%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL537+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 : n014.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 10.85s 2.41s
% Output : Refutation 13.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 42
% Syntax : Number of formulae : 269 ( 151 unt; 0 def)
% Number of atoms : 408 ( 94 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 239 ( 100 ~; 95 |; 2 &)
% ( 17 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 22 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 406 ( 405 !; 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(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(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
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(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(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_possibly) ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_op_possibly) ).
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,conjecture,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f84,negated_conjecture,
~ axiom_5,
inference(negated_conjecture,[status(cth)],[f83]) ).
fof(f85,plain,
~ axiom_5,
inference(flattening,[],[f84]) ).
fof(f86,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_5 ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f87,plain,
( axiom_B
=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f88,plain,
( axiom_4
=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f89,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f92,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(f93,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f95,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(f96,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f98,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f99,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f100,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f101,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(f102,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f103,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f104,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f105,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f106,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(f112,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f106]) ).
fof(f113,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f105]) ).
fof(f115,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f104]) ).
fof(f116,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f103]) ).
fof(f117,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f102]) ).
fof(f118,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f101]) ).
fof(f119,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f100]) ).
fof(f120,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f99]) ).
fof(f121,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f98]) ).
fof(f123,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f96]) ).
fof(f124,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,[],[f95]) ).
fof(f126,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f93]) ).
fof(f127,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f92]) ).
fof(f128,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f129,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f130,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f133,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f89]) ).
fof(f134,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(ennf_transformation,[],[f88]) ).
fof(f135,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(ennf_transformation,[],[f87]) ).
fof(f136,plain,
( axiom_5
| ? [X0] : ~ is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f86]) ).
fof(f137,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f138,plain,
( axiom_5
| ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f136]) ).
fof(f139,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f113]) ).
fof(f140,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f114]) ).
fof(f141,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f115]) ).
fof(f142,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f116]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f117]) ).
fof(f144,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f118]) ).
fof(f145,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f146,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f121]) ).
fof(f149,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f150,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,[],[f124]) ).
fof(f152,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f126]) ).
fof(f153,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f154,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f128]) ).
fof(f155,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f129]) ).
fof(f156,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f130]) ).
fof(f157,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f158,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f159,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f160,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f161,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f162,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f163,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f164,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f165,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f166,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f167,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f169,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f170,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f172,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f173,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f174,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f177,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f133]) ).
fof(f178,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[],[f134]) ).
fof(f179,plain,
! [X0] :
( is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(cnf_transformation,[],[f135]) ).
fof(f180,plain,
( axiom_5
| ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(cnf_transformation,[],[f138]) ).
fof(f181,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f137]) ).
fof(f182,plain,
op_possibly,
inference(cnf_transformation,[],[f77]) ).
fof(f185,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f186,plain,
axiom_4,
inference(cnf_transformation,[],[f81]) ).
fof(f187,plain,
axiom_B,
inference(cnf_transformation,[],[f82]) ).
fof(f188,plain,
~ axiom_5,
inference(cnf_transformation,[],[f85]) ).
fof(f189,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(forward_subsumption_resolution,[],[f181,f182]) ).
fof(f190,plain,
~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(forward_subsumption_resolution,[],[f180,f188]) ).
fof(f191,plain,
! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))),
inference(forward_subsumption_resolution,[],[f179,f187]) ).
fof(f192,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(forward_subsumption_resolution,[],[f178,f186]) ).
fof(f193,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f177,f185]) ).
fof(f196,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f156,f159]) ).
fof(f197,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f155,f158]) ).
fof(f198,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f154,f157]) ).
fof(f199,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[],[f153,f173]) ).
fof(f200,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f152,f172]) ).
fof(f202,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(forward_subsumption_resolution,[],[f150,f170]) ).
fof(f203,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(forward_subsumption_resolution,[],[f149,f169]) ).
fof(f205,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_subsumption_resolution,[],[f147,f167]) ).
fof(f206,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[],[f146,f166]) ).
fof(f207,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f145,f165]) ).
fof(f208,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f144,f164]) ).
fof(f209,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f143,f163]) ).
fof(f210,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f142,f162]) ).
fof(f211,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f141,f161]) ).
fof(f212,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f140,f174]) ).
fof(f213,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f139,f160]) ).
fof(f214,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f198,f197]) ).
fof(f216,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f209,f213]) ).
fof(f220,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f208,f213]) ).
fof(f221,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[],[f220,f216]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f220,f213]) ).
fof(f228,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f210,f216]) ).
fof(f233,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f205,f216]) ).
fof(f235,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f205,f213]) ).
