TSTP Solution File: LCL524+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : LCL524+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n021.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  : 600s
% DateTime : Sun Jul 17 10:11:41 EDT 2022

% Result   : Theorem 0.73s 65.91s
% Output   : CNFRefutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  126 (  59 unt;   0 def)
%            Number of atoms       :  237 (  28 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  192 (  81   ~;  77   |;  16   &)
%                                         (  12 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   19 (  17 usr;  17 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  21 con; 0-2 aty)
%            Number of variables   :  152 (   6 sgn  56   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
    ( modus_ponens
  <=> ! [X1,X2] :
        ( ( is_a_theorem(X1)
          & is_a_theorem(implies(X1,X2)) )
       => is_a_theorem(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).

fof(implies_3,axiom,
    ( implies_3
  <=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).

fof(and_3,axiom,
    ( and_3
  <=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).

fof(hilbert_modus_ponens,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).

fof(hilbert_implies_3,axiom,
    implies_3,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).

fof(op_implies_and,axiom,
    ( op_implies_and
   => ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).

fof(hilbert_and_3,axiom,
    and_3,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).

fof(axiom_M,axiom,
    ( axiom_M
  <=> ! [X1] : is_a_theorem(implies(necessarily(X1),X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_M) ).

fof(op_or,axiom,
    ( op_or
   => ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).

fof(hilbert_op_implies_and,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).

fof(op_possibly,axiom,
    ( op_possibly
   => ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_possibly) ).

fof(op_equiv,axiom,
    ( op_equiv
   => ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).

fof(km5_axiom_M,axiom,
    axiom_M,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).

fof(cn3,axiom,
    ( cn3
  <=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).

fof(hilbert_op_or,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).

fof(km5_op_possibly,axiom,
    op_possibly,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_op_possibly) ).

fof(implies_2,axiom,
    ( implies_2
  <=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).

fof(substitution_of_equivalents,axiom,
    ( substitution_of_equivalents
  <=> ! [X1,X2] :
        ( is_a_theorem(equiv(X1,X2))
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).

fof(hilbert_op_equiv,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).

fof(modus_tollens,axiom,
    ( modus_tollens
  <=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).

fof(hilbert_implies_2,axiom,
    implies_2,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).

fof(km4b_axiom_B,conjecture,
    axiom_B,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',km4b_axiom_B) ).

fof(substitution_of_equivalents_001,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).

fof(axiom_5,axiom,
    ( axiom_5
  <=> ! [X1] : is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_5) ).

fof(and_1,axiom,
    ( and_1
  <=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).

fof(hilbert_modus_tollens,axiom,
    modus_tollens,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).

fof(axiom_B,axiom,
    ( axiom_B
  <=> ! [X1] : is_a_theorem(implies(X1,necessarily(possibly(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_B) ).

fof(km5_axiom_5,axiom,
    axiom_5,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).

fof(hilbert_and_1,axiom,
    and_1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).

fof(or_1,axiom,
    ( or_1
  <=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).

fof(hilbert_or_1,axiom,
    or_1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).

fof(c_0_31,plain,
    ! [X3,X4] :
      ( ( ~ modus_ponens
        | ~ is_a_theorem(X3)
        | ~ is_a_theorem(implies(X3,X4))
        | is_a_theorem(X4) )
      & ( is_a_theorem(esk1_0)
        | modus_ponens )
      & ( is_a_theorem(implies(esk1_0,esk2_0))
        | modus_ponens )
      & ( ~ is_a_theorem(esk2_0)
        | modus_ponens ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])])]) ).

fof(c_0_32,plain,
    ! [X4,X5,X6] :
      ( ( ~ implies_3
        | is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6)))) )
      & ( ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))
        | implies_3 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])])])]) ).

fof(c_0_33,plain,
    ! [X3,X4] :
      ( ( ~ and_3
        | is_a_theorem(implies(X3,implies(X4,and(X3,X4)))) )
      & ( ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))
        | and_3 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])])]) ).

