TSTP Solution File: LCL528+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : LCL528+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 : Mon Jun 24 11:05:47 EDT 2024

% Result   : Theorem 202.12s 27.43s
% Output   : CNFRefutation 202.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  223 ( 130 unt;   0 def)
%            Number of atoms       :  343 (  72 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  212 (  92   ~;  85   |;   2   &)
%                                         (  11 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   18 (  16 usr;  16 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :  322 (  13 sgn 102   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
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(f2,axiom,
    ( substitution_of_equivalents
  <=> ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f3,axiom,
    ( modus_tollens
  <=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).

fof(f4,axiom,
    ( implies_1
  <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).

fof(f5,axiom,
    ( implies_2
  <=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).

fof(f7,axiom,
    ( and_1
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).

fof(f8,axiom,
    ( and_2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).

fof(f9,axiom,
    ( and_3
  <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).

fof(f27,axiom,
    ( op_or
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).

fof(f31,axiom,
    ( op_equiv
   => ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).

fof(f33,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

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

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

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

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

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

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

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

fof(f49,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f50,axiom,
    ( necessitation
  <=> ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).

fof(f55,axiom,
    ( axiom_M
  <=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).

fof(f63,axiom,
    ( axiom_m1
  <=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m1) ).

fof(f75,axiom,
    ( op_strict_implies
   => ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).

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

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

fof(f83,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_or) ).

fof(f85,axiom,
    op_strict_implies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).

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

fof(f88,conjecture,
    axiom_m1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).

fof(f89,negated_conjecture,
    ~ axiom_m1,
    inference(negated_conjecture,[],[f88]) ).

fof(f104,plain,
    ~ axiom_m1,
    inference(flattening,[],[f89]) ).

fof(f105,plain,
    ( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
   => axiom_m1 ),
    inference(unused_predicate_definition_removal,[],[f63]) ).

fof(f107,plain,
    ( axiom_M
   => ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
    inference(unused_predicate_definition_removal,[],[f55]) ).

fof(f109,plain,
    ( necessitation
   => ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    inference(unused_predicate_definition_removal,[],[f50]) ).

fof(f116,plain,
    ( and_3
   => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    inference(unused_predicate_definition_removal,[],[f9]) ).

fof(f117,plain,
    ( and_2
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
    inference(unused_predicate_definition_removal,[],[f8]) ).

fof(f118,plain,
    ( and_1
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f7]) ).

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(f121,plain,
    ( implies_1
   => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

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(f123,plain,
    ( substitution_of_equivalents
   => ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

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(f129,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f124]) ).

fof(f130,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f129]) ).

fof(f131,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ is_a_theorem(equiv(X0,X1)) )
    | ~ substitution_of_equivalents ),
    inference(ennf_transformation,[],[f123]) ).

fof(f132,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
    | ~ modus_tollens ),
    inference(ennf_transformation,[],[f122]) ).

fof(f133,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
    | ~ implies_1 ),
    inference(ennf_transformation,[],[f121]) ).

fof(f134,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
    | ~ implies_2 ),
    inference(ennf_transformation,[],[f120]) ).

fof(f136,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
    | ~ and_1 ),
    inference(ennf_transformation,[],[f118]) ).

fof(f137,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
    | ~ and_2 ),
    inference(ennf_transformation,[],[f117]) ).

fof(f138,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
    | ~ and_3 ),
    inference(ennf_transformation,[],[f116]) ).

fof(f145,plain,
    ( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
    | ~ op_or ),
    inference(ennf_transformation,[],[f27]) ).

fof(f146,plain,
    ( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
    | ~ op_implies_and ),
    inference(ennf_transformation,[],[f29]) ).

fof(f147,plain,
    ( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
    | ~ op_equiv ),
    inference(ennf_transformation,[],[f31]) ).

fof(f148,plain,
    ( ! [X0] :
        ( is_a_theorem(necessarily(X0))
        | ~ is_a_theorem(X0) )
    | ~ necessitation ),
    inference(ennf_transformation,[],[f109]) ).

