%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL541+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 : n005.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 11:52:53 AM UTC 2026
% Result : Theorem 32.26s 5.45s
% Output : Refutation 32.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 51
% Syntax : Number of formulae : 323 ( 105 unt; 3 def)
% Number of atoms : 619 ( 92 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 547 ( 251 ~; 242 |; 2 &)
% ( 22 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 30 ( 28 usr; 28 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 476 ( 0 sgn 474 !; 2 ?)
% 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(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
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(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
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(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
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(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
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(f63,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(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(f76,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(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(f88,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f89,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f90,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ axiom_m1,
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> axiom_m1 ),
inference(unused_predicate_definition_removal,[],[f63]) ).
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(f102,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
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(f106,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
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(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f106]) ).
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(f128,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f102]) ).
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_m1
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,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(f144,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f145,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f146,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f147,plain,
! [X0,X1] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f148,plain,
! [X0,X1] :
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f121]) ).
fof(f149,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f123]) ).
fof(f151,plain,
! [X0,X1] :
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f152,plain,
! [X0,X1] :
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f153,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f126]) ).
fof(f155,plain,
! [X0,X1] :
( ~ or_2
| is_a_theorem(implies(X1,or(X0,X1))) ),
inference(cnf_transformation,[],[f128]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ or_3
| is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(cnf_transformation,[],[f129]) ).
fof(f158,plain,
! [X0,X1] :
( ~ equivalence_2
| is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(cnf_transformation,[],[f131]) ).
fof(f159,plain,
! [X0,X1] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f160,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f133]) ).
fof(f161,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f134]) ).
fof(f164,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f166,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f167,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f168,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f169,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f170,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f171,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f172,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f173,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f175,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f176,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f178,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f179,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f180,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f181,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f182,plain,
! [X0,X1] :
( ~ axiom_K
| is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f183,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f184,plain,
! [X0] :
( ~ axiom_4
| is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(cnf_transformation,[],[f139]) ).
fof(f185,plain,
! [X0] :
( ~ axiom_B
| is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f140]) ).
fof(f186,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0)))
| axiom_m1 ),
inference(cnf_transformation,[],[f141]) ).
fof(f187,plain,
! [X0] :
( ~ op_possibly
| possibly(X0) = not(necessarily(not(X0))) ),
inference(cnf_transformation,[],[f142]) ).
fof(f188,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f189,plain,
! [X0,X1] :
( ~ op_strict_equiv
| strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f191,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f192,plain,
axiom_K,
inference(cnf_transformation,[],[f79]) ).
fof(f193,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f194,plain,
axiom_4,
inference(cnf_transformation,[],[f81]) ).
fof(f195,plain,
axiom_B,
inference(cnf_transformation,[],[f82]) ).
fof(f196,plain,
op_possibly,
inference(cnf_transformation,[],[f83]) ).
fof(f197,plain,
op_or,
inference(cnf_transformation,[],[f84]) ).
fof(f198,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f200,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f88]) ).
fof(f201,plain,
~ axiom_m1,
inference(cnf_transformation,[],[f91]) ).
fof(f202,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f189,f200]) ).
fof(f203,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f188,f198]) ).
fof(f204,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(forward_subsumption_resolution,[],[f187,f196]) ).
fof(f205,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
inference(forward_subsumption_resolution,[],[f186,f201]) ).
fof(f206,plain,
! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))),
inference(forward_subsumption_resolution,[],[f185,f195]) ).
fof(f207,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(forward_subsumption_resolution,[],[f184,f194]) ).
fof(f208,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f183,f193]) ).
fof(f209,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))),
inference(forward_subsumption_resolution,[],[f182,f192]) ).
fof(f210,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f181,f191]) ).
fof(f212,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f161,f164]) ).
fof(f213,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f160,f197]) ).
fof(f214,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[],[f159,f179]) ).
fof(f215,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f158,f178]) ).
fof(f217,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(forward_subsumption_resolution,[],[f156,f176]) ).
fof(f218,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(forward_subsumption_resolution,[],[f155,f175]) ).
fof(f220,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_subsumption_resolution,[],[f153,f173]) ).
fof(f221,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[],[f152,f172]) ).
fof(f222,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f151,f171]) ).
fof(f223,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f150,f170]) ).
fof(f224,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f149,f169]) ).
fof(f225,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f148,f168]) ).
fof(f226,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f147,f167]) ).
fof(f227,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f146,f180]) ).
fof(f228,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f145,f166]) ).
fof(f229,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))),
inference(forward_demodulation,[],[f209,f203]) ).
fof(f230,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f213,f212]) ).
fof(f233,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f220,f228]) ).
fof(f234,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f210,f203]) ).
fof(f235,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(resolution,[],[f234,f222]) ).
fof(f239,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f224,f228]) ).
fof(f240,plain,
! [X0] : is_a_theorem(strict_implies(necessarily(X0),X0)),
inference(resolution,[],[f208,f234]) ).
fof(f242,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f208,f203]) ).
fof(f243,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f239,f220]) ).
fof(f246,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f225,f239]) ).
fof(f248,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f225,f228]) ).
fof(f252,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f223,f228]) ).
fof(f253,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[],[f252,f239]) ).
fof(f255,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f252,f228]) ).
fof(f265,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f255,f208]) ).
fof(f270,plain,
! [X0,X1] : is_a_theorem(strict_implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f240,f203]) ).
fof(f274,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f214,f228]) ).
fof(f277,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f274,f228]) ).
fof(f280,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f277,f243]) ).
fof(f281,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,[],[f277,f233]) ).
fof(f283,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,[],[f277,f224]) ).
fof(f287,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,[],[f277,f274]) ).
fof(f291,plain,
! [X0,X1] :
( is_a_theorem(equiv(equiv(X0,X1),implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f287,f215]) ).
fof(f292,plain,
! [X0,X1] : is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))),
inference(forward_subsumption_resolution,[],[f283,f225]) ).
fof(f294,plain,
! [X0,X1] :
( is_a_theorem(equiv(and(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f281,f221]) ).
fof(f295,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f280,f221]) ).
fof(f297,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f246,f230]) ).
fof(f298,plain,
! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)),
inference(superposition,[],[f203,f230]) ).