cnf(c_0_34,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(X2)
    | ~ modus_ponens ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_35,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).

cnf(c_0_36,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
    | ~ implies_3 ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_37,plain,
    implies_3,
    inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).

fof(c_0_38,plain,
    ! [X3,X4] :
      ( ~ op_implies_and
      | implies(X3,X4) = not(and(X3,not(X4))) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])])]) ).

cnf(c_0_39,plain,
    ( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
    | ~ and_3 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_40,plain,
    and_3,
    inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).

cnf(c_0_41,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

cnf(c_0_42,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).

fof(c_0_43,plain,
    ! [X2] :
      ( ( ~ axiom_M
        | is_a_theorem(implies(necessarily(X2),X2)) )
      & ( ~ is_a_theorem(implies(necessarily(esk65_0),esk65_0))
        | axiom_M ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])])]) ).

fof(c_0_44,plain,
    ! [X3,X4] :
      ( ~ op_or
      | or(X3,X4) = not(and(not(X3),not(X4))) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])])]) ).

cnf(c_0_45,plain,
    ( implies(X1,X2) = not(and(X1,not(X2)))
    | ~ op_implies_and ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_46,plain,
    op_implies_and,
    inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).

fof(c_0_47,plain,
    ! [X2] :
      ( ~ op_possibly
      | possibly(X2) = not(necessarily(not(X2))) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])])]) ).

cnf(c_0_48,plain,
    is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).

fof(c_0_49,plain,
    ! [X3,X4] :
      ( ~ op_equiv
      | equiv(X3,X4) = and(implies(X3,X4),implies(X4,X3)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])])]) ).

cnf(c_0_50,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
    | ~ is_a_theorem(implies(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_51,plain,
    ( is_a_theorem(implies(necessarily(X1),X1))
    | ~ axiom_M ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_52,plain,
    axiom_M,
    inference(split_conjunct,[status(thm)],[km5_axiom_M]) ).

fof(c_0_53,plain,
    ! [X5] :
      ( ( ~ cn3
        | is_a_theorem(implies(implies(not(X5),X5),X5)) )
      & ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
        | cn3 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])])])]) ).

cnf(c_0_54,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_55,plain,
    not(and(X1,not(X2))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).

cnf(c_0_56,plain,
    op_or,
    inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).

cnf(c_0_57,plain,
    ( possibly(X1) = not(necessarily(not(X1)))
    | ~ op_possibly ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_58,plain,
    op_possibly,
    inference(split_conjunct,[status(thm)],[km5_op_possibly]) ).

fof(c_0_59,plain,
    ! [X3,X4] :
      ( ( ~ implies_2
        | is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4))) )
      & ( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
        | implies_2 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])])]) ).

fof(c_0_60,plain,
    ! [X3,X4] :
      ( ( ~ substitution_of_equivalents
        | ~ is_a_theorem(equiv(X3,X4))
        | X3 = X4 )
      & ( is_a_theorem(equiv(esk3_0,esk4_0))
        | substitution_of_equivalents )
      & ( esk3_0 != esk4_0
        | substitution_of_equivalents ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])])]) ).

cnf(c_0_61,plain,
    ( is_a_theorem(implies(X1,and(X2,X1)))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_41,c_0_48]) ).

cnf(c_0_62,plain,
    ( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
    | ~ op_equiv ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_63,plain,
    op_equiv,
    inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).

fof(c_0_64,plain,
    ! [X3,X4] :
      ( ( ~ modus_tollens
        | is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4))) )
      & ( ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))
        | modus_tollens ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])])]) ).

cnf(c_0_65,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X3,X2))
    | ~ is_a_theorem(implies(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_50]) ).

cnf(c_0_66,plain,
    is_a_theorem(implies(necessarily(X1),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).

cnf(c_0_67,plain,
    ( is_a_theorem(implies(implies(not(X1),X1),X1))
    | ~ cn3 ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_68,plain,
    implies(not(X1),X2) = or(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).