fof(f241,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(superposition,[],[f214,f189]) ).
fof(f277,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f199,f213]) ).
fof(f281,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f277,f213]) ).
fof(f284,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,[],[f281,f209]) ).
fof(f289,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,[],[f281,f277]) ).
fof(f293,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,[],[f281,f235]) ).
fof(f294,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f281,f233]) ).
fof(f297,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f294,f206]) ).
fof(f298,plain,
! [X0,X1] :
( is_a_theorem(equiv(and(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f293,f206]) ).
fof(f300,plain,
! [X0,X1] :
( is_a_theorem(equiv(equiv(X0,X1),implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f289,f200]) ).
fof(f302,plain,
! [X0,X1] : is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))),
inference(forward_subsumption_resolution,[],[f284,f210]) ).
fof(f306,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f212,f297]) ).
fof(f307,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| equiv(X0,X1) = implies(X1,X0) ),
inference(resolution,[],[f212,f300]) ).
fof(f310,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f197,f306]) ).
fof(f313,plain,
! [X0] : or(X0,X0) = not(not(X0)),
inference(forward_demodulation,[],[f310,f214]) ).
fof(f314,plain,
! [X0] : implies(X0,necessarily(X0)) = equiv(necessarily(X0),X0),
inference(resolution,[],[f307,f193]) ).
fof(f331,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(not(X1),not(X2))))
| is_a_theorem(implies(X0,implies(X2,X1))) ),
inference(resolution,[],[f211,f222]) ).
fof(f332,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f211,f213]) ).
fof(f342,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f332,f214]) ).
fof(f343,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,not(X2))))
| is_a_theorem(implies(X0,implies(X2,X1))) ),
inference(forward_demodulation,[],[f331,f214]) ).
fof(f376,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,necessarily(X0)))
| necessarily(X0) = X0 ),
inference(superposition,[],[f212,f314]) ).
fof(f380,plain,
! [X0] : necessarily(X0) = necessarily(necessarily(X0)),
inference(resolution,[],[f376,f192]) ).
fof(f390,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,implies(X0,X1)),
inference(resolution,[],[f302,f212]) ).
fof(f432,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| and(X0,X1) = X1 ),
inference(resolution,[],[f298,f212]) ).
fof(f435,plain,
! [X0,X1] : and(implies(necessarily(X0),X0),X1) = X1,
inference(resolution,[],[f432,f193]) ).
fof(f444,plain,
! [X0,X1] : and(implies(X0,X0),X1) = X1,
inference(resolution,[],[f432,f228]) ).
fof(f469,plain,
! [X0,X1] : not(not(X0)) = implies(implies(X1,X1),X0),
inference(superposition,[],[f197,f444]) ).
fof(f507,plain,
! [X0,X1] : implies(implies(X0,X0),X1) = not(not(implies(implies(X0,X0),X1))),
inference(superposition,[],[f390,f469]) ).
fof(f525,plain,
! [X1] : not(not(X1)) = not(not(not(not(X1)))),
inference(forward_demodulation,[],[f507,f469]) ).
fof(f587,plain,
! [X0,X1] : not(not(X0)) = implies(implies(necessarily(X1),X1),X0),
inference(superposition,[],[f197,f435]) ).
fof(f594,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,necessarily(X1)),not(not(implies(X0,X1))))),
inference(superposition,[],[f208,f587]) ).
fof(f675,plain,
! [X0] : not(possibly(X0)) = not(not(not(possibly(X0)))),
inference(superposition,[],[f525,f189]) ).
fof(f676,plain,
! [X0,X1] : not(implies(X0,X1)) = not(not(not(implies(X0,X1)))),
inference(superposition,[],[f525,f197]) ).
fof(f681,plain,
! [X0,X1] : implies(X1,not(not(not(X0)))) = not(and(X1,not(not(X0)))),
inference(superposition,[],[f197,f525]) ).
fof(f694,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(X1,not(not(not(X0)))),
inference(forward_demodulation,[],[f681,f197]) ).
fof(f698,plain,
! [X2,X0,X1] : implies(X2,implies(X0,X1)) = implies(X2,not(not(implies(X0,X1)))),
inference(superposition,[],[f694,f197]) ).
fof(f788,plain,
! [X0] : possibly(not(not(possibly(X0)))) = not(necessarily(not(possibly(X0)))),
inference(superposition,[],[f189,f675]) ).
fof(f807,plain,
! [X0] : possibly(possibly(X0)) = possibly(not(not(possibly(X0)))),
inference(forward_demodulation,[],[f788,f189]) ).
fof(f813,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f202,f213]) ).
