TSTP Solution File: LCL463+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : LCL463+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n026.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 18:12:51 EDT 2023

% Result   : Theorem 120.75s 16.13s
% Output   : CNFRefutation 120.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  115 (  44 unt;   0 def)
%            Number of atoms       :  230 (  26 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  209 (  94   ~;  94   |;  10   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   12 (  10 usr;  10 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;  12 con; 0-2 aty)
%            Number of variables   :  220 (  35 sgn;  36   !;   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/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',modus_ponens) ).

fof(cn1,axiom,
    ( cn1
  <=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6)))) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',cn1) ).

fof(luka_modus_ponens,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',luka_modus_ponens) ).

fof(luka_cn1,axiom,
    cn1,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',luka_cn1) ).

fof(op_implies_and,axiom,
    ( op_implies_and
   => ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',op_implies_and) ).

fof(op_or,axiom,
    ( op_or
   => ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',op_or) ).

fof(hilbert_op_implies_and,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',hilbert_op_implies_and) ).

fof(cn3,axiom,
    ( cn3
  <=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',cn3) ).

fof(luka_op_or,axiom,
    op_or,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',luka_op_or) ).

fof(luka_cn3,axiom,
    cn3,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',luka_cn3) ).

fof(cn2,axiom,
    ( cn2
  <=> ! [X4,X5] : is_a_theorem(implies(X4,implies(not(X4),X5))) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',cn2) ).

fof(luka_cn2,axiom,
    cn2,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',luka_cn2) ).

fof(op_equiv,axiom,
    ( op_equiv
   => ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',op_equiv) ).

fof(luka_op_equiv,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',luka_op_equiv) ).

fof(substitution_of_equivalents,axiom,
    ( substitution_of_equivalents
  <=> ! [X1,X2] :
        ( is_a_theorem(equiv(X1,X2))
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',substitution_of_equivalents) ).

fof(substitution_of_equivalents_0001,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',substitution_of_equivalents_0001) ).

fof(implies_1,axiom,
    ( implies_1
  <=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',implies_1) ).

fof(hilbert_implies_1,conjecture,
    implies_1,
    file('/export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p',hilbert_implies_1) ).

fof(c_0_18,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_19,plain,
    ! [X83,X84,X85] :
      ( ( ~ cn1
        | is_a_theorem(implies(implies(X83,X84),implies(implies(X84,X85),implies(X83,X85)))) )
      & ( ~ is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0))))
        | cn1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn1])])])]) ).

cnf(c_0_20,plain,
    ( is_a_theorem(X2)
    | ~ modus_ponens
    | ~ is_a_theorem(X1)
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_21,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[luka_modus_ponens]) ).

cnf(c_0_22,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
    | ~ cn1 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,plain,
    cn1,
    inference(split_conjunct,[status(thm)],[luka_cn1]) ).

fof(c_0_24,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_25,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_20,c_0_21])]) ).

cnf(c_0_26,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_22,c_0_23])]) ).

fof(c_0_27,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_28,plain,
    ( implies(X1,X2) = not(and(X1,not(X2)))
    | ~ op_implies_and ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,plain,
    op_implies_and,
    inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).

fof(c_0_30,plain,
    ! [X93] :
      ( ( ~ cn3
        | is_a_theorem(implies(implies(not(X93),X93),X93)) )
      & ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
        | cn3 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])]) ).

cnf(c_0_31,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
    | ~ is_a_theorem(implies(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,plain,
    not(and(X1,not(X2))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

cnf(c_0_34,plain,
    op_or,
    inference(split_conjunct,[status(thm)],[luka_op_or]) ).

cnf(c_0_35,plain,
    ( is_a_theorem(implies(implies(not(X1),X1),X1))
    | ~ cn3 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_36,plain,
    cn3,
    inference(split_conjunct,[status(thm)],[luka_cn3]) ).

fof(c_0_37,plain,
    ! [X89,X90] :
      ( ( ~ cn2
        | is_a_theorem(implies(X89,implies(not(X89),X90))) )
      & ( ~ is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0)))
        | cn2 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn2])])])]) ).

cnf(c_0_38,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_25,c_0_31]) ).

cnf(c_0_39,plain,
    implies(not(X1),X2) = or(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_40,plain,
    is_a_theorem(implies(implies(not(X1),X1),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).

cnf(c_0_41,plain,
    ( is_a_theorem(implies(X1,implies(not(X1),X2)))
    | ~ cn2 ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_42,plain,
    cn2,
    inference(split_conjunct,[status(thm)],[luka_cn2]) ).

cnf(c_0_43,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,not(X3)))
    | ~ is_a_theorem(or(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_44,plain,
    is_a_theorem(implies(or(X1,X1),X1)),
    inference(spm,[status(thm)],[c_0_40,c_0_39]) ).

cnf(c_0_45,plain,
    is_a_theorem(implies(X1,implies(not(X1),X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).

cnf(c_0_46,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(X1,not(X3)))
    | ~ is_a_theorem(or(X3,X2)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_39]) ).

cnf(c_0_47,plain,
    or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_39,c_0_33]) ).

cnf(c_0_48,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,or(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_38,c_0_44]) ).

cnf(c_0_49,plain,
    ( is_a_theorem(implies(implies(X1,X2),or(X3,X2)))
    | ~ is_a_theorem(or(X3,X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_39]) ).

cnf(c_0_50,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_45]) ).

cnf(c_0_51,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(X1,implies(X3,X4)))
    | ~ is_a_theorem(implies(implies(X3,X4),X2)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_33]),c_0_47]) ).

