TSTP Solution File: LCL528+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : LCL528+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n011.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 09:26:37 EDT 2022

% Result   : Theorem 9.74s 2.68s
% Output   : CNFRefutation 9.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  114 (  61 unt;   0 def)
%            Number of atoms       :  210 (  34 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  161 (  65   ~;  64   |;  15   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   17 (  15 usr;  15 prp; 0-2 aty)
%            Number of functors    :   26 (  26 usr;  19 con; 0-2 aty)
%            Number of variables   :  147 (   7 sgn  54   !;   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(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(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(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(hilbert_modus_ponens,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).

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

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_001,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).

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

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

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(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_1,axiom,
    and_1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).

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

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_or_1,axiom,
    or_1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).

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

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

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

fof(op_strict_implies,axiom,
    ( op_strict_implies
   => ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).

fof(axiom_m1,axiom,
    ( axiom_m1
  <=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).

fof(km5_necessitation,axiom,
    necessitation,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).

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

fof(implies_1,axiom,
    ( implies_1
  <=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).

fof(hilbert_implies_1,axiom,
    implies_1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).

fof(c_0_28,plain,
    ! [X7,X8] :
      ( ( ~ modus_ponens
        | ~ is_a_theorem(X7)
        | ~ is_a_theorem(implies(X7,X8))
        | is_a_theorem(X8) )
      & ( 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])]) ).

fof(c_0_29,plain,
    ! [X41,X42] :
      ( ( ~ and_3
        | is_a_theorem(implies(X41,implies(X42,and(X41,X42)))) )
      & ( ~ 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])]) ).

fof(c_0_30,plain,
    ! [X11,X12] :
      ( ( ~ substitution_of_equivalents
        | ~ is_a_theorem(equiv(X11,X12))
        | X11 = X12 )
      & ( 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])]) ).

fof(c_0_31,plain,
    ! [X125,X126] :
      ( ~ op_equiv
      | equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).

cnf(c_0_32,plain,
    ( is_a_theorem(X2)
    | ~ modus_ponens
    | ~ is_a_theorem(X1)
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_33,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).

cnf(c_0_34,plain,
    ( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
    | ~ and_3 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,plain,
    and_3,
    inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).

fof(c_0_36,plain,
    ! [X23,X24] :
      ( ( ~ implies_2
        | is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24))) )
      & ( ~ 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])]) ).

cnf(c_0_37,plain,
    ( X1 = X2
    | ~ substitution_of_equivalents
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_38,plain,
    substitution_of_equivalents,
    inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).

cnf(c_0_39,plain,
    ( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
    | ~ op_equiv ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_40,plain,
    op_equiv,
    inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).

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_32,c_0_33])]) ).

cnf(c_0_42,plain,
    is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

cnf(c_0_43,plain,
    ( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
    | ~ implies_2 ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_44,plain,
    implies_2,
    inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).

cnf(c_0_45,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).

cnf(c_0_46,plain,
    equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).

cnf(c_0_47,plain,
    ( is_a_theorem(implies(X1,and(X2,X1)))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_48,plain,
    is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).

fof(c_0_49,plain,
    ! [X33,X34] :
      ( ( ~ and_1
        | is_a_theorem(implies(and(X33,X34),X33)) )
      & ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
        | and_1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])]) ).

fof(c_0_50,plain,
    ! [X121,X122] :
      ( ~ op_implies_and
      | implies(X121,X122) = not(and(X121,not(X122))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).

cnf(c_0_51,plain,
    ( X1 = X2
    | ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_52,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_41,c_0_47]) ).

cnf(c_0_53,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
    inference(spm,[status(thm)],[c_0_41,c_0_48]) ).

cnf(c_0_54,plain,
    ( is_a_theorem(implies(and(X1,X2),X1))
    | ~ and_1 ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_55,plain,
    and_1,
    inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).

fof(c_0_56,plain,
    ! [X117,X118] :
      ( ~ op_or
      | or(X117,X118) = not(and(not(X117),not(X118))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).

