TSTP Solution File: LCL535+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL535+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 : n018.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 13:43:36 EDT 2024

% Result   : Theorem 3.67s 0.88s
% Output   : Refutation 3.67s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)

% Comments : 
%------------------------------------------------------------------------------
fof(f13758,plain,
    $false,
    inference(subsumption_resolution,[],[f13675,f643]) ).

fof(f643,plain,
    ! [X0] : is_a_theorem(equiv(X0,X0)),
    inference(subsumption_resolution,[],[f641,f607]) ).

fof(f607,plain,
    ! [X0] : is_a_theorem(implies(X0,X0)),
    inference(resolution,[],[f367,f225]) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',or_2) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_M) ).

fof(f219,plain,
    ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(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_m9
    | ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f157,plain,
    ( axiom_m9
    | ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f135,f156]) ).

fof(f156,plain,
    ( ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
   => ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( axiom_m9
    | ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
    inference(ennf_transformation,[],[f105]) ).

fof(f105,plain,
    ( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
   => axiom_m9 ),
    inference(unused_predicate_definition_removal,[],[f71]) ).

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(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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).

fof(f186,plain,
    op_equiv,
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).

fof(f185,plain,
    op_possibly,
    inference(cnf_transformation,[],[f77]) ).

fof(f77,axiom,
    op_possibly,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_op_possibly) ).

fof(f184,plain,
    op_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).

fof(f183,plain,
    op_equiv,
    inference(cnf_transformation,[],[f86]) ).

fof(f86,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_equiv) ).

fof(f182,plain,
    op_possibly,
    inference(cnf_transformation,[],[f82]) ).

fof(f82,axiom,
    op_possibly,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_possibly) ).

fof(f181,plain,
    op_or,
    inference(cnf_transformation,[],[f83]) ).

fof(f83,axiom,
    op_or,
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

fof(f177,plain,
    or_2,
    inference(cnf_transformation,[],[f44]) ).

fof(f44,axiom,
    or_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).

fof(f176,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).

fof(f175,plain,
    modus_tollens,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    modus_tollens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).

fof(f174,plain,
    implies_1,
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    implies_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).

fof(f173,plain,
    implies_2,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    implies_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).

fof(f172,plain,
    implies_3,
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    implies_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).

fof(f171,plain,
    and_1,
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    and_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).

fof(f170,plain,
    and_2,
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    and_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).

fof(f169,plain,
    and_3,
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    and_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).

fof(f168,plain,
    or_1,
    inference(cnf_transformation,[],[f43]) ).

fof(f43,axiom,
    or_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).

fof(f167,plain,
    or_3,
    inference(cnf_transformation,[],[f45]) ).

fof(f45,axiom,
    or_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).

fof(f166,plain,
    equivalence_1,
    inference(cnf_transformation,[],[f46]) ).

fof(f46,axiom,
    equivalence_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).

fof(f165,plain,
    equivalence_2,
    inference(cnf_transformation,[],[f47]) ).

fof(f47,axiom,
    equivalence_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).

fof(f164,plain,
    equivalence_3,
    inference(cnf_transformation,[],[f48]) ).

fof(f48,axiom,
    equivalence_3,
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f162,plain,
    necessitation,
    inference(cnf_transformation,[],[f78]) ).

fof(f78,axiom,
    necessitation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).

fof(f161,plain,
    axiom_K,
    inference(cnf_transformation,[],[f79]) ).

fof(f79,axiom,
    axiom_K,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_K) ).

fof(f160,plain,
    axiom_M,
    inference(cnf_transformation,[],[f80]) ).

fof(f80,axiom,
    axiom_M,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).

fof(f159,plain,
    axiom_5,
    inference(cnf_transformation,[],[f81]) ).

fof(f81,axiom,
    axiom_5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).

fof(f158,plain,
    ~ axiom_m9,
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ~ axiom_m9,
    inference(flattening,[],[f89]) ).

fof(f89,negated_conjecture,
    ~ axiom_m9,
    inference(negated_conjecture,[],[f88]) ).

fof(f88,conjecture,
    axiom_m9,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).

fof(f367,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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',equivalence_1) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',and_2) ).