fof(f855,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,[],[f813,f213]) ).
fof(f882,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,[],[f855,f313]) ).
fof(f886,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X0)),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(duplicate_literal_removal,[],[f882]) ).
fof(f888,plain,
! [X0,X1] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f886,f214]) ).
fof(f890,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(implies(X1,not(X0))) ),
inference(resolution,[],[f888,f342]) ).
fof(f903,plain,
! [X0] : is_a_theorem(implies(X0,not(necessarily(not(X0))))),
inference(resolution,[],[f890,f193]) ).
fof(f919,plain,
! [X0] : is_a_theorem(implies(X0,possibly(X0))),
inference(forward_demodulation,[],[f903,f189]) ).
fof(f920,plain,
! [X0] : equiv(X0,possibly(X0)) = implies(possibly(X0),X0),
inference(resolution,[],[f919,f307]) ).
fof(f924,plain,
! [X0,X1] : and(implies(X0,possibly(X0)),X1) = X1,
inference(resolution,[],[f919,f432]) ).
fof(f928,plain,
! [X0] :
( ~ is_a_theorem(implies(possibly(X0),X0))
| possibly(X0) = X0 ),
inference(superposition,[],[f212,f920]) ).
fof(f975,plain,
! [X0,X1] : not(not(X0)) = implies(implies(X1,possibly(X1)),X0),
inference(superposition,[],[f197,f924]) ).
fof(f1007,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(implies(X1,possibly(X1)))),not(not(X0)))),
inference(superposition,[],[f211,f975]) ).
fof(f1056,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,not(implies(X1,possibly(X1)))),not(not(X0)))),
inference(forward_demodulation,[],[f1007,f214]) ).
fof(f1204,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[],[f207,f444]) ).
fof(f1206,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,possibly(X1)))),
inference(superposition,[],[f207,f924]) ).
fof(f1208,plain,
! [X0] : implies(X0,X0) = possibly(implies(X0,X0)),
inference(resolution,[],[f1204,f928]) ).
fof(f1233,plain,
! [X0] : implies(X0,possibly(X0)) = possibly(implies(X0,possibly(X0))),
inference(resolution,[],[f1206,f928]) ).
fof(f1351,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,necessarily(X2))))
| is_a_theorem(implies(X0,not(not(implies(X1,X2))))) ),
inference(resolution,[],[f594,f222]) ).
fof(f1380,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,necessarily(X2))))
| is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(forward_demodulation,[],[f1351,f698]) ).
fof(f1664,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[],[f343,f203]) ).
fof(f1690,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(forward_demodulation,[],[f1664,f214]) ).
fof(f1692,plain,
! [X0,X1] : is_a_theorem(or(not(X0),or(X0,X1))),
inference(superposition,[],[f1690,f214]) ).
fof(f2672,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(not(X0)),implies(X1,possibly(X1))))
| is_a_theorem(implies(not(not(X0)),X0)) ),
inference(superposition,[],[f221,f975]) ).
fof(f2682,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f2672,f1206]) ).
fof(f2694,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f2682,f214]) ).
fof(f2705,plain,
! [X0,X1] : and(or(not(X0),X0),X1) = X1,
inference(resolution,[],[f2694,f432]) ).
fof(f2985,plain,
! [X0] : not(not(possibly(implies(X0,X0)))) = possibly(not(not(possibly(implies(X0,X0))))),
inference(superposition,[],[f1233,f469]) ).
fof(f2987,plain,
! [X0] : not(not(possibly(implies(X0,possibly(X0))))) = possibly(not(not(possibly(implies(X0,possibly(X0)))))),
inference(superposition,[],[f1233,f975]) ).
fof(f3025,plain,
! [X0] : not(not(possibly(implies(X0,possibly(X0))))) = possibly(possibly(implies(X0,possibly(X0)))),
inference(forward_demodulation,[],[f2987,f807]) ).
fof(f3027,plain,
! [X0] : not(not(possibly(implies(X0,X0)))) = possibly(possibly(implies(X0,X0))),
inference(forward_demodulation,[],[f2985,f807]) ).
fof(f3030,plain,
! [X0] : possibly(implies(X0,possibly(X0))) = not(not(implies(X0,possibly(X0)))),
inference(forward_demodulation,[],[f3025,f1233]) ).
fof(f3032,plain,
! [X0] : not(not(implies(X0,X0))) = possibly(implies(X0,X0)),
inference(forward_demodulation,[],[f3027,f1208]) ).
fof(f3033,plain,
! [X0] : implies(X0,possibly(X0)) = not(not(implies(X0,possibly(X0)))),
inference(forward_demodulation,[],[f3030,f1233]) ).