cnf(c_0_69,plain,
    not(necessarily(not(X1))) = possibly(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).

cnf(c_0_70,plain,
    ( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
    | ~ implies_2 ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_71,plain,
    implies_2,
    inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).

fof(c_0_72,negated_conjecture,
    ~ axiom_B,
    inference(assume_negation,[status(cth)],[km4b_axiom_B]) ).

cnf(c_0_73,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2))
    | ~ substitution_of_equivalents ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_74,plain,
    substitution_of_equivalents,
    inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).

cnf(c_0_75,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_41,c_0_61]) ).

cnf(c_0_76,plain,
    and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).

fof(c_0_77,plain,
    ! [X2] :
      ( ( ~ axiom_5
        | is_a_theorem(implies(possibly(X2),necessarily(possibly(X2)))) )
      & ( ~ is_a_theorem(implies(possibly(esk68_0),necessarily(possibly(esk68_0))))
        | axiom_5 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])])])]) ).

fof(c_0_78,plain,
    ! [X3,X4] :
      ( ( ~ and_1
        | is_a_theorem(implies(and(X3,X4),X3)) )
      & ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
        | and_1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])])]) ).

cnf(c_0_79,plain,
    ( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
    | ~ modus_tollens ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_80,plain,
    modus_tollens,
    inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).

cnf(c_0_81,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,necessarily(X2))) ),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_82,plain,
    ( is_a_theorem(implies(or(X1,X1),X1))
    | ~ cn3 ),
    inference(rw,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_83,plain,
    not(and(X1,possibly(X2))) = implies(X1,necessarily(not(X2))),
    inference(spm,[status(thm)],[c_0_55,c_0_69]) ).

cnf(c_0_84,plain,
    is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).

fof(c_0_85,plain,
    ! [X2] :
      ( ( ~ axiom_B
        | is_a_theorem(implies(X2,necessarily(possibly(X2)))) )
      & ( ~ is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0))))
        | axiom_B ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_B])])])])])]) ).

fof(c_0_86,negated_conjecture,
    ~ axiom_B,
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

cnf(c_0_87,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).

cnf(c_0_88,plain,
    ( is_a_theorem(equiv(X1,X2))
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_89,plain,
    ( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
    | ~ axiom_5 ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_90,plain,
    axiom_5,
    inference(split_conjunct,[status(thm)],[km5_axiom_5]) ).

cnf(c_0_91,plain,
    ( is_a_theorem(implies(and(X1,X2),X1))
    | ~ and_1 ),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_92,plain,
    and_1,
    inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).

cnf(c_0_93,plain,
    is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_68]),c_0_80])]) ).

cnf(c_0_94,plain,
    ( is_a_theorem(implies(or(necessarily(X1),necessarily(X1)),X1))
    | ~ cn3 ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_95,plain,
    or(necessarily(not(X1)),X2) = implies(possibly(X1),X2),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_96,plain,
    implies(implies(X1,necessarily(not(X2))),X3) = or(and(X1,possibly(X2)),X3),
    inference(spm,[status(thm)],[c_0_68,c_0_83]) ).

fof(c_0_97,plain,
    ! [X3,X4] :
      ( ( ~ or_1
        | is_a_theorem(implies(X3,or(X3,X4))) )
      & ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
        | or_1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])])])]) ).

cnf(c_0_98,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
    inference(spm,[status(thm)],[c_0_41,c_0_84]) ).

cnf(c_0_99,plain,
    ( axiom_B
    | ~ is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0)))) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_100,negated_conjecture,
    ~ axiom_B,
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_101,plain,
    ( X1 = X2
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_102,plain,
    is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).

cnf(c_0_103,plain,
    is_a_theorem(implies(and(X1,X2),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).

cnf(c_0_104,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(or(X2,not(X1))) ),
    inference(spm,[status(thm)],[c_0_41,c_0_93]) ).

cnf(c_0_105,plain,
    ( is_a_theorem(or(and(possibly(X1),possibly(X1)),not(X1)))
    | ~ cn3 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).