fof(f332,plain,
! [X0,X1] : is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X1))),
inference(superposition,[],[f235,f202]) ).
fof(f350,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f227,f295]) ).
fof(f351,plain,
! [X0,X1] :
( and(X0,X1) = X1
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f227,f294]) ).
fof(f366,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f212,f350]) ).
fof(f369,plain,
! [X0] : or(X0,X0) = not(not(X0)),
inference(forward_demodulation,[],[f366,f230]) ).
fof(f371,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[],[f218,f369]) ).
fof(f397,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),implies(not(X1),not(X0))))
| is_a_theorem(equiv(implies(X0,X1),implies(not(X1),not(X0)))) ),
inference(resolution,[],[f226,f277]) ).
fof(f400,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f226,f228]) ).
fof(f405,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f400,f230]) ).
fof(f408,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),or(X1,not(X0))))
| is_a_theorem(equiv(implies(X0,X1),implies(not(X1),not(X0)))) ),
inference(forward_demodulation,[],[f397,f230]) ).
fof(f409,plain,
! [X0,X1] :
( is_a_theorem(equiv(implies(X0,X1),or(X1,not(X0))))
| ~ is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))) ),
inference(forward_demodulation,[],[f408,f230]) ).
fof(f430,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f217,f239]) ).
fof(f434,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f217,f228]) ).
fof(f439,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(not(X0)),X1))),
inference(forward_demodulation,[],[f430,f369]) ).
fof(f440,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(not(X0),X1))),
inference(forward_demodulation,[],[f439,f230]) ).
fof(f444,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,[],[f434,f228]) ).
fof(f453,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,[],[f444,f369]) ).
fof(f454,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X0)),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(duplicate_literal_removal,[],[f453]) ).
fof(f455,plain,
! [X0,X1] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f454,f230]) ).
fof(f456,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(implies(X1,not(X0))) ),
inference(resolution,[],[f455,f405]) ).
fof(f485,plain,
! [X0] : is_a_theorem(implies(X0,not(necessarily(not(X0))))),
inference(resolution,[],[f456,f208]) ).
fof(f488,plain,
! [X0] : is_a_theorem(implies(X0,possibly(X0))),
inference(forward_demodulation,[],[f485,f204]) ).
fof(f546,plain,
! [X0,X1] :
( equiv(X0,X1) = implies(X1,X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f291,f227]) ).
fof(f559,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f220,f351]) ).
fof(f572,plain,
! [X0,X1] :
( implies(X0,X1) = not(not(X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f212,f351]) ).
fof(f591,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,implies(X0,X1)),
inference(resolution,[],[f292,f227]) ).
fof(f601,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,implies(X0,X1)),
inference(superposition,[],[f203,f591]) ).
fof(f631,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,implies(X0,X1)),
inference(forward_demodulation,[],[f601,f203]) ).
fof(f643,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| X0 = X1
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f227,f546]) ).
fof(f651,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,and(X1,X0)),X1))
| implies(X0,and(X1,X0)) = X1 ),
inference(resolution,[],[f643,f220]) ).
fof(f652,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X1))
| implies(X0,X1) = X1 ),
inference(resolution,[],[f643,f225]) ).
fof(f653,plain,
! [X0] :
( not(not(X0)) = X0
| ~ is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[],[f643,f371]) ).
fof(f657,plain,
! [X0] :
( ~ is_a_theorem(implies(necessarily(possibly(X0)),X0))
| necessarily(possibly(X0)) = X0 ),
inference(resolution,[],[f643,f206]) ).
fof(f658,plain,
! [X0] :
( ~ is_a_theorem(implies(possibly(X0),X0))
| possibly(X0) = X0 ),
inference(resolution,[],[f643,f488]) ).
fof(f667,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,and(X0,X1)))
| and(X0,X1) = X0 ),
inference(resolution,[],[f643,f222]) ).
fof(f670,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,necessarily(X0)))
| necessarily(X0) = X0 ),
inference(resolution,[],[f643,f208]) ).
fof(f671,plain,
! [X0] :
( necessarily(X0) = necessarily(necessarily(X0))
| ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0))) ),
inference(resolution,[],[f643,f207]) ).
fof(f675,plain,
! [X0] : necessarily(X0) = necessarily(necessarily(X0)),
inference(forward_subsumption_resolution,[],[f671,f208]) ).
fof(f676,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| not(not(X0)) = X0 ),
inference(forward_demodulation,[],[f653,f230]) ).
fof(f718,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f229,f228]) ).
fof(f810,plain,
! [X0] :
( possibly(X0) = X0
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f248,f658]) ).
fof(f815,plain,
! [X0] :
( is_a_theorem(implies(X0,necessarily(X0)))
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f206,f810]) ).
fof(f818,plain,
! [X0] :
( necessarily(X0) = X0
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f815,f670]) ).
fof(f832,plain,
! [X0,X1] :
( implies(X0,X1) = strict_implies(X0,X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f818,f203]) ).
fof(f840,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f718,f818]) ).
fof(f883,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0)))
| ~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(superposition,[],[f205,f832]) ).
fof(f887,plain,
~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))),
inference(duplicate_literal_removal,[],[f883]) ).
fof(f1137,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(not(X1)),X0))
| is_a_theorem(implies(not(not(X1)),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f253,f572]) ).
fof(f1227,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X1)),X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f1137,f248]) ).
fof(f1237,plain,
! [X0,X1] :
( is_a_theorem(or(not(X1),X1))
| ~ is_a_theorem(X0) ),
inference(forward_demodulation,[],[f1227,f230]) ).
fof(f1240,definition,
( spl2_4
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f1241,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f1243,definition,
( spl2_5
<=> ! [X1] : is_a_theorem(or(not(X1),X1)) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f1244,plain,
( ! [X1] : is_a_theorem(or(not(X1),X1))
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f1245,plain,
( spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f1237,f1243,f1240]) ).
fof(f1688,plain,
( $false
| ~ spl2_4 ),
inference(backward_subsumption_resolution,[],[f332,f1241]) ).
fof(f1820,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f1688]) ).
fof(f1821,plain,
( ! [X0] : not(not(X0)) = X0
| ~ spl2_5 ),
inference(backward_subsumption_resolution,[],[f676,f1244]) ).