fof(f3035,plain,
! [X0] : implies(X0,X0) = not(not(implies(X0,X0))),
inference(forward_demodulation,[],[f3032,f1208]) ).
fof(f3167,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(X0),implies(X1,X0))),
inference(resolution,[],[f1380,f210]) ).
fof(f3223,plain,
! [X2,X0,X1] : and(implies(necessarily(X0),implies(X1,X0)),X2) = X2,
inference(resolution,[],[f3167,f432]) ).
fof(f3418,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(necessarily(X1),implies(X2,X1)))),
inference(superposition,[],[f207,f3223]) ).
fof(f3424,plain,
! [X2,X0,X1] : not(not(X0)) = implies(implies(necessarily(X1),implies(X2,X1)),X0),
inference(superposition,[],[f197,f3223]) ).
fof(f3551,plain,
! [X0,X1] : not(not(possibly(implies(necessarily(X0),implies(X1,X0))))) = possibly(not(not(possibly(implies(necessarily(X0),implies(X1,X0)))))),
inference(superposition,[],[f1233,f3424]) ).
fof(f3561,plain,
! [X0,X1] : not(not(possibly(implies(necessarily(X0),implies(X1,X0))))) = possibly(possibly(implies(necessarily(X0),implies(X1,X0)))),
inference(forward_demodulation,[],[f3551,f807]) ).
fof(f3955,plain,
! [X0,X1] : implies(necessarily(X0),implies(X1,X0)) = possibly(implies(necessarily(X0),implies(X1,X0))),
inference(resolution,[],[f3418,f928]) ).
fof(f4732,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(not(X0)),or(X0,not(implies(X1,possibly(X1))))))
| is_a_theorem(equiv(not(not(X0)),or(X0,not(implies(X1,possibly(X1)))))) ),
inference(resolution,[],[f1056,f281]) ).
fof(f4771,plain,
! [X0,X1] :
( ~ is_a_theorem(or(not(X0),or(X0,not(implies(X1,possibly(X1))))))
| is_a_theorem(equiv(not(not(X0)),or(X0,not(implies(X1,possibly(X1)))))) ),
inference(forward_demodulation,[],[f4732,f214]) ).
fof(f4778,plain,
! [X0,X1] : is_a_theorem(equiv(not(not(X0)),or(X0,not(implies(X1,possibly(X1)))))),
inference(forward_subsumption_resolution,[],[f4771,f1692]) ).
fof(f4781,plain,
! [X0,X1] : not(not(X0)) = or(X0,not(implies(X1,possibly(X1)))),
inference(resolution,[],[f4778,f212]) ).
fof(f4871,plain,
! [X0,X1] : not(not(necessarily(not(X0)))) = implies(possibly(X0),not(implies(X1,possibly(X1)))),
inference(superposition,[],[f241,f4781]) ).
fof(f4874,plain,
! [X0,X1] : not(possibly(X0)) = implies(possibly(X0),not(implies(X1,possibly(X1)))),
inference(forward_demodulation,[],[f4871,f189]) ).
fof(f4908,plain,
! [X0,X1] : not(implies(X0,X0)) = implies(implies(X0,X0),not(implies(X1,possibly(X1)))),
inference(superposition,[],[f4874,f1208]) ).
fof(f5040,plain,
! [X0,X1] : not(implies(X0,X0)) = not(not(not(implies(X1,possibly(X1))))),
inference(forward_demodulation,[],[f4908,f469]) ).
fof(f5061,plain,
! [X0,X1] : not(implies(X0,X0)) = not(implies(X1,possibly(X1))),
inference(forward_demodulation,[],[f5040,f676]) ).
fof(f5087,plain,
! [X0,X1] : implies(X1,X1) = not(not(implies(X0,possibly(X0)))),
inference(superposition,[],[f3035,f5061]) ).
fof(f5295,plain,
! [X0,X1] : implies(X1,X1) = implies(X0,possibly(X0)),
inference(forward_demodulation,[],[f5087,f3033]) ).
fof(f5579,plain,
! [X2,X0,X1] : implies(X0,X0) = not(not(possibly(implies(necessarily(X1),implies(X2,X1))))),
inference(superposition,[],[f3424,f5295]) ).
fof(f5591,plain,
! [X2,X0,X1] : implies(X0,X0) = possibly(possibly(implies(necessarily(X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f5579,f3561]) ).
fof(f5647,plain,
! [X2,X0,X1] : implies(X0,X0) = possibly(implies(necessarily(X1),implies(X2,X1))),
inference(forward_demodulation,[],[f5591,f3955]) ).