fof(f150,plain,
    ( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
    | ~ axiom_M ),
    inference(ennf_transformation,[],[f107]) ).

fof(f152,plain,
    ( axiom_m1
    | ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
    inference(ennf_transformation,[],[f105]) ).

fof(f154,plain,
    ( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
    | ~ op_strict_implies ),
    inference(ennf_transformation,[],[f75]) ).

fof(f156,plain,
    ( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
   => ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ( axiom_m1
    | ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f152,f156]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f130]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ is_a_theorem(equiv(X0,X1))
      | ~ substitution_of_equivalents ),
    inference(cnf_transformation,[],[f131]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
      | ~ modus_tollens ),
    inference(cnf_transformation,[],[f132]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,implies(X1,X0)))
      | ~ implies_1 ),
    inference(cnf_transformation,[],[f133]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
      | ~ implies_2 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ and_1 ),
    inference(cnf_transformation,[],[f136]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X1))
      | ~ and_2 ),
    inference(cnf_transformation,[],[f137]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
      | ~ and_3 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f145]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f146]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f147]) ).

fof(f177,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f179,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f180,plain,
    modus_tollens,
    inference(cnf_transformation,[],[f36]) ).

fof(f181,plain,
    implies_1,
    inference(cnf_transformation,[],[f37]) ).

fof(f182,plain,
    implies_2,
    inference(cnf_transformation,[],[f38]) ).

fof(f184,plain,
    and_1,
    inference(cnf_transformation,[],[f40]) ).

fof(f185,plain,
    and_2,
    inference(cnf_transformation,[],[f41]) ).

fof(f186,plain,
    and_3,
    inference(cnf_transformation,[],[f42]) ).

fof(f193,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f49]) ).

fof(f194,plain,
    ! [X0] :
      ( is_a_theorem(necessarily(X0))
      | ~ is_a_theorem(X0)
      | ~ necessitation ),
    inference(cnf_transformation,[],[f148]) ).

fof(f196,plain,
    ! [X0] :
      ( is_a_theorem(implies(necessarily(X0),X0))
      | ~ axiom_M ),
    inference(cnf_transformation,[],[f150]) ).

fof(f198,plain,
    ( axiom_m1
    | ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f200,plain,
    ! [X0,X1] :
      ( strict_implies(X0,X1) = necessarily(implies(X0,X1))
      | ~ op_strict_implies ),
    inference(cnf_transformation,[],[f154]) ).

fof(f203,plain,
    necessitation,
    inference(cnf_transformation,[],[f78]) ).

fof(f205,plain,
    axiom_M,
    inference(cnf_transformation,[],[f80]) ).

fof(f208,plain,
    op_or,
    inference(cnf_transformation,[],[f83]) ).

fof(f209,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f85]) ).

fof(f210,plain,
    op_equiv,
    inference(cnf_transformation,[],[f86]) ).

fof(f212,plain,
    ~ axiom_m1,
    inference(cnf_transformation,[],[f104]) ).

cnf(c_49,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | ~ modus_ponens
    | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_50,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | ~ substitution_of_equivalents
    | X0 = X1 ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_51,plain,
    ( ~ modus_tollens
    | is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_52,plain,
    ( ~ implies_1
    | is_a_theorem(implies(X0,implies(X1,X0))) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_53,plain,
    ( ~ implies_2
    | is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_55,plain,
    ( ~ and_1
    | is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_56,plain,
    ( ~ and_2
    | is_a_theorem(implies(and(X0,X1),X1)) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_57,plain,
    ( ~ and_3
    | is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_64,plain,
    ( ~ op_or
    | not(and(not(X0),not(X1))) = or(X0,X1) ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_65,plain,
    ( ~ op_implies_and
    | not(and(X0,not(X1))) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_66,plain,
    ( ~ op_equiv
    | and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_68,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f177]) ).

cnf(c_70,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f179]) ).

cnf(c_71,plain,
    modus_tollens,
    inference(cnf_transformation,[],[f180]) ).

cnf(c_72,plain,
    implies_1,
    inference(cnf_transformation,[],[f181]) ).