cnf(c_0_106,plain,
    ( is_a_theorem(implies(X1,or(X1,X2)))
    | ~ or_1 ),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_107,plain,
    or_1,
    inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).

cnf(c_0_108,plain,
    is_a_theorem(implies(X1,and(X1,X1))),
    inference(spm,[status(thm)],[c_0_98,c_0_48]) ).

cnf(c_0_109,plain,
    ~ is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0)))),
    inference(sr,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_110,plain,
    necessarily(possibly(X1)) = possibly(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_66])]) ).

cnf(c_0_111,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,and(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_65,c_0_103]) ).

cnf(c_0_112,plain,
    ( is_a_theorem(implies(X1,and(possibly(X1),possibly(X1))))
    | ~ cn3 ),
    inference(spm,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_113,plain,
    is_a_theorem(implies(X1,or(X1,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).

cnf(c_0_114,plain,
    and(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_108]),c_0_103])]) ).

cnf(c_0_115,plain,
    ( cn3
    | ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_116,plain,
    ~ is_a_theorem(implies(esk67_0,possibly(esk67_0))),
    inference(rw,[status(thm)],[c_0_109,c_0_110]) ).

cnf(c_0_117,plain,
    ( is_a_theorem(implies(X1,possibly(X1)))
    | ~ cn3 ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_118,plain,
    is_a_theorem(or(X1,or(not(X1),X2))),
    inference(spm,[status(thm)],[c_0_113,c_0_68]) ).

cnf(c_0_119,plain,
    or(X1,X1) = not(not(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_114]),c_0_68]) ).

cnf(c_0_120,plain,
    ( cn3
    | ~ is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)) ),
    inference(rw,[status(thm)],[c_0_115,c_0_68]) ).

cnf(c_0_121,plain,
    ~ cn3,
    inference(spm,[status(thm)],[c_0_116,c_0_117]) ).

cnf(c_0_122,plain,
    is_a_theorem(or(X1,not(not(not(X1))))),
    inference(spm,[status(thm)],[c_0_118,c_0_119]) ).

cnf(c_0_123,plain,
    ~ is_a_theorem(or(not(esk44_0),esk44_0)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_119]),c_0_68]),c_0_121]) ).

cnf(c_0_124,plain,
    is_a_theorem(or(not(X1),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_122]),c_0_68]) ).