fof(f1912,plain,
( ! [X0] : not(possibly(X0)) = necessarily(not(X0))
| ~ spl2_5 ),
inference(superposition,[],[f1821,f204]) ).
fof(f1915,plain,
( ! [X0,X1] :
( implies(X1,X0) = X0
| ~ is_a_theorem(X1) )
| ~ spl2_5 ),
inference(superposition,[],[f572,f1821]) ).
fof(f1917,plain,
( ! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0))
| ~ spl2_5 ),
inference(superposition,[],[f212,f1821]) ).
fof(f2047,plain,
( ! [X2,X0,X1] : or(and(X1,X0),X2) = implies(implies(X1,not(X0)),X2)
| ~ spl2_5 ),
inference(superposition,[],[f230,f1917]) ).
fof(f2462,plain,
( ! [X0,X1] :
( is_a_theorem(implies(strict_implies(X1,X0),X0))
| ~ is_a_theorem(X1) )
| ~ spl2_5 ),
inference(superposition,[],[f242,f1915]) ).
fof(f2477,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,and(X0,X1)))
| ~ is_a_theorem(X1) )
| ~ spl2_5 ),
inference(superposition,[],[f220,f1915]) ).
fof(f2585,plain,
( ! [X0] : possibly(possibly(X0)) = not(necessarily(necessarily(not(X0))))
| ~ spl2_5 ),
inference(superposition,[],[f204,f1912]) ).
fof(f2605,plain,
( ! [X0] : possibly(possibly(X0)) = not(necessarily(not(X0)))
| ~ spl2_5 ),
inference(forward_demodulation,[],[f2585,f675]) ).
fof(f2606,plain,
( ! [X0] : possibly(X0) = possibly(possibly(X0))
| ~ spl2_5 ),
inference(forward_demodulation,[],[f2605,f204]) ).
fof(f2638,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ spl2_5 ),
inference(superposition,[],[f206,f2606]) ).
fof(f2643,plain,
( ! [X0] : possibly(X0) = necessarily(possibly(X0))
| ~ spl2_5 ),
inference(resolution,[],[f2638,f670]) ).
fof(f3062,plain,
( ! [X0,X1] :
( and(X1,X0) = X1
| ~ is_a_theorem(X0) )
| ~ spl2_5 ),
inference(resolution,[],[f2477,f667]) ).
fof(f3114,plain,
( ! [X0,X1] :
( not(X1) = implies(X1,not(X0))
| ~ is_a_theorem(X0) )
| ~ spl2_5 ),
inference(superposition,[],[f1917,f3062]) ).
fof(f3340,plain,
( ! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X1,X0)) )
| ~ spl2_5 ),
inference(superposition,[],[f2462,f1915]) ).
fof(f3917,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| implies(X1,X1) = X0
| ~ is_a_theorem(implies(implies(X1,X1),X0)) ),
inference(resolution,[],[f559,f643]) ).
fof(f3935,plain,
! [X0,X1] :
( implies(X1,X1) = X0
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f3917,f248]) ).
fof(f3945,plain,
! [X0,X1] :
( necessarily(X0) = strict_implies(X1,X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f203,f3935]) ).
fof(f3990,plain,
! [X2,X0,X1] :
( strict_implies(X0,X0) = strict_implies(X2,X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f3945,f3945]) ).
fof(f4038,plain,
! [X0,X1] :
( necessarily(X0) = implies(X1,X1)
| ~ is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f832,f3945]) ).
fof(f4053,plain,
! [X2,X0,X1] :
( strict_implies(X0,X0) = strict_implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(duplicate_literal_removal,[],[f3990]) ).
fof(f4054,plain,
! [X0,X1] :
( necessarily(X0) = implies(X1,X1)
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f4038,f246]) ).
fof(f4175,definition,
( spl2_6
<=> ! [X2,X0] : strict_implies(X0,X0) = strict_implies(X2,X2) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f4176,plain,
( ! [X2,X0] : strict_implies(X0,X0) = strict_implies(X2,X2)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f4175]) ).
fof(f4177,plain,
( spl2_4
| spl2_6 ),
inference(avatar_split_clause,[],[f4053,f4175,f1240]) ).
fof(f4241,plain,
( ! [X0,X1] : strict_implies(X1,X1) = necessarily(or(X0,not(X0)))
| ~ spl2_6 ),
inference(superposition,[],[f298,f4176]) ).
fof(f4390,plain,
( ! [X2,X0,X1] :
( implies(X1,X1) = strict_implies(X2,X2)
| ~ is_a_theorem(or(X0,not(X0))) )
| ~ spl2_6 ),
inference(superposition,[],[f4241,f4054]) ).
fof(f4455,plain,
( ! [X2,X1] : implies(X1,X1) = strict_implies(X2,X2)
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f4390,f297]) ).
fof(f4501,plain,
( ! [X0,X1] : strict_implies(X0,X0) = strict_implies(X0,strict_implies(X1,X1))
| ~ spl2_6 ),
inference(superposition,[],[f631,f4455]) ).
fof(f5667,plain,
( ! [X2,X0,X1] : implies(X2,X2) = strict_implies(X0,strict_implies(X1,X1))
| ~ spl2_6 ),
inference(superposition,[],[f4455,f4501]) ).
fof(f8461,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(X1)),X1)),
inference(resolution,[],[f265,f221]) ).
fof(f8464,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f265,f718]) ).
fof(f8498,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(possibly(X0),X0))
| necessarily(possibly(X0)) = X0 ),
inference(resolution,[],[f8464,f657]) ).
fof(f8548,plain,
( ! [X0] :
( ~ is_a_theorem(strict_implies(possibly(X0),X0))
| possibly(X0) = X0 )
| ~ spl2_5 ),
inference(forward_demodulation,[],[f8498,f2643]) ).
fof(f8608,plain,
( ! [X0,X1] :
( is_a_theorem(not(and(X1,necessarily(not(X0)))))
| ~ is_a_theorem(X0) )
| ~ spl2_5 ),
inference(superposition,[],[f8461,f3114]) ).
