%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 11:58:54 AM UTC 2026
% Result : Theorem 2.93s 1.00s
% Output : Refutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 132 ( 62 unt; 0 def)
% Number of atoms : 222 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 155 ( 65 ~; 55 |; 2 &)
% ( 12 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 146 ( 145 !; 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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',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/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(f56,axiom,
( axiom_4
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_4) ).
fof(f71,axiom,
( axiom_m9
<=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m9) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_4) ).
fof(f83,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(f90,negated_conjecture,
~ axiom_m9,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ axiom_m9,
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
=> axiom_m9 ),
inference(unused_predicate_definition_removal,[],[f71]) ).
fof(f94,plain,
( axiom_4
=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f95,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f97,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f98,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f104,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f105,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f108,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f109,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f110,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f111,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f112,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f117,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f111]) ).
fof(f120,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f110]) ).
fof(f121,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f109]) ).
fof(f122,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f108]) ).
fof(f125,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f105]) ).
fof(f126,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f132,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f98]) ).
fof(f134,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f136,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f97]) ).
fof(f138,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f95]) ).
fof(f139,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(ennf_transformation,[],[f94]) ).
fof(f141,plain,
( axiom_m9
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(ennf_transformation,[],[f92]) ).
fof(f142,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f143,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f145,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f141]) ).
fof(f146,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f147,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f119]) ).
fof(f148,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f120]) ).
fof(f149,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f121]) ).
fof(f150,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f122]) ).
fof(f153,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f154,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f126]) ).
fof(f160,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f132]) ).
fof(f162,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f134]) ).
fof(f165,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f167,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f168,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f169,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f170,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f173,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f174,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f180,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f181,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f182,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f136]) ).
fof(f184,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f138]) ).
fof(f185,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[],[f139]) ).
fof(f187,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(cnf_transformation,[],[f145]) ).
fof(f188,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f142]) ).
fof(f189,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f143]) ).
fof(f192,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f194,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f195,plain,
axiom_4,
inference(cnf_transformation,[],[f81]) ).
fof(f197,plain,
op_possibly,
inference(cnf_transformation,[],[f83]) ).
fof(f199,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f202,plain,
~ axiom_m9,
inference(cnf_transformation,[],[f91]) ).
fof(f204,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f189,f199]) ).
fof(f205,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(forward_subsumption_resolution,[],[f188,f197]) ).
fof(f206,plain,
~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))),
inference(forward_subsumption_resolution,[],[f187,f202]) ).
fof(f208,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(forward_subsumption_resolution,[],[f185,f195]) ).
fof(f209,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f184,f194]) ).
fof(f211,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f182,f192]) ).
fof(f213,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f162,f165]) ).
fof(f215,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[],[f160,f180]) ).
fof(f221,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_subsumption_resolution,[],[f154,f174]) ).
fof(f222,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[],[f153,f173]) ).
fof(f225,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f150,f170]) ).
fof(f226,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f149,f169]) ).
fof(f227,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(forward_subsumption_resolution,[],[f148,f168]) ).
fof(f228,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f147,f181]) ).
fof(f229,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f146,f167]) ).
fof(f230,plain,
~ is_a_theorem(necessarily(implies(possibly(possibly(sK0)),possibly(sK0)))),
inference(forward_demodulation,[],[f206,f204]) ).
fof(f233,plain,
~ is_a_theorem(necessarily(implies(possibly(not(necessarily(not(sK0)))),not(necessarily(not(sK0)))))),
inference(forward_demodulation,[],[f230,f205]) ).
fof(f234,plain,
~ is_a_theorem(necessarily(implies(not(necessarily(not(not(necessarily(not(sK0)))))),not(necessarily(not(sK0)))))),
inference(forward_demodulation,[],[f233,f205]) ).
fof(f235,plain,
~ is_a_theorem(implies(not(necessarily(not(not(necessarily(not(sK0)))))),not(necessarily(not(sK0))))),
inference(resolution,[],[f211,f234]) ).
fof(f256,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f225,f229]) ).
fof(f257,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f227,f229]) ).
fof(f278,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f215,f229]) ).
fof(f289,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f256,f226]) ).
fof(f290,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f256,f221]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(not(X2),implies(X0,X1)))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f257,f213]) ).
fof(f315,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f278,f229]) ).
fof(f700,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f315,f290]) ).
fof(f734,plain,
! [X0] :
( ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))
| is_a_theorem(equiv(necessarily(necessarily(X0)),necessarily(X0))) ),
inference(resolution,[],[f315,f208]) ).