cnf(c_73,plain,
    implies_2,
    inference(cnf_transformation,[],[f182]) ).

cnf(c_75,plain,
    and_1,
    inference(cnf_transformation,[],[f184]) ).

cnf(c_76,plain,
    and_2,
    inference(cnf_transformation,[],[f185]) ).

cnf(c_77,plain,
    and_3,
    inference(cnf_transformation,[],[f186]) ).

cnf(c_84,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f193]) ).

cnf(c_85,plain,
    ( ~ is_a_theorem(X0)
    | ~ necessitation
    | is_a_theorem(necessarily(X0)) ),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_87,plain,
    ( ~ axiom_M
    | is_a_theorem(implies(necessarily(X0),X0)) ),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_89,plain,
    ( ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0)))
    | axiom_m1 ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_91,plain,
    ( ~ op_strict_implies
    | necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_94,plain,
    necessitation,
    inference(cnf_transformation,[],[f203]) ).

cnf(c_96,plain,
    axiom_M,
    inference(cnf_transformation,[],[f205]) ).

cnf(c_99,plain,
    op_or,
    inference(cnf_transformation,[],[f208]) ).

cnf(c_100,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f209]) ).

cnf(c_101,plain,
    op_equiv,
    inference(cnf_transformation,[],[f210]) ).

cnf(c_103,negated_conjecture,
    ~ axiom_m1,
    inference(cnf_transformation,[],[f212]) ).

cnf(c_128,plain,
    is_a_theorem(implies(necessarily(X0),X0)),
    inference(global_subsumption_just,[status(thm)],[c_87,c_96,c_87]) ).

cnf(c_131,plain,
    ( ~ is_a_theorem(X0)
    | is_a_theorem(necessarily(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_85,c_94,c_85]) ).

cnf(c_139,plain,
    is_a_theorem(implies(and(X0,X1),X1)),
    inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).

cnf(c_142,plain,
    is_a_theorem(implies(and(X0,X1),X0)),
    inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).

cnf(c_144,plain,
    is_a_theorem(implies(X0,implies(X1,X0))),
    inference(global_subsumption_just,[status(thm)],[c_52,c_72,c_52]) ).

cnf(c_153,plain,
    ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
    inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).

cnf(c_160,plain,
    is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
    inference(global_subsumption_just,[status(thm)],[c_57,c_77,c_57]) ).

cnf(c_163,plain,
    necessarily(implies(X0,X1)) = strict_implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_91,c_100,c_91]) ).

cnf(c_166,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).

cnf(c_169,plain,
    not(and(X0,not(X1))) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_65,c_68,c_65]) ).

cnf(c_172,plain,
    is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
    inference(global_subsumption_just,[status(thm)],[c_53,c_73,c_53]) ).

cnf(c_175,plain,
    is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
    inference(global_subsumption_just,[status(thm)],[c_51,c_71,c_51]) ).

cnf(c_178,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_70,c_49]) ).

cnf(c_179,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_178]) ).

cnf(c_183,plain,
    not(and(not(X0),not(X1))) = or(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_64,c_99,c_64]) ).

cnf(c_189,plain,
    and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_66,c_101,c_66]) ).

cnf(c_313,plain,
    implies(not(X0),X1) = or(X0,X1),
    inference(demodulation,[status(thm)],[c_183,c_169]) ).

cnf(c_314,plain,
    is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
    inference(demodulation,[status(thm)],[c_175,c_313]) ).

cnf(c_6059,plain,
    or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
    inference(superposition,[status(thm)],[c_169,c_313]) ).

cnf(c_6819,plain,
    is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X2,and(X0,not(X1))))),
    inference(superposition,[status(thm)],[c_6059,c_314]) ).

cnf(c_56873,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(strict_implies(X0,X1)) ),
    inference(superposition,[status(thm)],[c_163,c_131]) ).

cnf(c_56879,plain,
    is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))),
    inference(superposition,[status(thm)],[c_313,c_314]) ).

cnf(c_56900,plain,
    or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
    inference(superposition,[status(thm)],[c_169,c_313]) ).

