
inference(superposition,[],[f204,f832]) ).
fof(f1036,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X1,implies(X0,X0)))
| is_a_theorem(implies(not(strict_implies(X2,X2)),X1)) ),
inference(superposition,[],[f327,f833]) ).
fof(f1044,plain,
! [X2,X1] : is_a_theorem(implies(not(strict_implies(X2,X2)),X1)),
inference(forward_subsumption_resolution,[],[f1036,f902]) ).
fof(f1060,plain,
! [X2,X1] : is_a_theorem(or(strict_implies(X2,X2),X1)),
inference(forward_demodulation,[],[f1044,f231]) ).
fof(f1180,plain,
! [X0,X1] : is_a_theorem(implies(X0,strict_implies(X1,X1))),
inference(resolution,[],[f1060,f327]) ).
fof(f1257,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(or(X1,not(X1)),strict_implies(X0,X0)))
| strict_implies(X0,X0) = or(X1,not(X1)) ),
inference(superposition,[],[f407,f930]) ).
fof(f1259,plain,
! [X0,X1] : strict_implies(X0,X0) = or(X1,not(X1)),
inference(forward_subsumption_resolution,[],[f1257,f1180]) ).
fof(f1299,plain,
! [X0,X1] : strict_implies(X0,X0) = implies(X1,X1),
inference(superposition,[],[f832,f1259]) ).
fof(f1338,plain,
! [X0,X1] : implies(X0,X0) = necessarily(not(not(implies(X1,X1)))),
inference(superposition,[],[f536,f1299]) ).
fof(f2058,plain,
! [X0,X1] : not(not(X0)) = implies(strict_implies(necessarily(X1),X1),X0),
inference(superposition,[],[f213,f505]) ).
fof(f2472,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,implies(X0,X1)),
inference(resolution,[],[f367,f228]) ).
fof(f2526,plain,
! [X0,X1] : implies(X0,X0) = implies(X1,implies(X0,X0)),
inference(superposition,[],[f2472,f738]) ).
fof(f2545,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,implies(X0,X1)),
inference(superposition,[],[f204,f2472]) ).
fof(f2574,plain,
! [X0,X1] : implies(strict_implies(necessarily(X0),X0),X1) = not(not(implies(strict_implies(necessarily(X0),X0),X1))),
inference(superposition,[],[f2058,f2472]) ).
fof(f2575,plain,
! [X1] : not(not(X1)) = not(not(not(not(X1)))),
inference(forward_demodulation,[],[f2574,f2058]) ).
fof(f2580,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,implies(X0,X1)),
inference(forward_demodulation,[],[f2545,f204]) ).
fof(f2689,plain,
! [X0,X1] : necessarily(implies(X0,X0)) = strict_implies(X1,implies(X0,X0)),
inference(superposition,[],[f204,f2526]) ).
fof(f2732,plain,
! [X0,X1] : strict_implies(X0,X0) = strict_implies(X1,implies(X0,X0)),
inference(forward_demodulation,[],[f2689,f204]) ).
fof(f2951,plain,
! [X0,X1] : not(implies(X0,X1)) = not(not(not(implies(X0,X1)))),
inference(superposition,[],[f2575,f213]) ).
fof(f2966,plain,
! [X0,X1] : implies(X1,not(not(not(X0)))) = not(and(X1,not(not(X0)))),
inference(superposition,[],[f213,f2575]) ).
fof(f2985,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(X1,not(not(not(X0)))),
inference(forward_demodulation,[],[f2966,f213]) ).
fof(f2989,plain,
! [X2,X0,X1] : implies(X2,implies(X0,X1)) = implies(X2,not(not(implies(X0,X1)))),
inference(superposition,[],[f2985,f213]) ).
fof(f3068,plain,
! [X0,X1] : implies(not(X0),not(X1)) = or(X0,not(not(not(X1)))),
inference(superposition,[],[f231,f2985]) ).
fof(f3076,plain,
! [X0,X1] : or(X0,not(X1)) = or(X0,not(not(not(X1)))),
inference(forward_demodulation,[],[f3068,f231]) ).
