%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL535+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 : n002.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 11:52:52 AM UTC 2026
% Result : Theorem 11.77s 2.92s
% Output : Refutation 15.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 28
% Syntax : Number of formulae : 131 ( 64 unt; 0 def)
% Number of atoms : 219 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 147 ( 59 ~; 55 |; 2 &)
% ( 11 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 156 ( 155 !; 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(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(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(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(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(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(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(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(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
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(f71,axiom,
( axiom_m9
<=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m9) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_possibly) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f82,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(f89,negated_conjecture,
~ axiom_m9,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m9,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
=> axiom_m9 ),
inference(unused_predicate_definition_removal,[],[f71]) ).
fof(f92,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f93,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f96,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(f102,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f103,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f106,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f107,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f109,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f110,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(f115,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f110]) ).
fof(f116,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f109]) ).
fof(f119,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f107]) ).
fof(f120,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f106]) ).
fof(f123,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f103]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f102]) ).
fof(f130,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f96]) ).
fof(f132,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f134,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f95]) ).
fof(f136,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f93]) ).
fof(f137,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(ennf_transformation,[],[f92]) ).
fof(f138,plain,
( axiom_m9
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(ennf_transformation,[],[f91]) ).
fof(f139,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f140,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f142,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f138]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f116]) ).
fof(f144,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f117]) ).
fof(f146,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f150,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f151,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f157,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f130]) ).
fof(f159,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f132]) ).
fof(f162,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f164,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f166,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f167,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f170,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f171,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f177,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f178,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f179,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f134]) ).
fof(f181,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f136]) ).
fof(f182,plain,
! [X0] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f137]) ).
fof(f183,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(cnf_transformation,[],[f142]) ).
fof(f184,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f139]) ).
fof(f185,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f140]) ).
fof(f188,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f190,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f191,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f192,plain,
op_possibly,
inference(cnf_transformation,[],[f82]) ).
fof(f194,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
~ axiom_m9,
inference(cnf_transformation,[],[f90]) ).
fof(f199,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f185,f194]) ).
fof(f200,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(forward_subsumption_resolution,[],[f184,f192]) ).
fof(f201,plain,
~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))),
inference(forward_subsumption_resolution,[],[f183,f197]) ).
fof(f202,plain,
! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(forward_subsumption_resolution,[],[f182,f191]) ).
fof(f203,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f181,f190]) ).
fof(f205,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f179,f188]) ).
fof(f207,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f159,f162]) ).
fof(f209,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[],[f157,f177]) ).
fof(f215,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_subsumption_resolution,[],[f151,f171]) ).
fof(f216,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[],[f150,f170]) ).
fof(f219,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f147,f167]) ).
fof(f220,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f146,f166]) ).
fof(f222,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f144,f178]) ).
fof(f223,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f143,f164]) ).
fof(f226,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f205,f199]) ).
fof(f232,plain,
! [X0] : is_a_theorem(strict_implies(necessarily(X0),X0)),
inference(resolution,[],[f203,f226]) ).
fof(f252,plain,
! [X0] : possibly(necessarily(not(X0))) = not(necessarily(possibly(X0))),
inference(superposition,[],[f200,f200]) ).
fof(f269,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f215,f223]) ).
fof(f340,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f209,f223]) ).
fof(f345,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f340,f223]) ).
fof(f352,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,[],[f345,f269]) ).
fof(f354,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,[],[f345,f219]) ).
fof(f365,plain,
! [X0] :
( ~ is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))
| is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))) ),
inference(resolution,[],[f345,f202]) ).
fof(f367,plain,
! [X0] : is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))),
inference(forward_subsumption_resolution,[],[f365,f203]) ).
fof(f371,plain,
! [X0,X1] : is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))),
inference(forward_subsumption_resolution,[],[f354,f220]) ).
fof(f373,plain,
! [X0,X1] :
( is_a_theorem(equiv(and(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f352,f216]) ).
fof(f377,plain,
! [X0] : possibly(X0) = necessarily(possibly(X0)),
inference(resolution,[],[f367,f222]) ).
fof(f524,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| and(X0,X1) = X1 ),
inference(resolution,[],[f373,f222]) ).
fof(f565,plain,
! [X0,X1] : and(strict_implies(necessarily(X0),X0),X1) = X1,
inference(resolution,[],[f524,f232]) ).