fof(f5670,plain,
! [X2,X0,X1] : implies(X0,X0) = implies(necessarily(X1),implies(X2,X1)),
inference(forward_demodulation,[],[f5647,f3955]) ).
fof(f6848,plain,
! [X0,X1] : implies(X1,X1) = implies(necessarily(X0),not(not(X0))),
inference(superposition,[],[f5670,f3424]) ).
fof(f9504,plain,
! [X0,X1] : implies(X1,X1) = implies(necessarily(X0),not(not(necessarily(X0)))),
inference(superposition,[],[f6848,f380]) ).
fof(f11585,plain,
! [X0,X1] : equiv(not(not(necessarily(X1))),necessarily(X1)) = and(implies(not(not(necessarily(X1))),necessarily(X1)),implies(X0,X0)),
inference(superposition,[],[f196,f9504]) ).
fof(f11661,plain,
! [X0,X1] : equiv(not(not(necessarily(X1))),necessarily(X1)) = and(or(not(necessarily(X1)),necessarily(X1)),implies(X0,X0)),
inference(forward_demodulation,[],[f11585,f214]) ).
fof(f11721,plain,
! [X0,X1] : implies(X0,X0) = equiv(not(not(necessarily(X1))),necessarily(X1)),
inference(forward_demodulation,[],[f11661,f2705]) ).
fof(f11922,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| necessarily(X1) = not(not(necessarily(X1))) ),
inference(superposition,[],[f212,f11721]) ).
fof(f11929,plain,
! [X1] : necessarily(X1) = not(not(necessarily(X1))),
inference(forward_subsumption_resolution,[],[f11922,f228]) ).
fof(f12035,plain,
! [X0] : not(possibly(X0)) = necessarily(not(X0)),
inference(superposition,[],[f11929,f189]) ).
fof(f12188,plain,
! [X0] : possibly(possibly(X0)) = not(necessarily(necessarily(not(X0)))),
inference(superposition,[],[f189,f12035]) ).
fof(f12194,plain,
! [X0,X1] : implies(possibly(possibly(X0)),X1) = or(necessarily(necessarily(not(X0))),X1),
inference(superposition,[],[f241,f12035]) ).
fof(f12291,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(possibly(X0)),X1),
inference(forward_demodulation,[],[f12194,f380]) ).
fof(f12295,plain,
! [X0] : possibly(possibly(X0)) = not(necessarily(not(X0))),
inference(forward_demodulation,[],[f12188,f380]) ).
fof(f12318,plain,
! [X0,X1] : implies(possibly(X0),X1) = implies(possibly(possibly(X0)),X1),
inference(forward_demodulation,[],[f12291,f241]) ).
fof(f12320,plain,
! [X0] : possibly(X0) = possibly(possibly(X0)),
inference(forward_demodulation,[],[f12295,f189]) ).
fof(f12486,plain,
! [X0] :
( ~ is_a_theorem(implies(possibly(X0),necessarily(possibly(possibly(X0)))))
| possibly(possibly(X0)) = necessarily(possibly(possibly(X0))) ),
inference(superposition,[],[f376,f12318]) ).
fof(f12551,plain,
! [X0] : possibly(possibly(X0)) = necessarily(possibly(possibly(X0))),
inference(forward_subsumption_resolution,[],[f12486,f191]) ).
fof(f12642,plain,
! [X0] : possibly(X0) = necessarily(possibly(X0)),
inference(forward_demodulation,[],[f12551,f12320]) ).
fof(f12764,plain,
~ is_a_theorem(implies(possibly(sK0),possibly(sK0))),
inference(superposition,[],[f190,f12642]) ).
fof(f12833,plain,
$false,
inference(forward_subsumption_resolution,[],[f12764,f228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL537+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:57:46 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/1.15 % (968325)Detected formulas, will run a generic FOF schedule.