fof(f3220,plain,
! [X0,X1] : not(not(X0)) = implies(implies(necessarily(X1),X1),X0),
inference(superposition,[],[f213,f483]) ).
fof(f3260,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,necessarily(X1)),not(not(implies(X0,X1))))),
inference(superposition,[],[f224,f3220]) ).
fof(f3370,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,necessarily(X1)),implies(X0,X1))),
inference(forward_demodulation,[],[f3260,f2989]) ).
fof(f3444,plain,
! [X0,X1] : is_a_theorem(strict_implies(implies(X0,necessarily(X1)),implies(X0,X1))),
inference(resolution,[],[f3370,f232]) ).
fof(f3482,plain,
! [X0,X1] : is_a_theorem(implies(implies(strict_implies(necessarily(X1),X1),necessarily(X0)),not(not(X0)))),
inference(superposition,[],[f3370,f2058]) ).
fof(f3492,plain,
! [X0] : is_a_theorem(implies(not(not(necessarily(X0))),not(not(X0)))),
inference(forward_demodulation,[],[f3482,f2058]) ).
fof(f3507,plain,
! [X0] : is_a_theorem(or(not(necessarily(X0)),not(not(X0)))),
inference(forward_demodulation,[],[f3492,f231]) ).
fof(f3688,plain,
! [X0] : is_a_theorem(or(possibly(X0),not(not(not(X0))))),
inference(superposition,[],[f3507,f205]) ).
fof(f3715,plain,
! [X0] : is_a_theorem(or(possibly(X0),not(X0))),
inference(forward_demodulation,[],[f3688,f3076]) ).
fof(f3730,plain,
! [X0] : is_a_theorem(implies(X0,possibly(X0))),
inference(resolution,[],[f3715,f327]) ).
fof(f3744,plain,
! [X0] : equiv(X0,possibly(X0)) = implies(possibly(X0),X0),
inference(resolution,[],[f3730,f379]) ).
fof(f3749,plain,
! [X0,X1] : and(implies(X0,possibly(X0)),X1) = X1,
inference(resolution,[],[f3730,f480]) ).
fof(f3750,plain,
! [X0] : implies(X0,possibly(X0)) = necessarily(possibly(implies(X0,possibly(X0)))),
inference(resolution,[],[f3730,f446]) ).
fof(f3768,plain,
! [X0] :
( ~ is_a_theorem(implies(possibly(X0),X0))
| possibly(X0) = X0 ),
inference(superposition,[],[f228,f3744]) ).
fof(f3785,plain,
! [X0] : implies(X0,X0) = possibly(implies(X0,X0)),
inference(resolution,[],[f3768,f813]) ).
fof(f6813,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f218,f229]) ).
fof(f7000,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X2),X1))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f6813,f229]) ).
fof(f7106,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X0)),X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f7000,f377]) ).
fof(f7130,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X0)),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(duplicate_literal_removal,[],[f7106]) ).
fof(f7136,plain,
! [X0,X1] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f7130,f231]) ).
fof(f7162,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(necessarily(not(X0)),X1))
| is_a_theorem(or(possibly(X0),X1)) ),
inference(superposition,[],[f7136,f205]) ).
fof(f7360,plain,
! [X0] : is_a_theorem(or(possibly(X0),necessarily(not(X0)))),
inference(resolution,[],[f7162,f253]) ).
fof(f8584,plain,
! [X0,X1] : not(necessarily(not(implies(X0,X1)))) = possibly(not(not(implies(X0,X1)))),
inference(superposition,[],[f205,f2951]) ).
fof(f8624,plain,
! [X0,X1] : possibly(implies(X0,X1)) = possibly(not(not(implies(X0,X1)))),
inference(forward_demodulation,[],[f8584,f205]) ).
fof(f10315,plain,
! [X0,X1] : not(not(X0)) = implies(implies(X1,possibly(X1)),X0),
inference(superposition,[],[f213,f3749]) ).