fof(f1123,plain,
! [X0,X1] : not(not(X0)) = implies(strict_implies(necessarily(X1),X1),X0),
inference(superposition,[],[f207,f565]) ).
fof(f1660,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,implies(X0,X1)),
inference(resolution,[],[f371,f222]) ).
fof(f1775,plain,
! [X0,X1] : implies(strict_implies(necessarily(X0),X0),X1) = not(not(implies(strict_implies(necessarily(X0),X0),X1))),
inference(superposition,[],[f1123,f1660]) ).
fof(f1776,plain,
! [X1] : not(not(X1)) = not(not(not(not(X1)))),
inference(forward_demodulation,[],[f1775,f1123]) ).
fof(f1858,plain,
! [X0,X1] : implies(X1,not(not(not(X0)))) = not(and(X1,not(not(X0)))),
inference(superposition,[],[f207,f1776]) ).
fof(f1880,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(X1,not(not(not(X0)))),
inference(forward_demodulation,[],[f1858,f207]) ).
fof(f1945,plain,
! [X0] : is_a_theorem(implies(necessarily(not(not(not(X0)))),not(X0))),
inference(superposition,[],[f203,f1880]) ).
fof(f2019,plain,
! [X0] : is_a_theorem(implies(necessarily(not(not(possibly(X0)))),possibly(X0))),
inference(superposition,[],[f1945,f200]) ).
fof(f2549,plain,
! [X0] : not(necessarily(possibly(necessarily(not(X0))))) = possibly(necessarily(possibly(X0))),
inference(superposition,[],[f252,f200]) ).
fof(f2615,plain,
! [X0] : possibly(possibly(X0)) = not(necessarily(possibly(necessarily(not(X0))))),
inference(forward_demodulation,[],[f2549,f377]) ).
fof(f2633,plain,
! [X0] : possibly(possibly(X0)) = not(possibly(necessarily(not(X0)))),
inference(forward_demodulation,[],[f2615,f377]) ).
fof(f2642,plain,
! [X0] : possibly(possibly(X0)) = not(not(necessarily(possibly(X0)))),
inference(forward_demodulation,[],[f2633,f252]) ).
fof(f2644,plain,
! [X0] : possibly(possibly(X0)) = not(not(possibly(X0))),
inference(forward_demodulation,[],[f2642,f377]) ).
fof(f2654,plain,
! [X0] : is_a_theorem(implies(necessarily(possibly(possibly(X0))),possibly(X0))),
inference(superposition,[],[f2019,f2644]) ).
fof(f2700,plain,
! [X0] : is_a_theorem(implies(possibly(possibly(X0)),possibly(X0))),
inference(forward_demodulation,[],[f2654,f377]) ).
fof(f2725,plain,
! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))),
inference(resolution,[],[f2700,f226]) ).
fof(f2744,plain,
$false,
inference(resolution,[],[f2725,f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:59:22 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 10.07/2.38 % (3707686)Detected formulas, will run a generic FOF schedule.
% 10.07/2.38 % (3707695)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2523422543:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.07/2.38 % (3707695)Refutation not found, incomplete strategy
% 10.07/2.38 % (3707695)------------------------------
% 10.07/2.38 % (3707695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.07/2.38 % (3707695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.07/2.38 % (3707695)CaDiCaL version: 2.1.3
% 10.07/2.38 % (3707695)Termination reason: Refutation not found, incomplete strategy
% 10.07/2.38 % (3707695)Time elapsed: 0.0000 s
% 10.07/2.38 % (3707695)Peak memory usage: 87 MB
% 10.07/2.38 % (3707693)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=339790628:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.07/2.38 % (3707691)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=3897346268:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.07/2.38 % (3707694)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3707687736:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.07/2.38 % (3707692)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=1603721997:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.07/2.38 % (3707694)Refutation not found, incomplete strategy
% 10.07/2.38 % (3707694)------------------------------
% 10.07/2.38 % (3707694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.07/2.38 % (3707694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.07/2.38 % (3707694)CaDiCaL version: 2.1.3
% 10.07/2.38 % (3707694)Termination reason: Refutation not found, incomplete strategy
% 10.07/2.38 % (3707694)Time elapsed: 0.001 s
% 10.07/2.38 % (3707694)Peak memory usage: 87 MB
% 10.07/2.38 % (3707696)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1394197591:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.07/2.38 % (3707697)dis-21_1_sil=8000:lcm=predicate:random_seed=74104071: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)
% 10.07/2.38 % (3707697)Refutation not found, incomplete strategy
% 10.07/2.38 % (3707697)------------------------------
% 10.07/2.38 % (3707697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.07/2.38 % (3707697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.07/2.38 % (3707697)CaDiCaL version: 2.1.3
% 10.07/2.38 % (3707697)Termination reason: Refutation not found, incomplete strategy
% 10.07/2.38 % (3707697)Time elapsed: 0.002 s
% 10.07/2.38 % (3707697)Peak memory usage: 88 MB
% 10.07/2.38 % (3707697)Instructions burned: 1 (million)
% 10.07/2.38 % (3707695)------------------------------
% 10.07/2.38 % (3707695)------------------------------
% 10.07/2.38 % (3707696)Instruction limit reached!
