TSTP Solution File: LCL531+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:43:20 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 54
% Syntax : Number of formulae : 182 ( 84 unt; 0 def)
% Number of atoms : 299 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 190 ( 73 ~; 66 |; 2 &)
% ( 18 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 29 ( 27 usr; 27 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 210 ( 208 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f633,plain,
$false,
inference(resolution,[],[f609,f259]) ).
fof(f259,plain,
~ is_a_theorem(implies(sK0,and(sK0,sK0))),
inference(resolution,[],[f240,f219]) ).
fof(f219,plain,
~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193]) ).
fof(f193,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f135,f156]) ).
fof(f156,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0)))
=> ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( axiom_m4
| ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
=> axiom_m4 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f66,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
fof(f218,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192]) ).
fof(f192,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f217,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191]) ).
fof(f191,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f216,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190]) ).
fof(f190,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_possibly) ).
fof(f215,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189]) ).
fof(f189,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f214,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188]) ).
fof(f188,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f213,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187]) ).
fof(f187,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f186,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f185,plain,
op_possibly,
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_op_possibly) ).
fof(f184,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f183,plain,
op_equiv,
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f182,plain,
op_possibly,
inference(cnf_transformation,[],[f82]) ).
fof(f82,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f181,plain,
op_or,
inference(cnf_transformation,[],[f83]) ).
fof(f83,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f180,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f179,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f87]) ).
fof(f87,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f178,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f177,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f176,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f175,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f174,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f173,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f172,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f171,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f170,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f169,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f168,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f167,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f166,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f165,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f164,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f163,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f162,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f161,plain,
axiom_K,
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
axiom_K,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_K) ).
fof(f160,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f159,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f158,plain,
~ axiom_m4,
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
~ axiom_m4,
inference(flattening,[],[f89]) ).
fof(f89,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[],[f88]) ).
fof(f88,conjecture,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f240,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f222,f213]) ).
fof(f222,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196]) ).
fof(f196,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
fof(f221,plain,
! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195]) ).
fof(f195,plain,
! [X0] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f220,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194]) ).
fof(f194,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f107]) ).
fof(f107,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
fof(f609,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f365,f228]) ).
fof(f228,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202]) ).
fof(f202,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f227,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201]) ).
fof(f201,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f226,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200]) ).
fof(f200,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f225,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199]) ).
fof(f199,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
fof(f224,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198]) ).
fof(f198,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f223,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197]) ).
fof(f197,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f365,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f232,f236]) ).
fof(f236,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203,f229,f204,f230,f205,f231,f206,f232,f207,f233,f208,f234,f209,f235,f210]) ).
fof(f210,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f235,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203,f229,f204,f230,f205,f231,f206,f232,f207,f233,f208,f234,f209]) ).
fof(f209,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f234,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203,f229,f204,f230,f205,f231,f206,f232,f207,f233,f208]) ).
fof(f208,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,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(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/theBenchmark.p',equivalence_3) ).
fof(f233,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203,f229,f204,f230,f205,f231,f206,f232,f207]) ).
fof(f207,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,plain,
( axiom_K
=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f54,axiom,
( axiom_K
<=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_K) ).
fof(f206,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f231,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203,f229,f204,f230,f205]) ).
fof(f205,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f230,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203,f229,f204]) ).
fof(f204,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
fof(f229,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203]) ).
fof(f203,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,plain,
( equivalence_1
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
fof(f232,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption,[],[f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f213,f188,f214,f189,f215,f190,f216,f191,f217,f192,f218,f193,f219,f194,f220,f195,f221,f196,f222,f197,f223,f198,f224,f199,f225,f200,f226,f201,f227,f202,f228,f203,f229,f204,f230,f205,f231,f206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 22:43:48 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (23696)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (23699)WARNING: value z3 for option sas not known
% 0.15/0.38 % (23697)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (23698)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (23700)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (23701)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (23702)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (23703)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 % (23699)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (23699)First to succeed.
% 0.15/0.40 % (23702)Also succeeded, but the first one will report.
% 0.15/0.40 % (23699)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (23699)------------------------------
% 0.15/0.40 % (23699)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (23699)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (23699)Memory used [KB]: 1165
% 0.15/0.40 % (23699)Time elapsed: 0.022 s
% 0.15/0.40 % (23699)Instructions burned: 31 (million)
% 0.15/0.40 % (23699)------------------------------
% 0.15/0.40 % (23699)------------------------------
% 0.15/0.40 % (23696)Success in time 0.04 s
%------------------------------------------------------------------------------