fof(f10389,plain,
! [X0,X1] : implies(X1,X1) = necessarily(not(not(not(not(implies(X0,possibly(X0))))))),
inference(superposition,[],[f1338,f10315]) ).
fof(f10400,plain,
! [X0] : not(not(implies(X0,possibly(X0)))) = possibly(not(not(implies(X0,possibly(X0))))),
inference(superposition,[],[f3785,f10315]) ).
fof(f10525,plain,
! [X0] : possibly(implies(X0,possibly(X0))) = not(not(implies(X0,possibly(X0)))),
inference(forward_demodulation,[],[f10400,f8624]) ).
fof(f10532,plain,
! [X0,X1] : implies(X1,X1) = necessarily(not(not(implies(X0,possibly(X0))))),
inference(forward_demodulation,[],[f10389,f2575]) ).
fof(f10575,plain,
! [X0,X1] : implies(X1,X1) = necessarily(possibly(implies(X0,possibly(X0)))),
inference(forward_demodulation,[],[f10532,f10525]) ).
fof(f10587,plain,
! [X0,X1] : implies(X1,X1) = implies(X0,possibly(X0)),
inference(forward_demodulation,[],[f10575,f3750]) ).
fof(f10770,plain,
! [X0,X1] : strict_implies(X1,implies(X0,X0)) = strict_implies(X1,possibly(X1)),
inference(superposition,[],[f2580,f10587]) ).
fof(f10797,plain,
! [X0,X1] : strict_implies(X0,X0) = strict_implies(X1,possibly(X1)),
inference(forward_demodulation,[],[f10770,f2732]) ).
fof(f25174,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(necessarily(X1),necessarily(X2))))
| ~ is_a_theorem(implies(X0,strict_implies(X1,X2))) ),
inference(resolution,[],[f230,f246]) ).
fof(f25175,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f230,f229]) ).
fof(f25384,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,necessarily(X0)))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X2,necessarily(X1))) ),
inference(resolution,[],[f25175,f246]) ).
fof(f25385,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f25175,f229]) ).
fof(f26512,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(necessarily(X0),strict_implies(X0,X1)))
| is_a_theorem(implies(necessarily(X0),necessarily(X1))) ),
inference(superposition,[],[f25174,f2472]) ).
fof(f26672,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(necessarily(X1),strict_implies(X0,X0)))
| is_a_theorem(implies(necessarily(X1),necessarily(possibly(X1)))) ),
inference(superposition,[],[f26512,f10797]) ).
fof(f26678,plain,
! [X1] : is_a_theorem(implies(necessarily(X1),necessarily(possibly(X1)))),
inference(forward_subsumption_resolution,[],[f26672,f1180]) ).
fof(f27753,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,necessarily(X1))))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f25385,f3444]) ).
fof(f27840,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,necessarily(X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(forward_demodulation,[],[f27753,f204]) ).
fof(f27866,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,necessarily(X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f27840,f204]) ).
fof(f29521,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(strict_implies(possibly(X0),X1)) ),
inference(resolution,[],[f25384,f26678]) ).
fof(f31652,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(strict_implies(possibly(X0),X1)) ),
inference(resolution,[],[f29521,f232]) ).
fof(f32074,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(X0),X1))
| is_a_theorem(strict_implies(necessarily(X0),X1)) ),
inference(resolution,[],[f31652,f27866]) ).
fof(f32207,plain,
! [X0] : is_a_theorem(strict_implies(necessarily(X0),necessarily(possibly(possibly(X0))))),
inference(resolution,[],[f32074,f239]) ).
fof(f32273,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(possibly(possibly(X0))))),
inference(resolution,[],[f32207,f310]) ).
fof(f32360,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),possibly(possibly(X0)))),
inference(resolution,[],[f32273,f248]) ).
fof(f32458,plain,
! [X0,X1] : and(implies(necessarily(X0),possibly(possibly(X0))),X1) = X1,
inference(resolution,[],[f32360,f480]) ).
fof(f33905,plain,
! [X0,X1] : not(not(X0)) = implies(implies(necessarily(X1),possibly(possibly(X1))),X0),
inference(superposition,[],[f213,f32458]) ).