cnf(c_56902,plain,
    implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))),
    inference(superposition,[status(thm)],[c_169,c_169]) ).

cnf(c_56925,plain,
    is_a_theorem(strict_implies(and(X0,X1),X1)),
    inference(superposition,[status(thm)],[c_139,c_56873]) ).

cnf(c_57082,plain,
    ( ~ is_a_theorem(X0)
    | is_a_theorem(implies(X1,and(X0,X1))) ),
    inference(superposition,[status(thm)],[c_160,c_179]) ).

cnf(c_57091,plain,
    ( ~ is_a_theorem(or(X0,not(X1)))
    | is_a_theorem(implies(X1,X0)) ),
    inference(superposition,[status(thm)],[c_314,c_179]) ).

cnf(c_57198,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(X1)
    | is_a_theorem(and(X0,X1)) ),
    inference(superposition,[status(thm)],[c_57082,c_179]) ).

cnf(c_57401,plain,
    implies(implies(X0,X1),and(X1,not(X0))) = not(equiv(X0,X1)),
    inference(superposition,[status(thm)],[c_189,c_56902]) ).

cnf(c_57403,plain,
    implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))),
    inference(superposition,[status(thm)],[c_313,c_56902]) ).

cnf(c_57586,plain,
    is_a_theorem(implies(implies(or(X0,X1),not(X2)),implies(X2,and(not(X0),not(X1))))),
    inference(superposition,[status(thm)],[c_313,c_6819]) ).

cnf(c_57598,plain,
    is_a_theorem(implies(implies(or(X0,X1),not(X2)),not(and(X2,or(X0,X1))))),
    inference(demodulation,[status(thm)],[c_57586,c_57403]) ).

cnf(c_57956,plain,
    is_a_theorem(implies(and(X0,not(X1)),not(equiv(X1,X0)))),
    inference(superposition,[status(thm)],[c_57401,c_144]) ).

cnf(c_58041,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(implies(X1,X0))
    | is_a_theorem(equiv(X0,X1)) ),
    inference(superposition,[status(thm)],[c_189,c_57198]) ).

cnf(c_58714,plain,
    ( ~ is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X0,X1))))
    | is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))) ),
    inference(superposition,[status(thm)],[c_172,c_58041]) ).

cnf(c_58744,plain,
    ( ~ is_a_theorem(implies(and(X0,X1),X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(equiv(and(X0,X1),X1)) ),
    inference(superposition,[status(thm)],[c_57082,c_58041]) ).

cnf(c_58780,plain,
    ( ~ is_a_theorem(X0)
    | is_a_theorem(equiv(and(X0,X1),X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_58744,c_139]) ).

cnf(c_58784,plain,
    is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_58714,c_144]) ).

cnf(c_58884,plain,
    ( ~ is_a_theorem(X0)
    | and(X0,X1) = X1 ),
    inference(superposition,[status(thm)],[c_58780,c_166]) ).

cnf(c_59237,plain,
    and(implies(necessarily(X0),X0),X1) = X1,
    inference(superposition,[status(thm)],[c_128,c_58884]) ).

cnf(c_59860,plain,
    is_a_theorem(strict_implies(X0,X0)),
    inference(superposition,[status(thm)],[c_59237,c_56925]) ).

cnf(c_59864,plain,
    is_a_theorem(implies(X0,X0)),
    inference(superposition,[status(thm)],[c_59237,c_139]) ).

cnf(c_59942,plain,
    and(strict_implies(X0,X0),X1) = X1,
    inference(superposition,[status(thm)],[c_59860,c_58884]) ).

cnf(c_59945,plain,
    and(implies(X0,X0),X1) = X1,
    inference(superposition,[status(thm)],[c_59864,c_58884]) ).

cnf(c_60341,plain,
    is_a_theorem(implies(X0,strict_implies(X1,X1))),
    inference(superposition,[status(thm)],[c_59942,c_142]) ).

cnf(c_60353,plain,
    is_a_theorem(implies(not(X0),not(equiv(X0,strict_implies(X1,X1))))),
    inference(superposition,[status(thm)],[c_59942,c_57956]) ).