% 10.07/2.38 % (3707696)------------------------------
% 10.07/2.38 % (3707696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.07/2.38 % (3707696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.07/2.38 % (3707696)CaDiCaL version: 2.1.3
% 10.07/2.38 % (3707696)Termination reason: Instruction limit
% 10.07/2.38 % (3707696)Termination phase: Saturation
% 10.07/2.38 % (3707696)Time elapsed: 0.096 s
% 10.07/2.38 % (3707696)Peak memory usage: 90 MB
% 10.07/2.38 % (3707696)Instructions burned: 140 (million)
% 10.07/2.38 % (3707706)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1804018901:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.07/2.38 % (3707706)Refutation not found, incomplete strategy
% 10.07/2.38 % (3707706)------------------------------
% 10.07/2.38 % (3707706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.07/2.38 % (3707706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.07/2.38 % (3707706)CaDiCaL version: 2.1.3
% 10.07/2.38 % (3707706)Termination reason: Refutation not found, incomplete strategy
% 10.07/2.38 % (3707706)Time elapsed: 0.001 s
% 10.07/2.38 % (3707706)Peak memory usage: 87 MB
% 10.07/2.38 % (3707694)------------------------------
% 10.07/2.38 % (3707694)------------------------------
% 12.55/2.84 % (3707697)------------------------------
% 12.55/2.84 % (3707697)------------------------------
% 12.55/2.84 % (3707705)lrs+10_1_sil=8000:sp=occurrence:random_seed=4157063468:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.55/2.84 % (3707705)Refutation not found, incomplete strategy
% 12.55/2.84 % (3707705)------------------------------
% 12.55/2.84 % (3707705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.84 % (3707705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.55/2.84 % (3707705)CaDiCaL version: 2.1.3
% 12.55/2.84 % (3707705)Termination reason: Refutation not found, incomplete strategy
% 12.55/2.84 % (3707705)Time elapsed: 0.001 s
% 12.55/2.84 % (3707705)Peak memory usage: 87 MB
% 12.55/2.84 % (3707706)------------------------------
% 12.55/2.84 % (3707706)------------------------------
% 12.55/2.84 % (3707709)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1177632650:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 12.55/2.84 % (3707710)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=2965937800:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 12.55/2.84 % (3707709)Refutation not found, incomplete strategy
% 12.55/2.84 % (3707709)------------------------------
% 12.55/2.84 % (3707709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.84 % (3707709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.55/2.84 % (3707709)CaDiCaL version: 2.1.3
% 12.55/2.84 % (3707709)Termination reason: Refutation not found, incomplete strategy
% 12.55/2.84 % (3707709)Time elapsed: 0.001 s
% 12.55/2.84 % (3707709)Peak memory usage: 87 MB
% 12.55/2.84 % (3707711)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2273924503:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 12.55/2.84 % (3707711)Refutation not found, incomplete strategy
% 12.55/2.84 % (3707711)------------------------------
% 12.55/2.84 % (3707711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.84 % (3707711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.55/2.84 % (3707711)CaDiCaL version: 2.1.3
% 12.55/2.84 % (3707711)Termination reason: Refutation not found, incomplete strategy
% 12.55/2.84 % (3707711)Time elapsed: 0.0000 s
% 12.55/2.84 % (3707711)Peak memory usage: 87 MB
% 12.55/2.84 % (3707705)------------------------------
% 12.55/2.84 % (3707705)------------------------------
% 12.55/2.84 % (3707710)Instruction limit reached!