fof(f739,plain,
! [X0] : is_a_theorem(equiv(necessarily(necessarily(X0)),necessarily(X0))),
inference(forward_subsumption_resolution,[],[f734,f209]) ).
fof(f750,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f700,f222]) ).
fof(f757,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f750,f228]) ).
fof(f819,plain,
! [X0] : necessarily(X0) = necessarily(necessarily(X0)),
inference(resolution,[],[f739,f228]) ).
fof(f1025,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(not(X1))),X1)),
inference(resolution,[],[f302,f226]) ).
fof(f1450,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f1025,f757]) ).
fof(f1478,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f1450,f257]) ).
fof(f1505,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f1478,f315]) ).
fof(f1514,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f1505,f1450]) ).
fof(f1617,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f1514,f228]) ).
fof(f1643,plain,
~ is_a_theorem(implies(not(necessarily(necessarily(not(sK0)))),not(necessarily(not(sK0))))),
inference(superposition,[],[f235,f1617]) ).
fof(f1719,plain,
~ is_a_theorem(implies(not(necessarily(not(sK0))),not(necessarily(not(sK0))))),
inference(forward_demodulation,[],[f1643,f819]) ).
fof(f1723,plain,
$false,
inference(forward_subsumption_resolution,[],[f1719,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 16:00:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.93/1.00 % (1416636)Will run a generic schedule for satisfiability detection.
% 2.93/1.00 % (1416643)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3608222681:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.93/1.00 % (1416641)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1753179251_2999 on theBenchmark for (2999ds/0Mi)
% 2.93/1.00 % (1416644)dis+10_1_sil=32000:sp=arity:random_seed=3475030455:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.93/1.00 % (1416647)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3357870028:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.93/1.00 % (1416645)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=931114411:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.93/1.00 % (1416646)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=484354037:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.93/1.00 % TRYING [1]
% 2.93/1.00 % TRYING [2]
% 2.93/1.00 % (1416642)% WARNING: option uhcvi not known.
% 2.93/1.00 % TRYING [3]
% 2.93/1.00 % (1416642)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2247588807:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.93/1.00 % TRYING [4]
% 2.93/1.00 % (1416644)Instruction limit reached!
% 2.93/1.00 % (1416644)------------------------------
% 2.93/1.00 % (1416644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416644)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416644)Termination reason: Instruction limit
% 2.93/1.00 % (1416644)Termination phase: Saturation
% 2.93/1.00 % (1416644)Time elapsed: 0.070 s
% 2.93/1.00 % (1416644)Peak memory usage: 13 MB
% 2.93/1.00 % (1416644)Instructions burned: 104 (million)
% 2.93/1.00 % (1416645)Instruction limit reached!
% 2.93/1.00 % (1416645)------------------------------
% 2.93/1.00 % (1416645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416645)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416645)Termination reason: Instruction limit
% 2.93/1.00 % (1416645)Termination phase: Saturation
% 2.93/1.00 % (1416645)Time elapsed: 0.076 s
% 2.93/1.00 % (1416645)Peak memory usage: 13 MB
% 2.93/1.00 % (1416645)Instructions burned: 116 (million)
% 2.93/1.00 % (1416646)Instruction limit reached!
% 2.93/1.00 % (1416646)------------------------------
% 2.93/1.00 % (1416646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416646)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416646)Termination reason: Instruction limit
% 2.93/1.00 % (1416646)Termination phase: Saturation
% 2.93/1.00 % (1416646)Time elapsed: 0.088 s
% 2.93/1.00 % (1416646)Peak memory usage: 14 MB
% 2.93/1.00 % (1416646)Instructions burned: 132 (million)
% 2.93/1.00 % (1416655)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=643862023:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 2.93/1.00 % TRYING [1]
% 2.93/1.00 % TRYING [2]
% 2.93/1.00 % TRYING [3]
% 2.93/1.00 % (1416656)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2006574162:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.93/1.00 % (1416657)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1030661566:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.93/1.00 % TRYING [4]
% 2.93/1.00 % (1416647)Instruction limit reached!
% 2.93/1.00 % (1416647)------------------------------
% 2.93/1.00 % (1416647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416647)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416647)Termination reason: Instruction limit
% 2.93/1.00 % (1416647)Termination phase: Saturation
% 2.93/1.00 % (1416647)Time elapsed: 0.111 s
% 2.93/1.00 % (1416647)Peak memory usage: 14 MB
% 2.93/1.00 % (1416647)Instructions burned: 160 (million)
% 2.93/1.00 % TRYING [5]
% 2.93/1.00 % (1416661)ott-21_1_sil=16000:fs=off:random_seed=2408032915:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.93/1.00 % (1416656)Instruction limit reached!