cnf(c_60364,plain,
    implies(strict_implies(X0,X0),X1) = not(not(X1)),
    inference(superposition,[status(thm)],[c_59942,c_169]) ).

cnf(c_60412,plain,
    is_a_theorem(or(X0,not(equiv(X0,strict_implies(X1,X1))))),
    inference(demodulation,[status(thm)],[c_60353,c_313]) ).

cnf(c_60657,plain,
    and(implies(X0,strict_implies(X1,X1)),X2) = X2,
    inference(superposition,[status(thm)],[c_60341,c_58884]) ).

cnf(c_60688,plain,
    is_a_theorem(implies(X0,implies(X1,X1))),
    inference(superposition,[status(thm)],[c_59945,c_142]) ).

cnf(c_60712,plain,
    implies(implies(X0,X0),X1) = not(not(X1)),
    inference(superposition,[status(thm)],[c_59945,c_169]) ).

cnf(c_60790,plain,
    and(implies(X0,implies(X1,X1)),X2) = X2,
    inference(superposition,[status(thm)],[c_60688,c_58884]) ).

cnf(c_64136,plain,
    is_a_theorem(implies(equiv(X0,strict_implies(X1,X1)),X0)),
    inference(superposition,[status(thm)],[c_60412,c_57091]) ).

cnf(c_68025,plain,
    implies(X0,implies(X0,X1)) = implies(X0,X1),
    inference(superposition,[status(thm)],[c_58784,c_166]) ).

cnf(c_131492,plain,
    and(implies(X0,strict_implies(X1,X1)),not(not(X0))) = equiv(X0,strict_implies(X1,X1)),
    inference(superposition,[status(thm)],[c_60364,c_189]) ).

cnf(c_131496,plain,
    is_a_theorem(implies(X0,not(not(X0)))),
    inference(superposition,[status(thm)],[c_60364,c_144]) ).

cnf(c_132020,plain,
    equiv(X0,strict_implies(X1,X1)) = not(not(X0)),
    inference(demodulation,[status(thm)],[c_131492,c_60657]) ).

cnf(c_132168,plain,
    is_a_theorem(implies(not(not(X0)),X0)),
    inference(demodulation,[status(thm)],[c_64136,c_132020]) ).

cnf(c_132170,plain,
    is_a_theorem(or(not(X0),X0)),
    inference(demodulation,[status(thm)],[c_132168,c_313]) ).

cnf(c_133751,plain,
    ( ~ is_a_theorem(implies(not(not(X0)),X0))
    | is_a_theorem(equiv(not(not(X0)),X0)) ),
    inference(superposition,[status(thm)],[c_131496,c_58041]) ).

cnf(c_133755,plain,
    ( ~ is_a_theorem(or(not(X0),X0))
    | is_a_theorem(equiv(not(not(X0)),X0)) ),
    inference(demodulation,[status(thm)],[c_133751,c_313]) ).

cnf(c_133756,plain,
    is_a_theorem(equiv(not(not(X0)),X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_133755,c_132170]) ).

cnf(c_136410,plain,
    not(not(X0)) = X0,
    inference(superposition,[status(thm)],[c_133756,c_166]) ).

cnf(c_136444,plain,
    is_a_theorem(implies(or(X0,X1),or(X1,X0))),
    inference(demodulation,[status(thm)],[c_56879,c_136410]) ).

cnf(c_136471,plain,
    not(implies(X0,X1)) = and(X0,not(X1)),
    inference(superposition,[status(thm)],[c_169,c_136410]) ).

cnf(c_136580,plain,
    or(not(X0),X1) = implies(X0,X1),
    inference(superposition,[status(thm)],[c_136410,c_313]) ).

cnf(c_136694,plain,
    implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
    inference(superposition,[status(thm)],[c_136410,c_56900]) ).

cnf(c_136713,plain,
    implies(X0,not(X1)) = not(and(X0,X1)),
    inference(superposition,[status(thm)],[c_136410,c_169]) ).