% 3.66/1.15 % (968335)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=87295337:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.15 % (968331)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=1899805646:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.15 % (968336)dis-21_1_sil=8000:lcm=predicate:random_seed=134163518:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.66/1.15 % (968333)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2765547547:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.15 % (968330)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=710800141:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.15 % (968334)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=349917862:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.15 % (968332)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=3280914326:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.15 % (968334)Refutation not found, incomplete strategy
% 3.66/1.15 % (968334)------------------------------
% 3.66/1.15 % (968334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.15 % (968334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.15 % (968333)Refutation not found, incomplete strategy
% 3.66/1.15 % (968333)------------------------------
% 3.66/1.15 % (968333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.15 % (968334)CaDiCaL version: 2.1.3
% 3.66/1.15 % (968334)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.15 % (968334)Time elapsed: 0.001 s
% 3.66/1.15 % (968336)Refutation not found, incomplete strategy
% 3.66/1.15 % (968336)------------------------------
% 3.66/1.15 % (968336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.15 % (968334)Peak memory usage: 86 MB
% 3.66/1.15 % (968333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.15 % (968336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.15 % (968333)CaDiCaL version: 2.1.3
% 3.66/1.15 % (968333)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.15 % (968333)Time elapsed: 0.001 s
% 3.66/1.15 % (968333)Peak memory usage: 87 MB
% 3.66/1.15 % (968336)CaDiCaL version: 2.1.3
% 3.66/1.15 % (968336)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.15 % (968336)Time elapsed: 0.001 s
% 3.66/1.15 % (968336)Peak memory usage: 87 MB
% 3.66/1.15 % (968335)Instruction limit reached!
% 3.66/1.15 % (968335)------------------------------
% 3.66/1.15 % (968335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.15 % (968335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.15 % (968335)CaDiCaL version: 2.1.3
% 3.66/1.15 % (968335)Termination reason: Instruction limit
% 3.66/1.15 % (968335)Termination phase: Saturation
% 3.66/1.15 % (968335)Time elapsed: 0.090 s
% 3.66/1.15 % (968335)Peak memory usage: 90 MB
% 3.66/1.15 % (968335)Instructions burned: 140 (million)
% 3.66/1.15 % (968333)------------------------------
% 3.66/1.15 % (968333)------------------------------
% 3.66/1.15 % (968344)lrs+10_1_sil=8000:sp=occurrence:random_seed=873840309:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.66/1.15 % (968334)------------------------------
% 3.66/1.15 % (968334)------------------------------
% 3.66/1.15 % (968336)------------------------------
% 3.66/1.15 % (968336)------------------------------
% 3.66/1.15 % (968344)Refutation not found, incomplete strategy
% 3.66/1.15 % (968344)------------------------------
% 3.66/1.15 % (968344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.15 % (968344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.15 % (968344)CaDiCaL version: 2.1.3
% 3.66/1.15 % (968344)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.15 % (968344)Time elapsed: 0.0000 s
% 3.66/1.15 % (968344)Peak memory usage: 87 MB
% 6.21/1.55 [W927 15:57:47.200491313 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200491236 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200546193 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200545970 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200582863 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200584623 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200594250 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200596660 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200620700 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200621183 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200631770 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200632260 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200657390 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.
% 6.21/1.55 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.21/1.55 [W927 15:57:47.200658110 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200668803 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200672083 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200703360 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200703790 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200714527 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200727090 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200738727 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200749284 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200752187 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 [W927 15:57:47.200762390 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.
% 11.05/2.15 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.05/2.15 % (968344)------------------------------
% 11.05/2.15 % (968344)------------------------------
% 11.05/2.15 % (968346)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2224494579:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 11.05/2.15 % (968346)Refutation not found, incomplete strategy
% 11.05/2.15 % (968346)------------------------------
% 11.05/2.15 % (968346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.05/2.15 % (968346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.05/2.15 % (968346)CaDiCaL version: 2.1.3
% 11.05/2.15 % (968346)Termination reason: Refutation not found, incomplete strategy
% 11.05/2.15 % (968346)Time elapsed: 0.001 s
% 11.05/2.15 % (968346)Peak memory usage: 87 MB
% 11.50/2.29 % (968347)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1843268940:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 11.50/2.29 % (968348)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=4035022396:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 11.50/2.29 % (968347)Refutation not found, incomplete strategy
% 11.50/2.29 % (968347)------------------------------
% 11.50/2.29 % (968347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.50/2.29 % (968347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.50/2.29 % (968347)CaDiCaL version: 2.1.3
% 11.50/2.29 % (968347)Termination reason: Refutation not found, incomplete strategy
% 11.50/2.29 % (968347)Time elapsed: 0.001 s
% 11.50/2.29 % (968347)Peak memory usage: 87 MB
% 11.50/2.29 % (968349)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3559975777:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 11.50/2.29 % (968349)Refutation not found, incomplete strategy
% 11.50/2.29 % (968349)------------------------------
% 11.50/2.29 % (968349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.50/2.29 % (968349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.50/2.29 % (968349)CaDiCaL version: 2.1.3
% 11.50/2.29 % (968349)Termination reason: Refutation not found, incomplete strategy
% 11.50/2.29 % (968349)Time elapsed: 0.0000 s
% 11.50/2.29 % (968349)Peak memory usage: 87 MB
% 11.50/2.29 % (968332)Refutation not found, incomplete strategy
% 11.50/2.29 % (968332)------------------------------
% 11.50/2.29 % (968332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.50/2.29 % (968332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.50/2.29 % (968331)Refutation not found, incomplete strategy
% 11.50/2.29 % (968331)------------------------------
% 11.50/2.29 % (968331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.50/2.29 % (968332)CaDiCaL version: 2.1.3
% 11.50/2.29 % (968332)Termination reason: Refutation not found, incomplete strategy
% 11.50/2.29 % (968332)Time elapsed: 0.556 s
% 11.50/2.29 % (968332)Peak memory usage: 123 MB
% 11.50/2.29 % (968331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.50/2.29 % (968332)Instructions burned: 827 (million)
% 11.50/2.29 % (968331)CaDiCaL version: 2.1.3
% 11.50/2.29 % (968331)Termination reason: Refutation not found, incomplete strategy
% 11.50/2.29 % (968331)Time elapsed: 0.556 s
% 11.50/2.29 % (968331)Peak memory usage: 124 MB
% 11.50/2.29 % (968331)Instructions burned: 827 (million)
% 11.50/2.29 % (968348)Instruction limit reached!