fof(f8609,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X1,not(necessarily(not(X0)))))
| ~ is_a_theorem(X0) )
| ~ spl2_5 ),
inference(forward_demodulation,[],[f8608,f1917]) ).
fof(f8618,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X1,possibly(X0)))
| ~ is_a_theorem(X0) )
| ~ spl2_5 ),
inference(forward_demodulation,[],[f8609,f204]) ).
fof(f8664,plain,
( ! [X0,X1] :
( is_a_theorem(strict_implies(X1,possibly(X0)))
| ~ is_a_theorem(X0) )
| ~ spl2_5 ),
inference(resolution,[],[f8618,f234]) ).
fof(f13836,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| necessarily(X1) = X0
| ~ is_a_theorem(implies(necessarily(X1),X0)) ),
inference(resolution,[],[f840,f643]) ).
fof(f13896,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| necessarily(X1) = X0 ),
inference(forward_subsumption_resolution,[],[f13836,f248]) ).
fof(f13920,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| necessarily(possibly(X1)) = X0
| ~ is_a_theorem(X1) )
| ~ spl2_5 ),
inference(resolution,[],[f13896,f8664]) ).
fof(f13990,plain,
( ! [X0,X1] :
( possibly(X1) = X0
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ spl2_5 ),
inference(forward_demodulation,[],[f13920,f2643]) ).
fof(f14276,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| X0 = X1
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ spl2_5 ),
inference(superposition,[],[f8548,f13990]) ).
fof(f14291,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| X0 = X1
| ~ is_a_theorem(X0) )
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f14276,f3340]) ).
fof(f14326,plain,
( ! [X0,X1] :
( implies(X0,X1) = strict_implies(X0,X1)
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ spl2_5 ),
inference(resolution,[],[f14291,f270]) ).
fof(f14401,plain,
( ! [X2,X0,X1] :
( implies(X0,X0) = implies(X1,strict_implies(X2,X2))
| ~ is_a_theorem(implies(X0,X0)) )
| ~ spl2_5
| ~ spl2_6 ),
inference(superposition,[],[f14326,f5667]) ).
fof(f14541,plain,
( ! [X2,X0,X1] : implies(X0,X0) = implies(X1,strict_implies(X2,X2))
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f14401,f246]) ).
fof(f14838,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X1))
| is_a_theorem(implies(implies(strict_implies(X0,X0),X2),X2)) )
| ~ spl2_5
| ~ spl2_6 ),
inference(superposition,[],[f253,f14541]) ).
fof(f14858,plain,
( ! [X2,X0] : is_a_theorem(implies(implies(strict_implies(X0,X0),X2),X2))
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f14838,f246]) ).
fof(f17016,plain,
( ! [X0,X1] : implies(strict_implies(X0,X0),X1) = X1
| ~ spl2_5
| ~ spl2_6 ),
inference(resolution,[],[f14858,f652]) ).
fof(f17335,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(and(X1,strict_implies(X0,X0)),X1))
| and(X1,strict_implies(X0,X0)) = X1 )
| ~ spl2_5
| ~ spl2_6 ),
inference(superposition,[],[f651,f17016]) ).
fof(f17376,plain,
( ! [X0,X1] : and(X1,strict_implies(X0,X0)) = X1
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f17335,f222]) ).
fof(f18522,plain,
( ! [X0,X1] : not(X1) = implies(X1,not(strict_implies(X0,X0)))
| ~ spl2_5
| ~ spl2_6 ),
inference(superposition,[],[f1917,f17376]) ).
fof(f18653,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,not(strict_implies(X0,X0))),not(X1))))
| ~ spl2_5
| ~ spl2_6 ),
inference(superposition,[],[f223,f18522]) ).
fof(f18759,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),or(and(X2,strict_implies(X0,X0)),not(X1))))
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_demodulation,[],[f18653,f2047]) ).
fof(f18828,plain,
( ! [X2,X1] : is_a_theorem(implies(implies(X1,X2),or(X2,not(X1))))
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_demodulation,[],[f18759,f17376]) ).
fof(f18843,plain,
( ! [X0,X1] : is_a_theorem(equiv(implies(X0,X1),or(X1,not(X0))))
| ~ spl2_5
| ~ spl2_6 ),
inference(backward_subsumption_resolution,[],[f409,f18828]) ).
fof(f19263,plain,
( ! [X0,X1] : implies(X0,X1) = or(X1,not(X0))
| ~ spl2_5
| ~ spl2_6 ),
inference(resolution,[],[f18843,f227]) ).
fof(f19362,plain,
( ! [X2,X0,X1] : implies(and(X1,X0),X2) = or(X2,implies(X1,not(X0)))
| ~ spl2_5
| ~ spl2_6 ),
inference(superposition,[],[f19263,f1917]) ).
fof(f19394,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X1,not(X0)),implies(X0,not(X1))))
| ~ spl2_5
| ~ spl2_6 ),
inference(superposition,[],[f440,f19263]) ).
fof(f19411,plain,
( ! [X0,X1] : is_a_theorem(or(and(X1,X0),implies(X0,not(X1))))
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_demodulation,[],[f19394,f2047]) ).
fof(f19423,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),and(X1,X0)))
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_demodulation,[],[f19411,f19362]) ).
fof(f19425,plain,
( $false
| ~ spl2_5
| ~ spl2_6 ),
inference(backward_subsumption_resolution,[],[f887,f19423]) ).
fof(f19426,plain,
( ~ spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f19425]) ).
cnf(s615,plain,
( spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f1245]) ).
cnf(s745,plain,
~ spl2_4,
inference(sat_conversion,[],[f1820]) ).
cnf(s1540,plain,
( spl2_4
| spl2_6 ),
inference(sat_conversion,[],[f4177]) ).
cnf(s3084,plain,
( ~ spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f19426]) ).
cnf(s3088,plain,
spl2_6,
inference(rat,[],[s1540,s745]) ).
cnf(s3089,plain,
~ spl2_5,
inference(rat,[],[s3084,s3088]) ).
cnf(s3090,plain,
$false,
inference(rat,[],[s615,s3089,s745]) ).
fof(f19427,plain,
$false,
inference(avatar_sat_refutation,[],[s3090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL541+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:57:47 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 10.12/2.34 % (4169898)Detected formulas, will run a generic FOF schedule.