cnf(c_136998,plain,
    implies(X0,not(implies(not(X1),X2))) = not(and(X0,or(X1,X2))),
    inference(demodulation,[status(thm)],[c_57403,c_136471]) ).

cnf(c_137012,plain,
    implies(X0,not(or(X1,X2))) = not(and(X0,or(X1,X2))),
    inference(demodulation,[status(thm)],[c_136998,c_313]) ).

cnf(c_137015,plain,
    is_a_theorem(implies(implies(or(X0,X1),not(X2)),implies(X2,not(or(X0,X1))))),
    inference(demodulation,[status(thm)],[c_57598,c_137012]) ).

cnf(c_144949,plain,
    ( ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
    | is_a_theorem(equiv(or(X0,X1),or(X1,X0))) ),
    inference(superposition,[status(thm)],[c_136444,c_58041]) ).

cnf(c_144952,plain,
    is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
    inference(forward_subsumption_resolution,[status(thm)],[c_144949,c_136444]) ).

cnf(c_147342,plain,
    or(X0,X1) = or(X1,X0),
    inference(superposition,[status(thm)],[c_144952,c_166]) ).

cnf(c_150421,plain,
    or(X0,not(X1)) = implies(X1,X0),
    inference(superposition,[status(thm)],[c_136580,c_147342]) ).

cnf(c_151626,plain,
    implies(implies(X0,X0),X1) = X1,
    inference(demodulation,[status(thm)],[c_60712,c_136410]) ).

cnf(c_151642,plain,
    and(implies(X0,implies(X1,X1)),X0) = equiv(X0,implies(X1,X1)),
    inference(superposition,[status(thm)],[c_151626,c_189]) ).

cnf(c_151702,plain,
    is_a_theorem(implies(X0,and(X0,implies(X1,X1)))),
    inference(superposition,[status(thm)],[c_151626,c_160]) ).

cnf(c_151885,plain,
    equiv(X0,implies(X1,X1)) = X0,
    inference(demodulation,[status(thm)],[c_151642,c_60790]) ).

cnf(c_152676,plain,
    ( ~ is_a_theorem(X0)
    | implies(X1,X1) = X0 ),
    inference(superposition,[status(thm)],[c_151885,c_166]) ).

cnf(c_152856,plain,
    implies(and(X0,X1),X0) = implies(X2,X2),
    inference(superposition,[status(thm)],[c_142,c_152676]) ).

cnf(c_152944,plain,
    implies(X0,X0) = strict_implies(X1,X1),
    inference(superposition,[status(thm)],[c_59860,c_152676]) ).

cnf(c_153183,plain,
    implies(X0,X0) = sP0_iProver_def,
    inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_152944]) ).

cnf(c_153208,plain,
    implies(and(X0,X1),X0) = sP0_iProver_def,
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_152856]) ).

cnf(c_153453,plain,
    and(sP0_iProver_def,X0) = X0,
    inference(demodulation,[status(thm)],[c_59945,c_153183]) ).

cnf(c_153454,plain,
    is_a_theorem(sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_59864,c_153183]) ).

cnf(c_153455,plain,
    ( ~ is_a_theorem(X0)
    | X0 = sP0_iProver_def ),
    inference(demodulation,[status(thm)],[c_152676,c_153183]) ).

cnf(c_153462,plain,
    is_a_theorem(implies(X0,and(X0,sP0_iProver_def))),
    inference(demodulation,[status(thm)],[c_151702,c_153183]) ).

cnf(c_155468,plain,
    implies(X0,and(X0,sP0_iProver_def)) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_153462,c_153455]) ).

cnf(c_157071,plain,
    and(sP0_iProver_def,implies(and(X0,sP0_iProver_def),X0)) = equiv(X0,and(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_155468,c_189]) ).

cnf(c_157103,plain,
    equiv(X0,and(X0,sP0_iProver_def)) = sP0_iProver_def,
    inference(demodulation,[status(thm)],[c_157071,c_153208,c_153453]) ).

cnf(c_157142,plain,
    ( ~ is_a_theorem(sP0_iProver_def)
    | and(X0,sP0_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_157103,c_166]) ).