fof(f33965,plain,
! [X2,X0,X1] : not(not(X2)) = implies(implies(strict_implies(X0,X1),possibly(possibly(implies(X0,X1)))),X2),
inference(superposition,[],[f33905,f204]) ).
fof(f56149,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X1))
| implies(X0,X1) = X1 ),
inference(superposition,[],[f228,f391]) ).
fof(f56307,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| not(not(X0)) = X0 ),
inference(superposition,[],[f56149,f33965]) ).
fof(f56387,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| not(not(X0)) = X0 ),
inference(forward_demodulation,[],[f56307,f231]) ).
fof(f56971,plain,
! [X0] :
( ~ is_a_theorem(or(possibly(X0),necessarily(not(X0))))
| not(possibly(X0)) = necessarily(not(X0)) ),
inference(superposition,[],[f56387,f205]) ).
fof(f56985,plain,
! [X0] : not(possibly(X0)) = necessarily(not(X0)),
inference(forward_subsumption_resolution,[],[f56971,f7360]) ).
fof(f57317,plain,
! [X0] : possibly(possibly(X0)) = not(necessarily(necessarily(not(X0)))),
inference(superposition,[],[f205,f56985]) ).
fof(f57323,plain,
! [X0,X1] : implies(possibly(possibly(X0)),X1) = or(necessarily(necessarily(not(X0))),X1),
inference(superposition,[],[f264,f56985]) ).
fof(f57455,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(possibly(X0)),X1),
inference(forward_demodulation,[],[f57323,f408]) ).
fof(f57458,plain,
! [X0] : possibly(possibly(X0)) = not(necessarily(not(X0))),
inference(forward_demodulation,[],[f57317,f408]) ).
fof(f57488,plain,
! [X0,X1] : implies(possibly(X0),X1) = implies(possibly(possibly(X0)),X1),
inference(forward_demodulation,[],[f57455,f264]) ).
fof(f57489,plain,
! [X0] : possibly(X0) = possibly(possibly(X0)),
inference(forward_demodulation,[],[f57458,f205]) ).
fof(f57729,plain,
! [X0] :
( ~ is_a_theorem(implies(possibly(X0),necessarily(possibly(possibly(X0)))))
| possibly(possibly(X0)) = necessarily(possibly(possibly(X0))) ),
inference(superposition,[],[f407,f57488]) ).
fof(f57819,plain,
! [X0] : possibly(possibly(X0)) = necessarily(possibly(possibly(X0))),
inference(forward_subsumption_resolution,[],[f57729,f207]) ).
fof(f57937,plain,
! [X0] : possibly(X0) = necessarily(possibly(X0)),
inference(forward_demodulation,[],[f57819,f57489]) ).
fof(f62406,plain,
~ is_a_theorem(strict_implies(possibly(sK0),possibly(sK0))),
inference(superposition,[],[f206,f57937]) ).
fof(f62576,plain,
$false,
inference(forward_subsumption_resolution,[],[f62406,f259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL549+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 16:00:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 10.49/2.38 % (3697269)Detected formulas, will run a generic FOF schedule.