% 10.12/2.34 % (4169904)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=10219478:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.12/2.34 % (4169903)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=3452701401:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.12/2.34 % (4169907)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2761831854:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.12/2.34 % (4169905)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=3402144119:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.12/2.34 % (4169909)dis-21_1_sil=8000:lcm=predicate:random_seed=1976151829: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)
% 10.12/2.34 % (4169906)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2407104492:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.12/2.34 % (4169908)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3353596347:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.12/2.34 % (4169907)Refutation not found, incomplete strategy
% 10.12/2.34 % (4169907)------------------------------
% 10.12/2.34 % (4169907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.34 % (4169906)Refutation not found, incomplete strategy
% 10.12/2.34 % (4169906)------------------------------
% 10.12/2.34 % (4169906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.34 % (4169907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.34 % (4169906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.34 % (4169906)CaDiCaL version: 2.1.3
% 10.12/2.34 % (4169906)Termination reason: Refutation not found, incomplete strategy
% 10.12/2.34 % (4169906)Time elapsed: 0.001 s
% 10.12/2.34 % (4169906)Peak memory usage: 87 MB
% 10.12/2.34 % (4169907)CaDiCaL version: 2.1.3
% 10.12/2.34 % (4169907)Termination reason: Refutation not found, incomplete strategy
% 10.12/2.34 % (4169907)Time elapsed: 0.001 s
% 10.12/2.34 % (4169907)Peak memory usage: 86 MB
% 10.12/2.34 % (4169909)Refutation not found, incomplete strategy
% 10.12/2.34 % (4169909)------------------------------
% 10.12/2.34 % (4169909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.34 % (4169909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.34 % (4169909)CaDiCaL version: 2.1.3
% 10.12/2.34 % (4169909)Termination reason: Refutation not found, incomplete strategy
% 10.12/2.34 % (4169909)Time elapsed: 0.002 s
% 10.12/2.34 % (4169909)Peak memory usage: 88 MB
% 10.12/2.34 % (4169909)Instructions burned: 1 (million)
% 10.12/2.34 % (4169908)Instruction limit reached!
% 10.12/2.34 % (4169908)------------------------------
% 10.12/2.34 % (4169908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.34 % (4169908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.34 % (4169908)CaDiCaL version: 2.1.3
% 10.12/2.34 % (4169908)Termination reason: Instruction limit
% 10.12/2.34 % (4169908)Termination phase: Saturation
% 10.12/2.34 % (4169908)Time elapsed: 0.089 s
% 10.12/2.34 % (4169908)Peak memory usage: 90 MB
% 10.12/2.34 % (4169908)Instructions burned: 139 (million)
% 10.12/2.34 % (4169917)lrs+10_1_sil=8000:sp=occurrence:random_seed=570007352:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.12/2.34 % (4169917)Refutation not found, incomplete strategy
% 10.12/2.34 % (4169917)------------------------------
% 10.12/2.34 % (4169917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.34 % (4169917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.34 % (4169917)CaDiCaL version: 2.1.3
% 10.12/2.34 % (4169917)Termination reason: Refutation not found, incomplete strategy
% 10.12/2.34 % (4169917)Time elapsed: 0.001 s
% 10.12/2.34 % (4169917)Peak memory usage: 87 MB
% 10.12/2.34 % (4169909)------------------------------
% 10.12/2.34 % (4169909)------------------------------
% 10.12/2.34 % (4169906)------------------------------
% 10.12/2.34 % (4169906)------------------------------
% 12.08/2.76 % (4169907)------------------------------
% 12.08/2.76 % (4169907)------------------------------
% 12.08/2.76 % (4169919)lrs+10_1_sil=32000:urr=on:br=off:random_seed=77056002:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 12.08/2.76 % (4169919)Refutation not found, incomplete strategy
% 12.08/2.76 % (4169919)------------------------------
% 12.08/2.76 % (4169919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.08/2.76 % (4169919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.08/2.76 % (4169919)CaDiCaL version: 2.1.3
% 12.08/2.76 % (4169919)Termination reason: Refutation not found, incomplete strategy
% 12.08/2.76 % (4169919)Time elapsed: 0.001 s
% 12.08/2.76 % (4169919)Peak memory usage: 87 MB
% 12.08/2.76 % (4169920)lrs+1011_1_sil=32000:sp=occurrence:random_seed=832630349:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 12.08/2.76 % (4169921)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=3855519214:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 12.08/2.76 % (4169920)Refutation not found, incomplete strategy
% 12.08/2.76 % (4169920)------------------------------
% 12.08/2.76 % (4169920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.08/2.76 % (4169920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.08/2.76 % (4169920)CaDiCaL version: 2.1.3
% 12.08/2.76 % (4169920)Termination reason: Refutation not found, incomplete strategy
% 12.08/2.76 % (4169920)Time elapsed: 0.001 s
% 12.08/2.76 % (4169920)Peak memory usage: 87 MB
% 12.08/2.76 % (4169917)------------------------------
% 12.08/2.76 % (4169917)------------------------------
% 12.08/2.76 % (4169921)Instruction limit reached!