cnf(c_157157,plain,
    and(X0,sP0_iProver_def) = X0,
    inference(forward_subsumption_resolution,[status(thm)],[c_157142,c_153454]) ).

cnf(c_157176,plain,
    implies(X0,not(sP0_iProver_def)) = not(X0),
    inference(superposition,[status(thm)],[c_157157,c_136713]) ).

cnf(c_157217,plain,
    implies(X0,not(X0)) = not(X0),
    inference(superposition,[status(thm)],[c_157176,c_68025]) ).

cnf(c_157277,plain,
    implies(not(X0),X0) = X0,
    inference(superposition,[status(thm)],[c_136410,c_157217]) ).

cnf(c_157320,plain,
    or(X0,X0) = X0,
    inference(demodulation,[status(thm)],[c_157277,c_313]) ).

cnf(c_172265,plain,
    or(X0,implies(X1,not(X2))) = implies(and(X1,X2),X0),
    inference(superposition,[status(thm)],[c_136713,c_150421]) ).

cnf(c_173440,plain,
    is_a_theorem(implies(and(X0,or(X1,X2)),and(or(X1,X2),X0))),
    inference(demodulation,[status(thm)],[c_137015,c_136694,c_172265]) ).

cnf(c_173463,plain,
    is_a_theorem(implies(and(X0,X1),and(X1,X0))),
    inference(superposition,[status(thm)],[c_157320,c_173440]) ).

cnf(c_173610,plain,
    is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
    inference(superposition,[status(thm)],[c_173463,c_56873]) ).

cnf(c_173627,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_153,c_173610]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL528+1 : TPTP v8.2.0. Released v3.3.0.
% 0.12/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Jun 22 13:17:39 EDT 2024
% 0.19/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 202.12/27.43  % SZS status Started for theBenchmark.p
% 202.12/27.43  % SZS status Theorem for theBenchmark.p
% 202.12/27.43  
% 202.12/27.43  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 202.12/27.43  
% 202.12/27.43  ------  iProver source info
% 202.12/27.43  
% 202.12/27.43  git: date: 2024-06-12 09:56:46 +0000
% 202.12/27.43  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 202.12/27.43  git: non_committed_changes: false
% 202.12/27.43  
% 202.12/27.43  ------ Parsing...
% 202.12/27.43  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 202.12/27.43  
% 202.12/27.43  ------ Preprocessing... sup_sim: 3  sf_s  rm: 27 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 202.12/27.43  
% 202.12/27.43  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 202.12/27.43  
% 202.12/27.43  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 202.12/27.43  ------ Proving...
% 202.12/27.43  ------ Problem Properties 
% 202.12/27.43  
% 202.12/27.43  
% 202.12/27.43  clauses                                 26
% 202.12/27.43  conjectures                             0
% 202.12/27.43  EPR                                     0
% 202.12/27.43  Horn                                    26
% 202.12/27.43  unary                                   23
% 202.12/27.43  binary                                  2
% 202.12/27.43  lits                                    30
% 202.12/27.43  lits eq                                 7
% 202.12/27.43  fd_pure                                 0
% 202.12/27.43  fd_pseudo                               0
% 202.12/27.43  fd_cond                                 0
% 202.12/27.43  fd_pseudo_cond                          1
% 202.12/27.43  AC symbols                              0
% 202.12/27.43  
% 202.12/27.43  ------ Input Options Time Limit: Unbounded
% 202.12/27.43  
% 202.12/27.43  
% 202.12/27.43  ------ 
% 202.12/27.43  Current options:
% 202.12/27.43  ------ 
% 202.12/27.43  
% 202.12/27.43  
% 202.12/27.43  
% 202.12/27.43  
% 202.12/27.43  ------ Proving...
% 202.12/27.43  
% 202.12/27.43  
% 202.12/27.43  % SZS status Theorem for theBenchmark.p
% 202.12/27.43  
% 202.12/27.43  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 202.12/27.43  
% 202.12/27.44  
%------------------------------------------------------------------------------