cnf(c_0_125,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LCL524+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command  : run_ET %s %d
% 0.14/0.35  % Computer : n021.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  : 600
% 0.14/0.35  % DateTime : Sun Jul  3 03:43:15 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.42/23.43  eprover: CPU time limit exceeded, terminating
% 0.42/23.43  eprover: CPU time limit exceeded, terminating
% 0.42/23.44  eprover: CPU time limit exceeded, terminating
% 0.42/23.49  eprover: CPU time limit exceeded, terminating
% 0.58/46.46  eprover: CPU time limit exceeded, terminating
% 0.58/46.46  eprover: CPU time limit exceeded, terminating
% 0.58/46.47  eprover: CPU time limit exceeded, terminating
% 0.58/46.52  eprover: CPU time limit exceeded, terminating
% 0.73/65.91  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.73/65.91  
% 0.73/65.91  # Failure: Resource limit exceeded (time)
% 0.73/65.91  # OLD status Res
% 0.73/65.91  # Preprocessing time       : 0.013 s
% 0.73/65.91  # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.73/65.91  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.73/65.91  # Preprocessing time       : 0.016 s
% 0.73/65.91  
% 0.73/65.91  # Failure: Out of unprocessed clauses!
% 0.73/65.91  # OLD status GaveUp
% 0.73/65.91  # Parsed axioms                        : 82
% 0.73/65.91  # Removed by relevancy pruning/SinE    : 80
% 0.73/65.91  # Initial clauses                      : 3
% 0.73/65.91  # Removed in clause preprocessing      : 0
% 0.73/65.91  # Initial clauses in saturation        : 3
% 0.73/65.91  # Processed clauses                    : 3
% 0.73/65.91  # ...of these trivial                  : 0
% 0.73/65.91  # ...subsumed                          : 1
% 0.73/65.91  # ...remaining for further processing  : 2
% 0.73/65.91  # Other redundant clauses eliminated   : 0
% 0.73/65.91  # Clauses deleted for lack of memory   : 0
% 0.73/65.91  # Backward-subsumed                    : 0
% 0.73/65.91  # Backward-rewritten                   : 0
% 0.73/65.91  # Generated clauses                    : 0
% 0.73/65.91  # ...of the previous two non-trivial   : 0
% 0.73/65.91  # Contextual simplify-reflections      : 0
% 0.73/65.91  # Paramodulations                      : 0
% 0.73/65.91  # Factorizations                       : 0
% 0.73/65.91  # Equation resolutions                 : 0
% 0.73/65.91  # Current number of processed clauses  : 2
% 0.73/65.91  #    Positive orientable unit clauses  : 0
% 0.73/65.91  #    Positive unorientable unit clauses: 0
% 0.73/65.91  #    Negative unit clauses             : 2
% 0.73/65.91  #    Non-unit-clauses                  : 0
% 0.73/65.91  # Current number of unprocessed clauses: 0
% 0.73/65.91  # ...number of literals in the above   : 0
% 0.73/65.91  # Current number of archived formulas  : 0
% 0.73/65.91  # Current number of archived clauses   : 0
% 0.73/65.91  # Clause-clause subsumption calls (NU) : 0
% 0.73/65.91  # Rec. Clause-clause subsumption calls : 0
% 0.73/65.91  # Non-unit clause-clause subsumptions  : 0
% 0.73/65.91  # Unit Clause-clause subsumption calls : 0
% 0.73/65.91  # Rewrite failures with RHS unbound    : 0
% 0.73/65.91  # BW rewrite match attempts            : 0
% 0.73/65.91  # BW rewrite match successes           : 0
% 0.73/65.91  # Condensation attempts                : 0
% 0.73/65.91  # Condensation successes               : 0
% 0.73/65.91  # Termbank termtop insertions          : 784
% 0.73/65.91  
% 0.73/65.91  # -------------------------------------------------
% 0.73/65.91  # User time                : 0.013 s
% 0.73/65.91  # System time              : 0.003 s
% 0.73/65.91  # Total time               : 0.016 s
% 0.73/65.91  # Maximum resident set size: 2896 pages
% 0.73/65.91  # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 0.73/65.91  
% 0.73/65.91  # Failure: Resource limit exceeded (time)
% 0.73/65.91  # OLD status Res
% 0.73/65.91  # Preprocessing time       : 0.023 s
% 0.73/65.91  # Running protocol protocol_eprover_f8b0f932169414d689b89e2a8b18d4600533b975 for 23 seconds:
% 0.73/65.91  # Preprocessing time       : 0.012 s
% 0.73/65.91  
% 0.73/65.91  # Proof found!
% 0.73/65.91  # SZS status Theorem
% 0.73/65.91  # SZS output start CNFRefutation
% See solution above
% 0.73/65.91  # Proof object total steps             : 126
% 0.73/65.91  # Proof object clause steps            : 77
% 0.73/65.91  # Proof object formula steps           : 49
% 0.73/65.91  # Proof object conjectures             : 4
% 0.73/65.91  # Proof object clause conjectures      : 1
% 0.73/65.91  # Proof object formula conjectures     : 3
% 0.73/65.91  # Proof object initial clauses used    : 32