% 10.49/2.38 % (3697274)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=2504865393:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.49/2.38 % (3697277)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=930655068:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.49/2.38 % (3697277)Refutation not found, incomplete strategy
% 10.49/2.38 % (3697277)------------------------------
% 10.49/2.38 % (3697277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (3697277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (3697277)CaDiCaL version: 2.1.3
% 10.49/2.38 % (3697277)Termination reason: Refutation not found, incomplete strategy
% 10.49/2.38 % (3697277)Time elapsed: 0.001 s
% 10.49/2.38 % (3697277)Peak memory usage: 87 MB
% 10.49/2.38 % (3697276)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=1473977346:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.49/2.38 % (3697275)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=1315234671:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.49/2.38 % (3697279)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=855965552:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.49/2.38 % (3697278)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2152611715:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.49/2.38 % (3697280)dis-21_1_sil=8000:lcm=predicate:random_seed=4133868047: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)
% 10.49/2.38 % (3697278)Refutation not found, incomplete strategy
% 10.49/2.38 % (3697278)------------------------------
% 10.49/2.38 % (3697278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (3697278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (3697278)CaDiCaL version: 2.1.3
% 10.49/2.38 % (3697278)Termination reason: Refutation not found, incomplete strategy
% 10.49/2.38 % (3697278)Time elapsed: 0.001 s
% 10.49/2.38 % (3697278)Peak memory usage: 87 MB
% 10.49/2.38 % (3697280)Refutation not found, incomplete strategy
% 10.49/2.38 % (3697280)------------------------------
% 10.49/2.38 % (3697280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (3697280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.38 % (3697280)CaDiCaL version: 2.1.3
% 10.49/2.38 % (3697280)Termination reason: Refutation not found, incomplete strategy
% 10.49/2.38 % (3697280)Time elapsed: 0.002 s
% 10.49/2.38 % (3697280)Peak memory usage: 88 MB
% 10.49/2.38 % (3697280)Instructions burned: 1 (million)
% 10.49/2.38 % (3697279)Instruction limit reached!
% 10.49/2.38 % (3697279)------------------------------
% 10.49/2.38 % (3697279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.38 % (3697279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.39 % (3697279)CaDiCaL version: 2.1.3
% 10.49/2.39 % (3697279)Termination reason: Instruction limit
% 10.49/2.39 % (3697279)Termination phase: Saturation
% 10.49/2.39 % (3697279)Time elapsed: 0.095 s
% 10.49/2.39 % (3697279)Peak memory usage: 91 MB
% 10.49/2.39 % (3697279)Instructions burned: 139 (million)
% 10.49/2.39 % (3697277)------------------------------
% 10.49/2.39 % (3697277)------------------------------
% 10.49/2.39 % (3697288)lrs+10_1_sil=8000:sp=occurrence:random_seed=2617365311:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.49/2.39 % (3697288)Refutation not found, incomplete strategy
% 10.49/2.39 % (3697288)------------------------------
% 10.49/2.39 % (3697288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.49/2.39 % (3697288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.49/2.39 % (3697288)CaDiCaL version: 2.1.3
% 10.49/2.39 % (3697288)Termination reason: Refutation not found, incomplete strategy
% 10.49/2.39 % (3697288)Time elapsed: 0.001 s
% 10.49/2.39 % (3697288)Peak memory usage: 87 MB
% 10.49/2.39 % (3697280)------------------------------
% 10.49/2.39 % (3697280)------------------------------
% 13.96/2.98 % (3697278)------------------------------
% 13.96/2.98 % (3697278)------------------------------
% 13.96/2.98 % (3697289)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1820972300:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 13.96/2.98 % (3697289)Refutation not found, incomplete strategy
% 13.96/2.98 % (3697289)------------------------------
% 13.96/2.98 % (3697289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/2.98 % (3697289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/2.98 % (3697289)CaDiCaL version: 2.1.3
% 13.96/2.98 % (3697289)Termination reason: Refutation not found, incomplete strategy
% 13.96/2.98 % (3697289)Time elapsed: 0.001 s
% 13.96/2.98 % (3697289)Peak memory usage: 87 MB
% 13.96/2.98 % (3697291)lrs+1011_1_sil=32000:sp=occurrence:random_seed=47294871:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 13.96/2.98 % (3697292)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=3638631354:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 13.96/2.98 % (3697291)Refutation not found, incomplete strategy
% 13.96/2.98 % (3697291)------------------------------
% 13.96/2.98 % (3697291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/2.98 % (3697291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/2.98 % (3697291)CaDiCaL version: 2.1.3
% 13.96/2.98 % (3697291)Termination reason: Refutation not found, incomplete strategy
% 13.96/2.98 % (3697291)Time elapsed: 0.001 s
% 13.96/2.98 % (3697291)Peak memory usage: 87 MB
% 13.96/2.98 % (3697288)------------------------------
% 13.96/2.98 % (3697288)------------------------------
% 13.96/2.98 % (3697292)Instruction limit reached!