% 12.55/2.84 % (3707710)------------------------------
% 12.55/2.84 % (3707710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.84 % (3707710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.55/2.84 % (3707710)CaDiCaL version: 2.1.3
% 12.55/2.84 % (3707710)Termination reason: Instruction limit
% 12.55/2.84 % (3707710)Termination phase: Saturation
% 12.55/2.84 % (3707710)Time elapsed: 0.151 s
% 12.55/2.84 % (3707710)Peak memory usage: 92 MB
% 12.55/2.84 % (3707710)Instructions burned: 248 (million)
% 12.55/2.84 % (3707693)Refutation not found, incomplete strategy
% 12.55/2.84 % (3707693)------------------------------
% 12.55/2.84 % (3707693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.84 % (3707693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.55/2.84 % (3707693)CaDiCaL version: 2.1.3
% 12.55/2.84 % (3707693)Termination reason: Refutation not found, incomplete strategy
% 12.55/2.84 % (3707693)Time elapsed: 0.568 s
% 12.55/2.84 % (3707693)Peak memory usage: 125 MB
% 12.55/2.84 % (3707693)Instructions burned: 831 (million)
% 12.55/2.84 % (3707711)------------------------------
% 12.55/2.84 % (3707711)------------------------------
% 12.55/2.84 % (3707709)------------------------------
% 12.55/2.84 % (3707709)------------------------------
% 12.55/2.84 % (3707715)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3114744582:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 12.55/2.84 % (3707716)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2142404028:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 12.55/2.84 % (3707716)Refutation not found, incomplete strategy
% 12.55/2.84 % (3707716)------------------------------
% 12.55/2.84 % (3707716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.84 % (3707716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707716)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707716)Termination reason: Refutation not found, incomplete strategy
% 11.77/2.92 % (3707716)Time elapsed: 0.001 s
% 11.77/2.92 % (3707716)Peak memory usage: 88 MB
% 11.77/2.92 % (3707717)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2513769410:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 11.77/2.92 % (3707717)Instruction limit reached!
% 11.77/2.92 % (3707717)------------------------------
% 11.77/2.92 % (3707717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707717)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707717)Termination reason: Instruction limit
% 11.77/2.92 % (3707717)Termination phase: Saturation
% 11.77/2.92 % (3707717)Time elapsed: 0.038 s
% 11.77/2.92 % (3707717)Peak memory usage: 89 MB
% 11.77/2.92 % (3707717)Instructions burned: 128 (million)
% 11.77/2.92 % (3707693)------------------------------
% 11.77/2.92 % (3707693)------------------------------
% 11.77/2.92 % (3707718)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1911293942:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.77/2.92 % (3707718)Refutation not found, incomplete strategy
% 11.77/2.92 % (3707718)------------------------------
% 11.77/2.92 % (3707718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707718)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707718)Termination reason: Refutation not found, incomplete strategy
% 11.77/2.92 % (3707718)Time elapsed: 0.001 s
% 11.77/2.92 % (3707718)Peak memory usage: 87 MB
% 11.77/2.92 % (3707722)lrs+10_1_sil=8000:sp=occurrence:random_seed=2144498977:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 11.77/2.92 % (3707716)------------------------------
% 11.77/2.92 % (3707716)------------------------------
% 11.77/2.92 % (3707723)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1165150977:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 11.77/2.92 % (3707723)Refutation not found, incomplete strategy
% 11.77/2.92 % (3707723)------------------------------
% 11.77/2.92 % (3707723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707723)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707723)Termination reason: Refutation not found, incomplete strategy
% 11.77/2.92 % (3707723)Time elapsed: 0.002 s
% 11.77/2.92 % (3707723)Peak memory usage: 88 MB
% 11.77/2.92 % (3707718)------------------------------
% 11.77/2.92 % (3707718)------------------------------
% 11.77/2.92 % (3707726)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2722438912:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 11.77/2.92 % (3707722)Instruction limit reached!