% 2.93/1.00 % (1416656)------------------------------
% 2.93/1.00 % (1416656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416656)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416656)Termination reason: Instruction limit
% 2.93/1.00 % (1416656)Termination phase: Saturation
% 2.93/1.00 % (1416656)Time elapsed: 0.088 s
% 2.93/1.00 % (1416656)Peak memory usage: 14 MB
% 2.93/1.00 % (1416656)Instructions burned: 131 (million)
% 2.93/1.00 % (1416663)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1480756885:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.93/1.00 % (1416661)Instruction limit reached!
% 2.93/1.00 % (1416661)------------------------------
% 2.93/1.00 % (1416661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416661)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416661)Termination reason: Instruction limit
% 2.93/1.00 % (1416661)Termination phase: Saturation
% 2.93/1.00 % (1416661)Time elapsed: 0.097 s
% 2.93/1.00 % (1416661)Peak memory usage: 13 MB
% 2.93/1.00 % (1416661)Instructions burned: 181 (million)
% 2.93/1.00 % TRYING [5]
% 2.93/1.00 % (1416665)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1348647234:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.93/1.00 % TRYING [1]
% 2.93/1.00 % TRYING [2]
% 2.93/1.00 % TRYING [3]
% 2.93/1.00 % TRYING [4]
% 2.93/1.00 % (1416655)Instruction limit reached!
% 2.93/1.00 % (1416655)------------------------------
% 2.93/1.00 % (1416655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416655)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416655)Termination reason: Instruction limit
% 2.93/1.00 % (1416655)Termination phase: Finite model building SAT solving
% 2.93/1.00 % (1416655)Time elapsed: 0.391 s
% 2.93/1.00 % (1416655)Peak memory usage: 23 MB
% 2.93/1.00 % (1416655)Instructions burned: 714 (million)
% 2.93/1.00 % (1416667)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2843972898:i=1179_2994 on theBenchmark for (2994ds/1179Mi)
% 2.93/1.00 % TRYING [6]
% 2.93/1.00 % (1416657)Instruction limit reached!
% 2.93/1.00 % (1416657)------------------------------
% 2.93/1.00 % (1416657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416657)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416657)Termination reason: Instruction limit
% 2.93/1.00 % (1416657)Termination phase: Saturation
% 2.93/1.00 % (1416657)Time elapsed: 0.408 s
% 2.93/1.00 % (1416657)Peak memory usage: 20 MB
% 2.93/1.00 % (1416657)Instructions burned: 685 (million)
% 2.93/1.00 % (1416663)Instruction limit reached!
% 2.93/1.00 % (1416663)------------------------------
% 2.93/1.00 % (1416663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.00 % (1416663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.00 % (1416663)CaDiCaL version: 2.1.3
% 2.93/1.00 % (1416663)Termination reason: Instruction limit
% 2.93/1.00 % (1416663)Termination phase: Saturation
% 2.93/1.00 % (1416663)Time elapsed: 0.317 s
% 2.93/1.00 % (1416663)Peak memory usage: 14 MB
% 2.93/1.00 % (1416663)Instructions burned: 478 (million)
% 2.93/1.00 % (1416669)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1578305316:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 2.93/1.00 % (1416670)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1368639029:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 2.93/1.00 % (1416667) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1416636-1416667"...
% 2.93/1.00 % (1416667)...printing done.
% 2.93/1.00 % (1416667)Refutation found. Thanks to Tanya!
% 2.93/1.00 % SZS status Theorem for theBenchmark
% 2.93/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 2.93/1.01 % (1416667)------------------------------
% 2.93/1.01 % (1416667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/1.01 % (1416667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.01 % (1416667)CaDiCaL version: 2.1.3
% 2.93/1.01 % (1416667)Termination reason: Refutation
% 2.93/1.01 % (1416667)Time elapsed: 0.049 s
% 2.93/1.01 % (1416667)Peak memory usage: 12 MB
% 2.93/1.01 % (1416667)Instructions burned: 72 (million)
% 2.93/1.01 % (1416636)Success in time 0.593 s
% 2.93/1.01 % Vampire exiting
%------------------------------------------------------------------------------