% 0.73/65.91  # Proof object initial formulas used   : 31
% 0.73/65.91  # Proof object generating inferences   : 25
% 0.73/65.91  # Proof object simplifying inferences  : 46
% 0.73/65.91  # Training examples: 0 positive, 0 negative
% 0.73/65.91  # Parsed axioms                        : 82
% 0.73/65.91  # Removed by relevancy pruning/SinE    : 0
% 0.73/65.91  # Initial clauses                      : 140
% 0.73/65.91  # Removed in clause preprocessing      : 0
% 0.73/65.91  # Initial clauses in saturation        : 140
% 0.73/65.91  # Processed clauses                    : 21222
% 0.73/65.91  # ...of these trivial                  : 115
% 0.73/65.91  # ...subsumed                          : 15927
% 0.73/65.91  # ...remaining for further processing  : 5180
% 0.73/65.91  # Other redundant clauses eliminated   : 0
% 0.73/65.91  # Clauses deleted for lack of memory   : 1066037
% 0.73/65.91  # Backward-subsumed                    : 990
% 0.73/65.91  # Backward-rewritten                   : 744
% 0.73/65.91  # Generated clauses                    : 1264382
% 0.73/65.91  # ...of the previous two non-trivial   : 1254094
% 0.73/65.91  # Contextual simplify-reflections      : 19117
% 0.73/65.91  # Paramodulations                      : 1264382
% 0.73/65.91  # Factorizations                       : 0
% 0.73/65.91  # Equation resolutions                 : 0
% 0.73/65.91  # Current number of processed clauses  : 3446
% 0.73/65.91  #    Positive orientable unit clauses  : 242
% 0.73/65.91  #    Positive unorientable unit clauses: 0
% 0.73/65.91  #    Negative unit clauses             : 27
% 0.73/65.91  #    Non-unit-clauses                  : 3177
% 0.73/65.91  # Current number of unprocessed clauses: 86414
% 0.73/65.91  # ...number of literals in the above   : 294984
% 0.73/65.91  # Current number of archived formulas  : 0
% 0.73/65.91  # Current number of archived clauses   : 1734
% 0.73/65.91  # Clause-clause subsumption calls (NU) : 2257546
% 0.73/65.91  # Rec. Clause-clause subsumption calls : 1244477
% 0.73/65.91  # Non-unit clause-clause subsumptions  : 35827
% 0.73/65.91  # Unit Clause-clause subsumption calls : 36169
% 0.73/65.91  # Rewrite failures with RHS unbound    : 0
% 0.73/65.91  # BW rewrite match attempts            : 8912
% 0.73/65.91  # BW rewrite match successes           : 180
% 0.73/65.91  # Condensation attempts                : 0
% 0.73/65.91  # Condensation successes               : 0
% 0.73/65.91  # Termbank termtop insertions          : 23694006
% 0.73/65.91  
% 0.73/65.91  # -------------------------------------------------
% 0.73/65.91  # User time                : 18.292 s
% 0.73/65.91  # System time              : 0.147 s
% 0.73/65.91  # Total time               : 18.439 s
% 0.73/65.91  # Maximum resident set size: 143116 pages
% 0.73/69.48  eprover: CPU time limit exceeded, terminating
% 0.73/69.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.50  eprover: No such file or directory
% 0.73/69.51  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.51  eprover: No such file or directory
% 0.73/69.51  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.51  eprover: No such file or directory
% 0.73/69.52  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.52  eprover: No such file or directory
% 0.73/69.53  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.53  eprover: No such file or directory
% 0.73/69.53  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.53  eprover: No such file or directory
% 0.73/69.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.54  eprover: No such file or directory
% 0.73/69.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.54  eprover: No such file or directory
% 0.73/69.56  eprover: CPU time limit exceeded, terminating
% 0.73/69.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.58  eprover: No such file or directory
% 0.73/69.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.59  eprover: No such file or directory
% 0.73/69.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.59  eprover: No such file or directory
% 0.73/69.59  eprover: CPU time limit exceeded, terminating
% 0.73/69.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.60  eprover: No such file or directory
% 0.73/69.61  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.73/69.61  eprover: No such file or directory
% 0.73/69.61  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.73/69.61  eprover: No such file or directory
% 0.73/69.62  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.73/69.62  eprover: No such file or directory
%------------------------------------------------------------------------------