% 13.96/2.98 % (3697292)------------------------------
% 13.96/2.98 % (3697292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/2.98 % (3697292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/2.98 % (3697292)CaDiCaL version: 2.1.3
% 13.96/2.98 % (3697292)Termination reason: Instruction limit
% 13.96/2.98 % (3697292)Termination phase: Saturation
% 13.96/2.98 % (3697292)Time elapsed: 0.147 s
% 13.96/2.98 % (3697292)Peak memory usage: 93 MB
% 13.96/2.98 % (3697292)Instructions burned: 248 (million)
% 13.96/2.98 % (3697276)Refutation not found, incomplete strategy
% 13.96/2.98 % (3697276)------------------------------
% 13.96/2.98 % (3697276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/2.98 % (3697276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/2.98 % (3697276)CaDiCaL version: 2.1.3
% 13.96/2.98 % (3697276)Termination reason: Refutation not found, incomplete strategy
% 13.96/2.98 % (3697276)Time elapsed: 0.556 s
% 13.96/2.98 % (3697276)Peak memory usage: 126 MB
% 13.96/2.98 % (3697276)Instructions burned: 830 (million)
% 13.96/2.98 % (3697289)------------------------------
% 13.96/2.98 % (3697289)------------------------------
% 13.96/2.98 % (3697296)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3647855200:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 13.96/2.98 % (3697296)Refutation not found, incomplete strategy
% 13.96/2.98 % (3697296)------------------------------
% 13.96/2.98 % (3697296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/2.98 % (3697296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/2.98 % (3697296)CaDiCaL version: 2.1.3
% 13.96/2.98 % (3697296)Termination reason: Refutation not found, incomplete strategy
% 13.96/2.98 % (3697296)Time elapsed: 0.001 s
% 13.96/2.98 % (3697296)Peak memory usage: 87 MB
% 13.96/2.98 % (3697291)------------------------------
% 13.96/2.98 % (3697291)------------------------------
% 13.96/2.98 % (3697297)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1428364231:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 13.96/2.98 % (3697298)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3789865970:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 13.96/2.98 % (3697298)Refutation not found, incomplete strategy
% 13.96/2.98 % (3697298)------------------------------
% 13.96/2.98 % (3697298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/2.98 % (3697298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/2.98 % (3697298)CaDiCaL version: 2.1.3
% 13.96/2.98 % (3697298)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.03 % (3697298)Time elapsed: 0.001 s
% 13.96/3.03 % (3697298)Peak memory usage: 88 MB
% 13.96/3.03 % (3697300)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3245380880:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 13.96/3.03 % (3697276)------------------------------
% 13.96/3.03 % (3697276)------------------------------
% 13.96/3.03 % (3697300)Instruction limit reached!
% 13.96/3.03 % (3697300)------------------------------
% 13.96/3.03 % (3697300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/3.03 % (3697300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/3.03 % (3697300)CaDiCaL version: 2.1.3
% 13.96/3.03 % (3697300)Termination reason: Instruction limit
% 13.96/3.03 % (3697300)Termination phase: Saturation
% 13.96/3.03 % (3697300)Time elapsed: 0.070 s
% 13.96/3.03 % (3697300)Peak memory usage: 89 MB
% 13.96/3.03 % (3697300)Instructions burned: 128 (million)
% 13.96/3.03 % (3697296)------------------------------
% 13.96/3.03 % (3697296)------------------------------
% 13.96/3.03 % (3697304)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1043783467:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 13.96/3.03 % (3697304)Refutation not found, incomplete strategy
% 13.96/3.03 % (3697304)------------------------------
% 13.96/3.03 % (3697304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/3.03 % (3697304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/3.03 % (3697304)CaDiCaL version: 2.1.3
% 13.96/3.03 % (3697304)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.03 % (3697304)Time elapsed: 0.001 s
% 13.96/3.03 % (3697304)Peak memory usage: 87 MB