% 11.77/2.92 % (3707722)------------------------------
% 11.77/2.92 % (3707722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707722)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707722)Termination reason: Instruction limit
% 11.77/2.92 % (3707722)Termination phase: Saturation
% 11.77/2.92 % (3707722)Time elapsed: 0.294 s
% 11.77/2.92 % (3707722)Peak memory usage: 101 MB
% 11.77/2.92 % (3707722)Instructions burned: 910 (million)
% 11.77/2.92 % (3707723)------------------------------
% 11.77/2.92 % (3707723)------------------------------
% 11.77/2.92 % (3707728)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2364754666:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 11.77/2.92 % (3707728)Refutation not found, incomplete strategy
% 11.77/2.92 % (3707728)------------------------------
% 11.77/2.92 % (3707728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707728)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707728)Termination reason: Refutation not found, incomplete strategy
% 11.77/2.92 % (3707728)Time elapsed: 0.002 s
% 11.77/2.92 % (3707728)Peak memory usage: 89 MB
% 11.77/2.92 % (3707728)Instructions burned: 1 (million)
% 11.77/2.92 % (3707730)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=697443772:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 11.77/2.92 % (3707730)Refutation not found, incomplete strategy
% 11.77/2.92 % (3707730)------------------------------
% 11.77/2.92 % (3707730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707730)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707730)Termination reason: Refutation not found, incomplete strategy
% 11.77/2.92 % (3707730)Time elapsed: 0.001 s
% 11.77/2.92 % (3707730)Peak memory usage: 88 MB
% 11.77/2.92 % (3707730)Instructions burned: 1 (million)
% 11.77/2.92 % (3707732)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2426030527:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 11.77/2.92 % (3707728)------------------------------
% 11.77/2.92 % (3707728)------------------------------
% 11.77/2.92 % (3707730)------------------------------
% 11.77/2.92 % (3707730)------------------------------
% 11.77/2.92 % (3707735)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=1715660174:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/125Mi)
% 11.77/2.92 % (3707735)Refutation not found, incomplete strategy
% 11.77/2.92 % (3707735)------------------------------
% 11.77/2.92 % (3707735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707735)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707735)Termination reason: Refutation not found, incomplete strategy
% 11.77/2.92 % (3707735)Time elapsed: 0.001 s
% 11.77/2.92 % (3707735)Peak memory usage: 87 MB
% 11.77/2.92 % (3707735)Instructions burned: 1 (million)
% 11.77/2.92 % (3707715)First to succeed.
% 11.77/2.92 % (3707715)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3707686"
% 11.77/2.92 % (3707736)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3380331514:i=134:gtgl=5:slsql=off:gtg=exists_sym_2983 on theBenchmark for (2983ds/134Mi)
% 11.77/2.92 % (3707736)Instruction limit reached!
% 11.77/2.92 % (3707736)------------------------------
% 11.77/2.92 % (3707736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.77/2.92 % (3707736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.77/2.92 % (3707736)CaDiCaL version: 2.1.3
% 11.77/2.92 % (3707736)Termination reason: Instruction limit
% 11.77/2.92 % (3707736)Termination phase: Saturation
% 11.77/2.92 % (3707736)Time elapsed: 0.093 s
% 11.77/2.92 % (3707736)Peak memory usage: 90 MB
% 11.77/2.92 % (3707736)Instructions burned: 134 (million)
% 11.77/2.92 % (3707735)------------------------------
% 11.77/2.92 % (3707735)------------------------------
% 11.77/2.92 [W927 15:59:24.702511993 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702560980 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702602310 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702615630 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702642523 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702654967 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702688413 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702752687 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702787190 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702798557 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702823763 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 [W927 15:59:24.702834920 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.
% 11.77/2.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.77/2.92 % (3707715)Refutation found. Thanks to Tanya!
% 11.77/2.92 % SZS status Theorem for theBenchmark
% 11.77/2.92 % SZS output start Proof for theBenchmark
% See solution above
% 15.06/3.06 % (3707715)------------------------------
% 15.06/3.06 % (3707715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.06/3.06 % (3707715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.06/3.06 % (3707715)CaDiCaL version: 2.1.3
% 15.06/3.06 % (3707715)Termination reason: Refutation
% 15.06/3.06 % (3707715)Time elapsed: 0.935 s
% 15.06/3.06 % (3707715)Peak memory usage: 133 MB
% 15.06/3.06 % (3707715)Instructions burned: 1361 (million)
% 15.06/3.06 % (3707715)------------------------------
% 15.06/3.06 % (3707715)------------------------------
% 15.06/3.06 % (3707686)Success in time 2.06 s
% 15.06/3.06 % Vampire exiting
%------------------------------------------------------------------------------