% 12.08/2.76 % (4169921)------------------------------
% 12.08/2.76 % (4169921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.08/2.76 % (4169921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.08/2.76 % (4169921)CaDiCaL version: 2.1.3
% 12.08/2.76 % (4169921)Termination reason: Instruction limit
% 12.08/2.76 % (4169921)Termination phase: Saturation
% 12.08/2.76 % (4169921)Time elapsed: 0.149 s
% 12.08/2.76 % (4169921)Peak memory usage: 93 MB
% 12.08/2.76 % (4169921)Instructions burned: 249 (million)
% 12.08/2.76 % (4169905)Refutation not found, incomplete strategy
% 12.08/2.76 % (4169905)------------------------------
% 12.08/2.76 % (4169905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.08/2.76 % (4169905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.08/2.76 % (4169905)CaDiCaL version: 2.1.3
% 12.08/2.76 % (4169905)Termination reason: Refutation not found, incomplete strategy
% 12.08/2.76 % (4169905)Time elapsed: 0.563 s
% 12.08/2.76 % (4169905)Peak memory usage: 127 MB
% 12.08/2.76 % (4169905)Instructions burned: 826 (million)
% 12.08/2.76 % (4169925)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1927684921:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 12.08/2.76 % (4169925)Refutation not found, incomplete strategy
% 12.08/2.76 % (4169925)------------------------------
% 12.08/2.76 % (4169925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.08/2.76 % (4169925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.08/2.76 % (4169925)CaDiCaL version: 2.1.3
% 12.08/2.76 % (4169925)Termination reason: Refutation not found, incomplete strategy
% 12.08/2.76 % (4169925)Time elapsed: 0.001 s
% 12.08/2.76 % (4169925)Peak memory usage: 87 MB
% 12.08/2.76 % (4169919)------------------------------
% 12.08/2.76 % (4169919)------------------------------
% 12.08/2.76 % (4169920)------------------------------
% 12.08/2.76 % (4169920)------------------------------
% 12.08/2.76 % (4169926)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1672111305:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 12.08/2.76 % (4169928)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1307094708:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 12.08/2.76 % (4169928)Refutation not found, incomplete strategy
% 12.08/2.76 % (4169928)------------------------------
% 12.08/2.76 % (4169928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.08/2.76 % (4169928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.08/2.76 % (4169928)CaDiCaL version: 2.1.3
% 12.08/2.76 % (4169928)Termination reason: Refutation not found, incomplete strategy
% 16.42/3.18 % (4169928)Time elapsed: 0.001 s
% 16.42/3.18 % (4169928)Peak memory usage: 88 MB
% 16.42/3.18 % (4169929)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1240412999:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 16.42/3.18 % (4169905)------------------------------
% 16.42/3.18 % (4169905)------------------------------
% 16.42/3.18 % (4169929)Instruction limit reached!
% 16.42/3.18 % (4169929)------------------------------
% 16.42/3.18 % (4169929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.42/3.18 % (4169929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.42/3.18 % (4169929)CaDiCaL version: 2.1.3
% 16.42/3.18 % (4169929)Termination reason: Instruction limit
% 16.42/3.18 % (4169929)Termination phase: Saturation
% 16.42/3.18 % (4169929)Time elapsed: 0.070 s
% 16.42/3.18 % (4169929)Peak memory usage: 89 MB
% 16.42/3.18 % (4169929)Instructions burned: 128 (million)
% 16.42/3.18 % (4169925)------------------------------
% 16.42/3.18 % (4169925)------------------------------
% 16.42/3.18 % (4169933)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=185880095:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 16.42/3.18 % (4169933)Refutation not found, incomplete strategy
% 16.42/3.18 % (4169933)------------------------------
% 16.42/3.18 % (4169933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.42/3.18 % (4169933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.42/3.18 % (4169933)CaDiCaL version: 2.1.3
% 16.42/3.18 % (4169933)Termination reason: Refutation not found, incomplete strategy
% 16.42/3.18 % (4169933)Time elapsed: 0.001 s
% 16.42/3.18 % (4169933)Peak memory usage: 87 MB
% 16.42/3.18 % (4169934)lrs+10_1_sil=8000:sp=occurrence:random_seed=1611582499:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 16.42/3.18 % (4169934)Refutation not found, incomplete strategy
% 16.42/3.18 % (4169934)------------------------------
% 16.42/3.18 % (4169934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.42/3.18 % (4169934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.42/3.18 % (4169934)CaDiCaL version: 2.1.3
% 16.42/3.18 % (4169934)Termination reason: Refutation not found, incomplete strategy
% 16.42/3.18 % (4169934)Time elapsed: 0.001 s
% 16.42/3.18 % (4169934)Peak memory usage: 87 MB
% 16.42/3.18 % (4169935)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=415964816:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 16.42/3.18 % (4169935)Refutation not found, incomplete strategy
% 16.42/3.18 % (4169935)------------------------------
% 16.42/3.18 % (4169935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.42/3.18 % (4169935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.42/3.18 % (4169935)CaDiCaL version: 2.1.3
% 16.42/3.18 % (4169935)Termination reason: Refutation not found, incomplete strategy
% 16.42/3.18 % (4169935)Time elapsed: 0.001 s
% 16.42/3.18 % (4169935)Peak memory usage: 88 MB
% 16.42/3.18 % (4169928)------------------------------
% 16.42/3.18 % (4169928)------------------------------
% 16.42/3.18 % (4169939)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=763178891:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 16.42/3.18 % (4169933)------------------------------
% 16.42/3.18 % (4169933)------------------------------
% 16.42/3.18 % (4169934)------------------------------
% 16.42/3.18 % (4169934)------------------------------
% 16.42/3.18 % (4169935)------------------------------
% 16.42/3.18 % (4169935)------------------------------
% 16.42/3.18 % (4169941)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=329679953:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 16.42/3.18 % (4169941)Refutation not found, incomplete strategy
% 16.42/3.18 % (4169941)------------------------------
% 16.42/3.18 % (4169941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.42/3.18 % (4169941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.42/3.18 % (4169941)CaDiCaL version: 2.1.3
% 16.42/3.18 % (4169941)Termination reason: Refutation not found, incomplete strategy
% 16.42/3.18 % (4169941)Time elapsed: 0.002 s
% 16.42/3.18 % (4169941)Peak memory usage: 89 MB
% 16.42/3.18 % (4169941)Instructions burned: 1 (million)
% 16.42/3.18 % (4169942)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4092306266:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 19.75/3.84 % (4169942)Refutation not found, incomplete strategy
% 19.75/3.84 % (4169942)------------------------------
% 19.75/3.84 % (4169942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.75/3.84 % (4169942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.75/3.84 % (4169942)CaDiCaL version: 2.1.3
% 19.75/3.84 % (4169942)Termination reason: Refutation not found, incomplete strategy
% 19.75/3.84 % (4169942)Time elapsed: 0.001 s
% 19.75/3.84 % (4169942)Peak memory usage: 88 MB
% 19.75/3.84 % (4169942)Instructions burned: 1 (million)
% 19.75/3.84 % (4169943)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4266515960:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 19.75/3.84 % (4169941)------------------------------
% 19.75/3.84 % (4169941)------------------------------
% 19.75/3.84 % (4169942)------------------------------
% 19.75/3.84 % (4169942)------------------------------
% 19.75/3.84 % (4169947)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=3734948650:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2982 on theBenchmark for (2982ds/125Mi)
% 19.75/3.84 % (4169947)Refutation not found, incomplete strategy
% 19.75/3.84 % (4169947)------------------------------
% 19.75/3.84 % (4169947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.75/3.84 % (4169947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.75/3.84 % (4169947)CaDiCaL version: 2.1.3
% 19.75/3.84 % (4169947)Termination reason: Refutation not found, incomplete strategy
% 19.75/3.84 % (4169947)Time elapsed: 0.001 s
% 19.75/3.84 % (4169947)Peak memory usage: 87 MB
% 19.75/3.84 % (4169947)Instructions burned: 1 (million)
% 19.75/3.84 % (4169948)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2787448837:i=134:gtgl=5:slsql=off:gtg=exists_sym_2982 on theBenchmark for (2982ds/134Mi)
% 19.75/3.84 [W927 15:57:50.123196445 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.