% 13.96/3.03 % (3697298)------------------------------
% 13.96/3.03 % (3697298)------------------------------
% 13.96/3.03 % (3697305)lrs+10_1_sil=8000:sp=occurrence:random_seed=4210168739:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 13.96/3.03 % (3697306)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2323716835:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 13.96/3.03 % (3697306)Refutation not found, incomplete strategy
% 13.96/3.03 % (3697306)------------------------------
% 13.96/3.03 % (3697306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/3.03 % (3697306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/3.03 % (3697306)CaDiCaL version: 2.1.3
% 13.96/3.03 % (3697306)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.03 % (3697306)Time elapsed: 0.001 s
% 13.96/3.03 % (3697306)Peak memory usage: 88 MB
% 13.96/3.03 % (3697308)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3382943122:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 13.96/3.03 % (3697304)------------------------------
% 13.96/3.03 % (3697304)------------------------------
% 13.96/3.03 % (3697306)------------------------------
% 13.96/3.03 % (3697306)------------------------------
% 13.96/3.03 % (3697312)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2134541005:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 13.96/3.03 % (3697312)Refutation not found, incomplete strategy
% 13.96/3.03 % (3697312)------------------------------
% 13.96/3.03 % (3697312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/3.03 % (3697312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/3.03 % (3697312)CaDiCaL version: 2.1.3
% 13.96/3.03 % (3697312)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.03 % (3697312)Time elapsed: 0.001 s
% 13.96/3.03 % (3697312)Peak memory usage: 89 MB
% 13.96/3.03 % (3697312)Instructions burned: 1 (million)
% 13.96/3.03 % (3697313)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=767813905:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 13.96/3.03 % (3697313)Refutation not found, incomplete strategy
% 13.96/3.03 % (3697313)------------------------------
% 13.96/3.03 % (3697313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.96/3.03 % (3697313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.96/3.03 % (3697313)CaDiCaL version: 2.1.3
% 13.96/3.03 % (3697313)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.03 % (3697313)Time elapsed: 0.001 s
% 13.64/3.05 % (3697313)Peak memory usage: 88 MB
% 13.64/3.05 % (3697313)Instructions burned: 1 (million)
% 13.64/3.05 % (3697305)Instruction limit reached!
% 13.64/3.05 % (3697305)------------------------------
% 13.64/3.05 % (3697305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.64/3.05 % (3697305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.64/3.05 % (3697305)CaDiCaL version: 2.1.3
% 13.64/3.05 % (3697305)Termination reason: Instruction limit
% 13.64/3.05 % (3697305)Termination phase: Saturation
% 13.64/3.05 % (3697305)Time elapsed: 0.531 s
% 13.64/3.05 % (3697305)Peak memory usage: 101 MB
% 13.64/3.05 % (3697305)Instructions burned: 907 (million)
% 13.64/3.05 % (3697312)------------------------------
% 13.64/3.05 % (3697312)------------------------------
% 13.64/3.05 % (3697313)------------------------------
% 13.64/3.05 % (3697313)------------------------------
% 13.64/3.05 % (3697316)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2181041020:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 13.64/3.05 % (3697317)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=225326917:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/125Mi)
% 13.64/3.05 % (3697317)Refutation not found, incomplete strategy
% 13.64/3.05 % (3697317)------------------------------
% 13.64/3.05 % (3697317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.64/3.05 % (3697317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.64/3.05 % (3697317)CaDiCaL version: 2.1.3
% 13.64/3.05 % (3697317)Termination reason: Refutation not found, incomplete strategy
% 13.64/3.05 % (3697317)Time elapsed: 0.001 s
% 13.64/3.05 % (3697317)Peak memory usage: 87 MB
% 13.64/3.05 % (3697317)Instructions burned: 1 (million)
% 13.64/3.05 % (3697297)Instruction limit reached!