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]) ).

fof(f641,plain,
    ! [X0] :
      ( is_a_theorem(equiv(X0,X0))
      | ~ is_a_theorem(implies(X0,X0)) ),
    inference(superposition,[],[f631,f218]) ).

fof(f631,plain,
    ! [X0] :
      ( is_a_theorem(and(X0,X0))
      | ~ is_a_theorem(X0) ),
    inference(resolution,[],[f608,f236]) ).

fof(f608,plain,
    ! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
    inference(resolution,[],[f367,f228]) ).

fof(f13675,plain,
    ~ is_a_theorem(equiv(possibly(sK0),possibly(sK0))),
    inference(superposition,[],[f1068,f13515]) ).

fof(f13515,plain,
    ! [X0] : possibly(X0) = possibly(possibly(X0)),
    inference(superposition,[],[f13356,f5594]) ).

fof(f5594,plain,
    ! [X0] : possibly(X0) = necessarily(possibly(X0)),
    inference(subsumption_resolution,[],[f5579,f220]) ).

fof(f5579,plain,
    ! [X0] :
      ( ~ is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))
      | possibly(X0) = necessarily(possibly(X0)) ),
    inference(resolution,[],[f5467,f221]) ).

fof(f5467,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(X1,X0))
      | ~ is_a_theorem(implies(X0,X1))
      | X0 = X1 ),
    inference(resolution,[],[f1393,f235]) ).

fof(f1393,plain,
    ! [X0,X1] :
      ( is_a_theorem(equiv(X0,X1))
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(implies(X1,X0)) ),
    inference(resolution,[],[f530,f236]) ).

fof(f530,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
      | ~ is_a_theorem(implies(X1,X0)) ),
    inference(resolution,[],[f234,f236]) ).

fof(f13356,plain,
    ! [X0] : necessarily(X0) = possibly(necessarily(X0)),
    inference(superposition,[],[f11842,f7156]) ).

fof(f7156,plain,
    ! [X0] : necessarily(X0) = strict_implies(not(X0),X0),
    inference(superposition,[],[f280,f7115]) ).

fof(f7115,plain,
    ! [X0] : or(X0,X0) = X0,
    inference(subsumption_resolution,[],[f7104,f223]) ).

fof(f7104,plain,
    ! [X0] :
      ( ~ is_a_theorem(implies(X0,or(X0,X0)))
      | or(X0,X0) = X0 ),
    inference(resolution,[],[f7069,f5467]) ).

fof(f7069,plain,
    ! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
    inference(resolution,[],[f7027,f253]) ).

fof(f253,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(strict_implies(X0,X1))
      | is_a_theorem(implies(X0,X1)) ),
    inference(superposition,[],[f250,f213]) ).

fof(f250,plain,
    ! [X0] :
      ( ~ is_a_theorem(necessarily(X0))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f236,f220]) ).

fof(f7027,plain,
    ! [X0] : is_a_theorem(strict_implies(or(X0,X0),X0)),
    inference(superposition,[],[f6902,f5657]) ).

fof(f5657,plain,
    ! [X0] : or(X0,X0) = not(not(X0)),
    inference(superposition,[],[f217,f5586]) ).

fof(f5586,plain,
    ! [X0] : and(X0,X0) = X0,
    inference(subsumption_resolution,[],[f5530,f226]) ).

fof(f5530,plain,
    ! [X0] :
      ( ~ is_a_theorem(implies(and(X0,X0),X0))
      | and(X0,X0) = X0 ),
    inference(resolution,[],[f5467,f608]) ).

fof(f6902,plain,
    ! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
    inference(resolution,[],[f6039,f1337]) ).

fof(f1337,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(or(X1,not(X0)))
      | is_a_theorem(strict_implies(X0,X1)) ),
    inference(resolution,[],[f877,f313]) ).

fof(f313,plain,
    ! [X0,X1] :
      ( is_a_theorem(strict_implies(not(X0),X1))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(superposition,[],[f222,f280]) ).

fof(f877,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
      | is_a_theorem(strict_implies(X1,X0)) ),
    inference(forward_demodulation,[],[f876,f213]) ).

fof(f876,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
      | is_a_theorem(necessarily(implies(X1,X0))) ),
    inference(forward_demodulation,[],[f840,f280]) ).

fof(f840,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(necessarily(or(X0,not(X1))))
      | is_a_theorem(necessarily(implies(X1,X0))) ),
    inference(resolution,[],[f787,f323]) ).

fof(f323,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
    inference(forward_demodulation,[],[f231,f270]) ).

fof(f270,plain,
    ! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
    inference(superposition,[],[f217,f214]) ).

fof(f787,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(X1,X0))
      | ~ is_a_theorem(necessarily(X1))
      | is_a_theorem(necessarily(X0)) ),
    inference(resolution,[],[f694,f240]) ).

fof(f240,plain,
    ! [X0,X1] :
      ( is_a_theorem(strict_implies(X0,X1))
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(superposition,[],[f222,f213]) ).

fof(f694,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(strict_implies(X0,X1))
      | is_a_theorem(necessarily(X1))
      | ~ is_a_theorem(necessarily(X0)) ),
    inference(resolution,[],[f505,f236]) ).

fof(f505,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
      | ~ is_a_theorem(strict_implies(X0,X1)) ),
    inference(resolution,[],[f502,f236]) ).

fof(f502,plain,
    ! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))),
    inference(forward_demodulation,[],[f233,f213]) ).