cnf(c_0_57,plain,
    ( implies(X1,X2) = not(and(X1,not(X2)))
    | ~ op_implies_and ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_58,plain,
    op_implies_and,
    inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).

fof(c_0_59,plain,
    ! [X45,X46] :
      ( ( ~ or_1
        | is_a_theorem(implies(X45,or(X45,X46))) )
      & ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
        | or_1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])]) ).

cnf(c_0_60,plain,
    ( X1 = X2
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_61,plain,
    is_a_theorem(implies(X1,and(X1,X1))),
    inference(spm,[status(thm)],[c_0_53,c_0_42]) ).

cnf(c_0_62,plain,
    is_a_theorem(implies(and(X1,X2),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).

cnf(c_0_63,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_64,plain,
    not(and(X1,not(X2))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).

cnf(c_0_65,plain,
    op_or,
    inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).

fof(c_0_66,plain,
    ! [X15,X16] :
      ( ( ~ modus_tollens
        | is_a_theorem(implies(implies(not(X16),not(X15)),implies(X15,X16))) )
      & ( ~ 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])]) ).

cnf(c_0_67,plain,
    ( is_a_theorem(implies(X1,or(X1,X2)))
    | ~ or_1 ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_68,plain,
    or_1,
    inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).

cnf(c_0_69,plain,
    and(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).

cnf(c_0_70,plain,
    implies(not(X1),X2) = or(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).

cnf(c_0_71,plain,
    ( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
    | ~ modus_tollens ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_72,plain,
    modus_tollens,
    inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).

cnf(c_0_73,plain,
    is_a_theorem(implies(X1,or(X1,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).

cnf(c_0_74,plain,
    not(not(X1)) = or(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_69]),c_0_70]) ).

cnf(c_0_75,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_71,c_0_70]),c_0_72])]) ).

cnf(c_0_76,plain,
    is_a_theorem(or(X1,or(not(X1),X2))),
    inference(spm,[status(thm)],[c_0_73,c_0_70]) ).

cnf(c_0_77,plain,
    is_a_theorem(implies(X1,not(not(X1)))),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_78,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(or(X2,not(X1))) ),
    inference(spm,[status(thm)],[c_0_41,c_0_75]) ).

cnf(c_0_79,plain,
    is_a_theorem(or(X1,not(not(not(X1))))),
    inference(spm,[status(thm)],[c_0_76,c_0_74]) ).

cnf(c_0_80,plain,
    ( not(not(X1)) = X1
    | ~ is_a_theorem(or(not(X1),X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_77]),c_0_70]) ).

cnf(c_0_81,plain,
    is_a_theorem(or(not(X1),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_70]) ).

cnf(c_0_82,plain,
    is_a_theorem(implies(or(X1,not(not(X2))),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_75,c_0_70]) ).

cnf(c_0_83,plain,
    not(not(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).

fof(c_0_84,negated_conjecture,
    ~ axiom_m1,
    inference(assume_negation,[status(cth)],[s1_0_axiom_m1]) ).

fof(c_0_85,plain,
    ! [X127] :
      ( ( ~ necessitation
        | ~ is_a_theorem(X127)
        | is_a_theorem(necessarily(X127)) )
      & ( is_a_theorem(esk56_0)
        | necessitation )
      & ( ~ is_a_theorem(necessarily(esk56_0))
        | necessitation ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])]) ).

fof(c_0_86,plain,
    ! [X207,X208] :
      ( ~ op_strict_implies
      | strict_implies(X207,X208) = necessarily(implies(X207,X208)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).

cnf(c_0_87,plain,
    is_a_theorem(implies(or(X1,X2),or(X2,X1))),
    inference(rw,[status(thm)],[c_0_82,c_0_83]) ).

fof(c_0_88,plain,
    ! [X169,X170] :
      ( ( ~ axiom_m1
        | is_a_theorem(strict_implies(and(X169,X170),and(X170,X169))) )
      & ( ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))
        | axiom_m1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])]) ).