% 13.64/3.05 % (3697297)------------------------------
% 13.64/3.05 % (3697297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.64/3.05 % (3697297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.64/3.05 % (3697297)CaDiCaL version: 2.1.3
% 13.64/3.05 % (3697297)Termination reason: Instruction limit
% 13.64/3.05 % (3697297)Termination phase: Saturation
% 13.64/3.05 % (3697297)Time elapsed: 1.056 s
% 13.64/3.05 % (3697297)Peak memory usage: 142 MB
% 13.64/3.05 % (3697297)Instructions burned: 2351 (million)
% 13.64/3.05 % (3697274)First to succeed.
% 13.64/3.05 % (3697318)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3484673940:i=134:gtgl=5:slsql=off:gtg=exists_sym_2982 on theBenchmark for (2982ds/134Mi)
% 13.64/3.05 % (3697274)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3697269"
% 13.64/3.05 % (3697321)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=158949622:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/141Mi)
% 13.64/3.05 % (3697321)Refutation not found, incomplete strategy
% 13.64/3.05 % (3697321)------------------------------
% 13.64/3.05 % (3697321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.64/3.05 % (3697321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.64/3.05 % (3697321)CaDiCaL version: 2.1.3
% 13.64/3.05 % (3697321)Termination reason: Refutation not found, incomplete strategy
% 13.64/3.05 % (3697321)Time elapsed: 0.0000 s
% 13.64/3.05 % (3697321)Peak memory usage: 87 MB
% 13.64/3.05 % (3697318)Instruction limit reached!
% 13.64/3.05 % (3697318)------------------------------
% 13.64/3.05 % (3697318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.64/3.05 % (3697318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.64/3.05 % (3697318)CaDiCaL version: 2.1.3
% 13.64/3.05 % (3697318)Termination reason: Instruction limit
% 13.64/3.05 % (3697318)Termination phase: Saturation
% 13.64/3.05 % (3697318)Time elapsed: 0.091 s
% 13.64/3.05 % (3697318)Peak memory usage: 89 MB
% 13.64/3.05 % (3697318)Instructions burned: 134 (million)
% 13.64/3.05 % (3697317)------------------------------
% 13.64/3.05 % (3697317)------------------------------
% 13.64/3.05 % (3697324)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1441533201:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2980 on theBenchmark for (2980ds/431Mi)
% 13.64/3.05 % (3697321)------------------------------
% 13.64/3.05 % (3697321)------------------------------
% 13.64/3.05 % (3697324)Refutation not found, incomplete strategy
% 13.64/3.05 % (3697324)------------------------------
% 13.64/3.05 % (3697324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.64/3.05 % (3697324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.64/3.05 % (3697324)CaDiCaL version: 2.1.3
% 13.64/3.05 % (3697324)Termination reason: Refutation not found, incomplete strategy
% 13.64/3.05 % (3697324)Time elapsed: 0.001 s
% 13.64/3.05 % (3697324)Peak memory usage: 87 MB
% 13.64/3.05 [W927 16:00:10.839697615 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839739646 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839778953 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839790476 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839819976 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839830256 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839855153 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839865357 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839888817 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839898977 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839922930 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 [W927 16:00:10.839932867 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 13.64/3.05 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 13.64/3.05 % (3697325)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2726230206:i=6060:aac=none:ins=25_2979 on theBenchmark for (2979ds/6060Mi)
% 13.64/3.05 % (3697274)Refutation found. Thanks to Tanya!
% 13.64/3.05 % SZS status Theorem for theBenchmark
% 13.64/3.05 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/3.14 % (3697274)------------------------------
% 0.16/3.14 % (3697274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/3.14 % (3697274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/3.14 % (3697274)CaDiCaL version: 2.1.3
% 0.16/3.14 % (3697274)Termination reason: Refutation
% 0.16/3.14 % (3697274)Time elapsed: 1.801 s
% 0.16/3.14 % (3697274)Peak memory usage: 158 MB
% 0.16/3.14 % (3697274)Instructions burned: 4396 (million)
% 0.16/3.14 % (3697274)------------------------------
% 0.16/3.14 % (3697274)------------------------------
% 0.16/3.14 % (3697269)Success in time 2.197 s
% 0.16/3.14 % Vampire exiting
%------------------------------------------------------------------------------