% 11.50/2.29 % (968348)------------------------------
% 11.50/2.29 % (968348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.50/2.29 % (968348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.50/2.29 % (968348)CaDiCaL version: 2.1.3
% 11.50/2.29 % (968348)Termination reason: Instruction limit
% 11.50/2.29 % (968348)Termination phase: Saturation
% 11.50/2.29 % (968348)Time elapsed: 0.150 s
% 11.50/2.29 % (968348)Peak memory usage: 93 MB
% 11.50/2.29 % (968348)Instructions burned: 249 (million)
% 11.50/2.29 % (968346)------------------------------
% 11.50/2.29 % (968346)------------------------------
% 11.50/2.29 % (968347)------------------------------
% 11.50/2.29 % (968347)------------------------------
% 11.50/2.29 % (968349)------------------------------
% 11.50/2.29 % (968349)------------------------------
% 11.50/2.29 % (968354)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=874917517:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 11.50/2.29 % (968357)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2280402821:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.50/2.29 % (968357)Refutation not found, incomplete strategy
% 11.50/2.29 % (968357)------------------------------
% 11.50/2.29 % (968357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.50/2.29 % (968357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.50/2.29 % (968357)CaDiCaL version: 2.1.3
% 11.50/2.29 % (968357)Termination reason: Refutation not found, incomplete strategy
% 11.50/2.29 % (968357)Time elapsed: 0.001 s
% 11.50/2.29 % (968357)Peak memory usage: 87 MB
% 11.50/2.29 % (968355)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1973648120:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 10.85/2.41 % (968355)Refutation not found, incomplete strategy
% 10.85/2.41 % (968355)------------------------------
% 10.85/2.41 % (968355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968355)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968355)Termination reason: Refutation not found, incomplete strategy
% 10.85/2.41 % (968355)Time elapsed: 0.001 s
% 10.85/2.41 % (968355)Peak memory usage: 87 MB
% 10.85/2.41 % (968332)------------------------------
% 10.85/2.41 % (968332)------------------------------
% 10.85/2.41 % (968331)------------------------------
% 10.85/2.41 % (968331)------------------------------
% 10.85/2.41 % (968356)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=388379976:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 10.85/2.41 % (968356)Instruction limit reached!