% 19.75/3.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 19.75/3.84 [W927 15:57:50.123227965 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.
% 19.75/3.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 19.75/3.84 [W927 15:57:50.123267102 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.
% 19.75/3.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 19.75/3.84 [W927 15:57:50.123280005 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.
% 19.75/3.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 19.75/3.84 [W927 15:57:50.123307202 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.
% 19.75/3.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 19.75/3.84 [W927 15:57:50.123319106 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.
% 19.75/3.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 19.75/3.84 [W927 15:57:50.123344939 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.
% 19.75/3.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 19.75/3.84 [W927 15:57:50.123356219 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.
% 32.26/5.45 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 32.26/5.45 [W927 15:57:50.123380569 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.
% 32.26/5.45 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 32.26/5.45 [W927 15:57:50.123390696 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.
% 32.26/5.45 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 32.26/5.45 [W927 15:57:50.123414896 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.
% 32.26/5.45 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 32.26/5.45 [W927 15:57:50.123477322 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.
% 32.26/5.45 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 32.26/5.45 % (4169948)Instruction limit reached!
% 32.26/5.45 % (4169948)------------------------------
% 32.26/5.45 % (4169948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169948)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169948)Termination reason: Instruction limit
% 32.26/5.45 % (4169948)Termination phase: Saturation
% 32.26/5.45 % (4169948)Time elapsed: 0.091 s
% 32.26/5.45 % (4169948)Peak memory usage: 90 MB
% 32.26/5.45 % (4169948)Instructions burned: 134 (million)
% 32.26/5.45 % (4169943)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169943)------------------------------
% 32.26/5.45 % (4169943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169943)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169943)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169943)Time elapsed: 0.549 s
% 32.26/5.45 % (4169943)Peak memory usage: 126 MB
% 32.26/5.45 % (4169943)Instructions burned: 826 (million)
% 32.26/5.45 % (4169947)------------------------------
% 32.26/5.45 % (4169947)------------------------------
% 32.26/5.45 % (4169951)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3305881377:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/141Mi)
% 32.26/5.45 % (4169951)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169951)------------------------------
% 32.26/5.45 % (4169951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169951)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169951)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169951)Time elapsed: 0.001 s
% 32.26/5.45 % (4169951)Peak memory usage: 87 MB
% 32.26/5.45 % (4169953)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1636432212:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2979 on theBenchmark for (2979ds/431Mi)
% 32.26/5.45 % (4169953)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169953)------------------------------
% 32.26/5.45 % (4169953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169953)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169953)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169953)Time elapsed: 0.001 s
% 32.26/5.45 % (4169953)Peak memory usage: 87 MB
% 32.26/5.45 % (4169943)------------------------------
% 32.26/5.45 % (4169943)------------------------------
% 32.26/5.45 % (4169926)Instruction limit reached!
% 32.26/5.45 % (4169926)------------------------------
% 32.26/5.45 % (4169926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169926)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169926)Termination reason: Instruction limit
% 32.26/5.45 % (4169926)Termination phase: Saturation
% 32.26/5.45 % (4169926)Time elapsed: 1.498 s
% 32.26/5.45 % (4169926)Peak memory usage: 141 MB
% 32.26/5.45 % (4169926)Instructions burned: 2352 (million)
% 32.26/5.45 % (4169951)------------------------------
% 32.26/5.45 % (4169951)------------------------------
% 32.26/5.45 % (4169956)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1256778790:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2976 on theBenchmark for (2976ds/150Mi)
% 32.26/5.45 % (4169955)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=91990160:i=6060:aac=none:ins=25_2976 on theBenchmark for (2976ds/6060Mi)
% 32.26/5.45 % (4169953)------------------------------
% 32.26/5.45 % (4169953)------------------------------
% 32.26/5.45 % (4169957)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=2941887829:i=14155:bd=all_2976 on theBenchmark for (2976ds/14155Mi)
% 32.26/5.45 % (4169956)Instruction limit reached!
% 32.26/5.45 % (4169956)------------------------------
% 32.26/5.45 % (4169956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169956)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169956)Termination reason: Instruction limit
% 32.26/5.45 % (4169956)Termination phase: Saturation
% 32.26/5.45 % (4169956)Time elapsed: 0.086 s
% 32.26/5.45 % (4169956)Peak memory usage: 91 MB
% 32.26/5.45 % (4169956)Instructions burned: 151 (million)
% 32.26/5.45 % (4169961)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=4262802560:i=667:av=off:fsr=off_2975 on theBenchmark for (2975ds/667Mi)
% 32.26/5.45 % (4169961)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169961)------------------------------
% 32.26/5.45 % (4169961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169961)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169961)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169961)Time elapsed: 0.002 s
% 32.26/5.45 % (4169961)Peak memory usage: 88 MB
% 32.26/5.45 % (4169961)Instructions burned: 1 (million)
% 32.26/5.45 % (4169962)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=3527517549:s2a=on:i=185:s2at=1.8:fdi=4_2974 on theBenchmark for (2974ds/185Mi)
% 32.26/5.45 % (4169962)Instruction limit reached!