fof(f6039,plain,
    ! [X0] : is_a_theorem(or(X0,not(not(not(X0))))),
    inference(superposition,[],[f291,f5657]) ).

fof(f291,plain,
    ! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0)))),
    inference(superposition,[],[f223,f270]) ).

fof(f280,plain,
    ! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X0),X1),
    inference(superposition,[],[f213,f270]) ).

fof(f11842,plain,
    ! [X0,X1] : strict_implies(not(X0),X1) = possibly(strict_implies(not(X0),X1)),
    inference(forward_demodulation,[],[f11841,f7130]) ).

fof(f7130,plain,
    ! [X0] : not(not(X0)) = X0,
    inference(superposition,[],[f7115,f5657]) ).

fof(f11841,plain,
    ! [X0,X1] : not(not(strict_implies(not(X0),X1))) = possibly(strict_implies(not(X0),X1)),
    inference(forward_demodulation,[],[f11840,f258]) ).

fof(f258,plain,
    ! [X0,X1] : possibly(and(X0,not(X1))) = not(strict_implies(X0,X1)),
    inference(forward_demodulation,[],[f257,f213]) ).

fof(f257,plain,
    ! [X0,X1] : possibly(and(X0,not(X1))) = not(necessarily(implies(X0,X1))),
    inference(superposition,[],[f216,f214]) ).

fof(f11840,plain,
    ! [X0,X1] : not(possibly(and(not(X0),not(X1)))) = possibly(strict_implies(not(X0),X1)),
    inference(forward_demodulation,[],[f11839,f5594]) ).

fof(f11839,plain,
    ! [X0,X1] : not(necessarily(possibly(and(not(X0),not(X1))))) = possibly(strict_implies(not(X0),X1)),
    inference(forward_demodulation,[],[f307,f280]) ).

fof(f307,plain,
    ! [X0,X1] : not(necessarily(possibly(and(not(X0),not(X1))))) = possibly(necessarily(or(X0,X1))),
    inference(superposition,[],[f239,f217]) ).

fof(f239,plain,
    ! [X0] : possibly(necessarily(not(X0))) = not(necessarily(possibly(X0))),
    inference(superposition,[],[f216,f216]) ).

fof(f1068,plain,
    ~ is_a_theorem(equiv(possibly(possibly(sK0)),possibly(sK0))),
    inference(resolution,[],[f959,f219]) ).

fof(f959,plain,
    ! [X0,X1] :
      ( is_a_theorem(strict_implies(X0,X1))
      | ~ is_a_theorem(equiv(X0,X1)) ),
    inference(forward_demodulation,[],[f958,f213]) ).

fof(f958,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equiv(X0,X1))
      | is_a_theorem(necessarily(implies(X0,X1))) ),
    inference(superposition,[],[f950,f218]) ).

fof(f950,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(and(X0,X1))
      | is_a_theorem(necessarily(X0)) ),
    inference(resolution,[],[f839,f222]) ).

fof(f839,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(necessarily(and(X0,X1)))
      | is_a_theorem(necessarily(X0)) ),
    inference(resolution,[],[f787,f227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : LCL535+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Apr 29 23:15:28 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (21526)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (21529)WARNING: value z3 for option sas not known
% 0.21/0.38  % (21528)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (21532)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)
% 0.21/0.38  % (21533)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)
% 0.21/0.38  % (21530)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (21529)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)
% 0.21/0.38  % (21531)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)
% 0.21/0.38  % (21527)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.39  TRYING [3]
% 0.21/0.39  TRYING [1]
% 0.21/0.39  TRYING [2]
% 0.21/0.41  TRYING [4]
% 0.21/0.41  TRYING [3]
% 0.21/0.45  TRYING [1]
% 0.21/0.45  TRYING [2]
% 0.21/0.46  TRYING [3]
% 0.21/0.48  TRYING [4]
% 0.21/0.48  TRYING [4]
% 0.21/0.50  TRYING [5]
% 1.58/0.58  TRYING [5]
% 3.31/0.84  TRYING [5]
% 3.31/0.87  % (21529)First to succeed.
% 3.67/0.88  % (21529)Refutation found. Thanks to Tanya!
% 3.67/0.88  % SZS status Theorem for theBenchmark
% 3.67/0.88  % SZS output start Proof for theBenchmark
% See solution above
% 3.67/0.88  % (21529)------------------------------
% 3.67/0.88  % (21529)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 3.67/0.88  % (21529)Termination reason: Refutation
% 3.67/0.88  
% 3.67/0.88  % (21529)Memory used [KB]: 5866
% 3.67/0.88  % (21529)Time elapsed: 0.496 s
% 3.67/0.88  % (21529)Instructions burned: 959 (million)
% 3.67/0.88  % (21529)------------------------------
% 3.67/0.88  % (21529)------------------------------
% 3.67/0.88  % (21526)Success in time 0.515 s
%------------------------------------------------------------------------------