% 10.85/2.41 % (968356)------------------------------
% 10.85/2.41 % (968356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968356)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968356)Termination reason: Instruction limit
% 10.85/2.41 % (968356)Termination phase: Saturation
% 10.85/2.41 % (968356)Time elapsed: 0.074 s
% 10.85/2.41 % (968356)Peak memory usage: 89 MB
% 10.85/2.41 % (968356)Instructions burned: 127 (million)
% 10.85/2.41 % (968357)------------------------------
% 10.85/2.41 % (968357)------------------------------
% 10.85/2.41 % (968362)lrs+10_1_sil=8000:sp=occurrence:random_seed=2495600458:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 10.85/2.41 % (968363)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=984746827:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 10.85/2.41 % (968363)Refutation not found, incomplete strategy
% 10.85/2.41 % (968363)------------------------------
% 10.85/2.41 % (968363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968363)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968363)Termination reason: Refutation not found, incomplete strategy
% 10.85/2.41 % (968363)Time elapsed: 0.001 s
% 10.85/2.41 % (968363)Peak memory usage: 87 MB
% 10.85/2.41 % (968355)------------------------------
% 10.85/2.41 % (968355)------------------------------
% 10.85/2.41 % (968364)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1728269679:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 10.85/2.41 % (968365)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3055264549:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 10.85/2.41 % (968365)Refutation not found, incomplete strategy
% 10.85/2.41 % (968365)------------------------------
% 10.85/2.41 % (968365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968365)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968365)Termination reason: Refutation not found, incomplete strategy
% 10.85/2.41 % (968365)Time elapsed: 0.0000 s
% 10.85/2.41 % (968365)Peak memory usage: 87 MB
% 10.85/2.41 % (968365)------------------------------
% 10.85/2.41 % (968365)------------------------------
% 10.85/2.41 % (968370)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1091605378:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 10.85/2.41 % (968370)Refutation not found, incomplete strategy
% 10.85/2.41 % (968370)------------------------------
% 10.85/2.41 % (968370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968370)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968370)Termination reason: Refutation not found, incomplete strategy
% 10.85/2.41 % (968370)Time elapsed: 0.002 s
% 10.85/2.41 % (968370)Peak memory usage: 88 MB
% 10.85/2.41 % (968370)Instructions burned: 1 (million)
% 10.85/2.41 % (968363)------------------------------
% 10.85/2.41 % (968363)------------------------------
% 10.85/2.41 % (968371)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3230792192:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 10.85/2.41 % (968373)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=4149160591:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/125Mi)
% 10.85/2.41 % (968330)First to succeed.
% 10.85/2.41 % (968373)Refutation not found, incomplete strategy
% 10.85/2.41 % (968373)------------------------------
% 10.85/2.41 % (968373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968373)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968373)Termination reason: Refutation not found, incomplete strategy
% 10.85/2.41 % (968373)Time elapsed: 0.001 s
% 10.85/2.41 % (968373)Peak memory usage: 87 MB
% 10.85/2.41 % (968373)Instructions burned: 1 (million)
% 10.85/2.41 % (968330)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-968325"
% 10.85/2.41 % (968370)------------------------------
% 10.85/2.41 % (968370)------------------------------
% 10.85/2.41 % (968362)Instruction limit reached!
% 10.85/2.41 % (968362)------------------------------
% 10.85/2.41 % (968362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968362)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968362)Termination reason: Instruction limit
% 10.85/2.41 % (968362)Termination phase: Saturation
% 10.85/2.41 % (968362)Time elapsed: 0.531 s
% 10.85/2.41 % (968362)Peak memory usage: 101 MB
% 10.85/2.41 % (968362)Instructions burned: 908 (million)
% 10.85/2.41 [W927 15:57:48.353087967 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353112100 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353133460 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353143824 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353157936 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353164724 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353178737 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353185324 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353198141 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353204779 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353228657 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 [W927 15:57:48.353234494 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.
% 10.85/2.41 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 10.85/2.41 % (968376)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3703518944:i=134:gtgl=5:slsql=off:gtg=exists_sym_2983 on theBenchmark for (2983ds/134Mi)
% 10.85/2.41 % (968373)------------------------------
% 10.85/2.41 % (968373)------------------------------
% 10.85/2.41 % (968371)Refutation not found, incomplete strategy
% 10.85/2.41 % (968371)------------------------------
% 10.85/2.41 % (968371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.85/2.41 % (968371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.85/2.41 % (968371)CaDiCaL version: 2.1.3
% 10.85/2.41 % (968371)Termination reason: Refutation not found, incomplete strategy
% 10.85/2.41 % (968371)Time elapsed: 0.308 s
% 10.85/2.41 % (968371)Peak memory usage: 126 MB
% 10.85/2.41 % (968371)Instructions burned: 827 (million)
% 10.85/2.41 % (968330)Refutation found. Thanks to Tanya!
% 10.85/2.41 % SZS status Theorem for theBenchmark
% 10.85/2.41 % SZS output start Proof for theBenchmark
% See solution above
% 13.25/2.64 % (968330)------------------------------
% 13.25/2.64 % (968330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.25/2.64 % (968330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.25/2.64 % (968330)CaDiCaL version: 2.1.3
% 13.25/2.64 % (968330)Termination reason: Refutation
% 13.25/2.64 % (968330)Time elapsed: 1.396 s
% 13.25/2.64 % (968330)Peak memory usage: 138 MB
% 13.25/2.64 % (968330)Instructions burned: 2132 (million)
% 13.25/2.64 % (968330)------------------------------
% 13.25/2.64 % (968330)------------------------------
% 13.25/2.64 % (968325)Success in time 1.82 s
% 13.25/2.64 % Vampire exiting
%------------------------------------------------------------------------------