% 32.26/5.45 % (4169962)------------------------------
% 32.26/5.45 % (4169962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169962)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169962)Termination reason: Instruction limit
% 32.26/5.45 % (4169962)Termination phase: Saturation
% 32.26/5.45 % (4169962)Time elapsed: 0.101 s
% 32.26/5.45 % (4169962)Peak memory usage: 91 MB
% 32.26/5.45 % (4169962)Instructions burned: 186 (million)
% 32.26/5.45 % (4169961)------------------------------
% 32.26/5.45 % (4169961)------------------------------
% 32.26/5.45 % (4169965)dis+1010_14_anc=all:to=lpo:sil=8000:sp=arity:slsq=on:random_seed=1986747665:i=193:ins=10:fsr=off:ss=axioms:fsd=on_2972 on theBenchmark for (2972ds/193Mi)
% 32.26/5.45 % (4169965)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169965)------------------------------
% 32.26/5.45 % (4169965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169965)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169965)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169965)Time elapsed: 0.001 s
% 32.26/5.45 % (4169965)Peak memory usage: 86 MB
% 32.26/5.45 % (4169966)dis+1011_7_sil=8000:sp=occurrence:sos=all:fd=off:random_seed=1867849966:st=5.3:i=4850:sd=4:av=off:sup=off:ss=included:sgt=16_2971 on theBenchmark for (2971ds/4850Mi)
% 32.26/5.45 % (4169966)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169966)------------------------------
% 32.26/5.45 % (4169966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169966)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169966)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169966)Time elapsed: 0.002 s
% 32.26/5.45 % (4169966)Peak memory usage: 88 MB
% 32.26/5.45 % (4169966)Instructions burned: 1 (million)
% 32.26/5.45 % (4169965)------------------------------
% 32.26/5.45 % (4169965)------------------------------
% 32.26/5.45 % (4169966)------------------------------
% 32.26/5.45 % (4169966)------------------------------
% 32.26/5.45 % (4169970)lrs+1011_1_ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:sp=const_frequency:acc=on:urr=on:random_seed=2014116107:i=12111:sd=1:ss=included_2968 on theBenchmark for (2968ds/12111Mi)
% 32.26/5.45 % (4169971)lrs-11_32_anc=all:sil=8000:spb=goal_then_units:sac=on:random_seed=1194886120:i=319:kws=precedence:fsr=off_2967 on theBenchmark for (2967ds/319Mi)
% 32.26/5.45 % (4169971)Instruction limit reached!
% 32.26/5.45 % (4169971)------------------------------
% 32.26/5.45 % (4169971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169971)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169971)Termination reason: Instruction limit
% 32.26/5.45 % (4169971)Termination phase: Saturation
% 32.26/5.45 % (4169971)Time elapsed: 0.199 s
% 32.26/5.45 % (4169971)Peak memory usage: 91 MB
% 32.26/5.45 % (4169971)Instructions burned: 320 (million)
% 32.26/5.45 % (4169974)dis+2_1024_sil=8000:sp=reverse_arity:sos=on:lcm=reverse:sac=on:random_seed=910952820:i=2064:ep=RST_2964 on theBenchmark for (2964ds/2064Mi)
% 32.26/5.45 % (4169974)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169974)------------------------------
% 32.26/5.45 % (4169974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169974)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169974)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169974)Time elapsed: 0.002 s
% 32.26/5.45 % (4169974)Peak memory usage: 88 MB
% 32.26/5.45 % (4169974)Instructions burned: 2 (million)
% 32.26/5.45 % (4169974)------------------------------
% 32.26/5.45 % (4169974)------------------------------
% 32.26/5.45 % (4169976)dis-1011_128_sil=32000:random_seed=1496081512:i=3706:ep=RST:av=off_2960 on theBenchmark for (2960ds/3706Mi)
% 32.26/5.45 % (4169955)First to succeed.
% 32.26/5.45 % (4169955)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4169898"
% 32.26/5.45 % (4169939)Instruction limit reached!
% 32.26/5.45 % (4169939)------------------------------
% 32.26/5.45 % (4169939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169939)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169939)Termination reason: Instruction limit
% 32.26/5.45 % (4169939)Termination phase: Saturation
% 32.26/5.45 % (4169939)Time elapsed: 2.993 s
% 32.26/5.45 % (4169939)Peak memory usage: 176 MB
% 32.26/5.45 % (4169939)Instructions burned: 5202 (million)
% 32.26/5.45 % (4169978)lrs-1002_1_sil=8000:plsq=on:plsqr=32,1:sp=occurrence:sos=on:fs=off:gs=on:newcnf=on:random_seed=3833162138:i=757:sd=2:fsr=off:ss=axioms:sgt=40_2956 on theBenchmark for (2956ds/757Mi)
% 32.26/5.45 % (4169978)Refutation not found, incomplete strategy
% 32.26/5.45 % (4169978)------------------------------
% 32.26/5.45 % (4169978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.26/5.45 % (4169978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.26/5.45 % (4169978)CaDiCaL version: 2.1.3
% 32.26/5.45 % (4169978)Termination reason: Refutation not found, incomplete strategy
% 32.26/5.45 % (4169978)Time elapsed: 0.001 s
% 32.26/5.45 % (4169978)Peak memory usage: 87 MB
% 32.26/5.45 % (4169955)Refutation found. Thanks to Tanya!
% 32.26/5.45 % SZS status Theorem for theBenchmark
% 32.26/5.45 % SZS output start Proof for theBenchmark
% See solution above
% 32.98/5.65 % (4169955)------------------------------
% 32.98/5.65 % (4169955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.98/5.65 % (4169955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.98/5.65 % (4169955)CaDiCaL version: 2.1.3
% 32.98/5.65 % (4169955)Termination reason: Refutation
% 32.98/5.65 % (4169955)Time elapsed: 1.833 s
% 32.98/5.65 % (4169955)Peak memory usage: 145 MB
% 32.98/5.65 % (4169955)Instructions burned: 2740 (million)
% 32.98/5.65 % (4169955)------------------------------
% 32.98/5.65 % (4169955)------------------------------
% 32.98/5.65 % (4169898)Success in time 4.585 s
% 32.98/5.65 % Vampire exiting
%------------------------------------------------------------------------------