fof(c_0_89,negated_conjecture,
    ~ axiom_m1,
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

cnf(c_0_90,plain,
    ( is_a_theorem(necessarily(X1))
    | ~ necessitation
    | ~ is_a_theorem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_91,plain,
    necessitation,
    inference(split_conjunct,[status(thm)],[km5_necessitation]) ).

cnf(c_0_92,plain,
    ( strict_implies(X1,X2) = necessarily(implies(X1,X2))
    | ~ op_strict_implies ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_93,plain,
    op_strict_implies,
    inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).

cnf(c_0_94,plain,
    not(and(X1,X2)) = implies(X1,not(X2)),
    inference(spm,[status(thm)],[c_0_64,c_0_83]) ).

cnf(c_0_95,plain,
    or(not(X1),X2) = implies(X1,X2),
    inference(spm,[status(thm)],[c_0_70,c_0_83]) ).

cnf(c_0_96,plain,
    or(X1,X2) = or(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_87]),c_0_87])]) ).

fof(c_0_97,plain,
    ! [X19,X20] :
      ( ( ~ implies_1
        | is_a_theorem(implies(X19,implies(X20,X19))) )
      & ( ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))
        | implies_1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])]) ).

cnf(c_0_98,plain,
    ( axiom_m1
    | ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_88]) ).

cnf(c_0_99,negated_conjecture,
    ~ axiom_m1,
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_100,plain,
    ( is_a_theorem(necessarily(X1))
    | ~ is_a_theorem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).

cnf(c_0_101,plain,
    necessarily(implies(X1,X2)) = strict_implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).

cnf(c_0_102,plain,
    not(implies(X1,not(X2))) = and(X1,X2),
    inference(spm,[status(thm)],[c_0_83,c_0_94]) ).

cnf(c_0_103,plain,
    or(X1,not(X2)) = implies(X2,X1),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_104,plain,
    ( is_a_theorem(implies(X1,implies(X2,X1)))
    | ~ implies_1 ),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_105,plain,
    implies_1,
    inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).

cnf(c_0_106,plain,
    ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))),
    inference(sr,[status(thm)],[c_0_98,c_0_99]) ).

cnf(c_0_107,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_108,plain,
    and(not(X1),X2) = not(implies(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_70]),c_0_103]) ).

cnf(c_0_109,plain,
    is_a_theorem(implies(X1,implies(X2,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).

cnf(c_0_110,plain,
    ~ is_a_theorem(implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))),
    inference(spm,[status(thm)],[c_0_106,c_0_107]) ).

cnf(c_0_111,plain,
    and(X1,X2) = and(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_83]),c_0_102]) ).

cnf(c_0_112,plain,
    is_a_theorem(implies(X1,X1)),
    inference(spm,[status(thm)],[c_0_53,c_0_109]) ).

cnf(c_0_113,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111]),c_0_112])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL528+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.33  % Computer : n011.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  : 600
% 0.12/0.33  % DateTime : Sun Jul  3 03:31:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  # ENIGMATIC: Selected SinE mode:
% 0.19/0.45  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.19/0.45  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.19/0.45  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 9.74/2.68  # ENIGMATIC: Solved by autoschedule:
% 9.74/2.68  # No SInE strategy applied
% 9.74/2.68  # Trying AutoSched0 for 150 seconds
% 9.74/2.68  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 9.74/2.68  # and selection function SelectComplexExceptUniqMaxHorn.
% 9.74/2.68  #
% 9.74/2.68  # Preprocessing time       : 0.031 s
% 9.74/2.68  # Presaturation interreduction done
% 9.74/2.68  
% 9.74/2.68  # Proof found!
% 9.74/2.68  # SZS status Theorem
% 9.74/2.68  # SZS output start CNFRefutation
% See solution above
% 9.74/2.68  # Training examples: 0 positive, 0 negative
% 9.74/2.68  
% 9.74/2.68  # -------------------------------------------------
% 9.74/2.68  # User time                : 0.194 s
% 9.74/2.68  # System time              : 0.016 s
% 9.74/2.68  # Total time               : 0.210 s
% 9.74/2.68  # Maximum resident set size: 7120 pages
% 9.74/2.68  
%------------------------------------------------------------------------------