cnf(c_0_52,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_53,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(X1) ),
    inference(rw,[status(thm)],[c_0_50,c_0_39]) ).

cnf(c_0_54,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(X1,or(X3,X4)))
    | ~ is_a_theorem(implies(or(X3,X4),X2)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_39]) ).

cnf(c_0_55,plain,
    is_a_theorem(or(X1,or(not(X1),X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39]),c_0_39]) ).

cnf(c_0_56,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_57,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(implies(or(not(X1),X3),X2)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_58,plain,
    ( is_a_theorem(implies(or(X1,X2),X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_56,c_0_39]) ).

cnf(c_0_59,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_60,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_59]) ).

cnf(c_0_61,plain,
    ( is_a_theorem(implies(implies(X1,or(X2,X2)),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_60]) ).

cnf(c_0_62,plain,
    is_a_theorem(implies(X1,or(X1,X2))),
    inference(spm,[status(thm)],[c_0_45,c_0_39]) ).

fof(c_0_63,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_64,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,or(X1,X1)))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_61]) ).

cnf(c_0_65,plain,
    ( is_a_theorem(implies(X1,or(X2,X3)))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_62]) ).

cnf(c_0_66,plain,
    ( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
    | ~ op_equiv ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_67,plain,
    op_equiv,
    inference(split_conjunct,[status(thm)],[luka_op_equiv]) ).

cnf(c_0_68,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_64,c_0_49]) ).

cnf(c_0_69,plain,
    ( is_a_theorem(or(X1,or(X2,X3)))
    | ~ is_a_theorem(or(X1,X2)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_39]),c_0_39]) ).

cnf(c_0_70,plain,
    not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
    inference(spm,[status(thm)],[c_0_33,c_0_33]) ).

cnf(c_0_71,plain,
    and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).

fof(c_0_72,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])])])])]) ).

cnf(c_0_73,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(or(X2,X3),X1))
    | ~ is_a_theorem(or(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_74,plain,
    ( is_a_theorem(implies(or(X1,X2),X2))
    | ~ is_a_theorem(not(X1)) ),
    inference(spm,[status(thm)],[c_0_60,c_0_39]) ).

cnf(c_0_75,plain,
    implies(implies(X1,X2),and(X2,not(X1))) = not(equiv(X1,X2)),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_76,plain,
    ( X1 = X2
    | ~ substitution_of_equivalents
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

cnf(c_0_77,plain,
    substitution_of_equivalents,
    inference(split_conjunct,[status(thm)],[substitution_of_equivalents_0001]) ).

cnf(c_0_78,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_79,plain,
    ( is_a_theorem(or(equiv(X1,X2),and(X2,not(X1))))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_75]),c_0_39]) ).

cnf(c_0_80,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(X3,X2)))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_38,c_0_60]) ).

cnf(c_0_81,plain,
    is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X1,X3)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_39]) ).

cnf(c_0_82,plain,
    implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
    inference(spm,[status(thm)],[c_0_70,c_0_39]) ).

cnf(c_0_83,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(implies(X3,X1))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_65]) ).

cnf(c_0_84,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).

cnf(c_0_85,plain,
    ( is_a_theorem(equiv(X1,X2))
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_33]) ).

cnf(c_0_86,plain,
    ( is_a_theorem(implies(or(X1,X2),or(X1,X3)))
    | ~ is_a_theorem(implies(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_87,plain,
    is_a_theorem(implies(X1,not(and(not(X1),or(X2,X3))))),
    inference(spm,[status(thm)],[c_0_45,c_0_82]) ).

cnf(c_0_88,plain,
    ( is_a_theorem(or(implies(X1,X2),X3))
    | ~ is_a_theorem(implies(X4,X2))
    | ~ is_a_theorem(implies(X1,X4)) ),
    inference(spm,[status(thm)],[c_0_83,c_0_31]) ).

cnf(c_0_89,plain,
    ( X1 = X2
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_90,plain,
    ( is_a_theorem(implies(or(X1,X2),X1))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_86]) ).

cnf(c_0_91,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(or(and(not(X1),or(X3,X4)),X2)) ),
    inference(spm,[status(thm)],[c_0_43,c_0_87]) ).

cnf(c_0_92,plain,
    ( is_a_theorem(or(or(X1,X2),X3))
    | ~ is_a_theorem(implies(X4,X1))
    | ~ is_a_theorem(X4) ),
    inference(spm,[status(thm)],[c_0_83,c_0_65]) ).

cnf(c_0_93,plain,
    ( is_a_theorem(or(implies(X1,X2),X3))
    | ~ is_a_theorem(implies(X1,or(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_88,c_0_44]) ).

cnf(c_0_94,plain,
    ( or(X1,X2) = X1
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_62])]) ).

cnf(c_0_95,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_91,c_0_59]) ).

cnf(c_0_96,plain,
    ( is_a_theorem(or(or(X1,X2),X3))
    | ~ is_a_theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_92,c_0_44]) ).

cnf(c_0_97,plain,
    is_a_theorem(or(implies(X1,X1),X2)),
    inference(spm,[status(thm)],[c_0_93,c_0_62]) ).

cnf(c_0_98,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(X1,implies(X4,X3)))
    | ~ is_a_theorem(implies(X2,X4)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_31]) ).

cnf(c_0_99,plain,
    ( or(X1,not(X2)) = X1
    | ~ is_a_theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_94,c_0_39]) ).

cnf(c_0_100,plain,
    is_a_theorem(or(implies(or(or(X1,X1),or(X1,X1)),X1),X2)),
    inference(spm,[status(thm)],[c_0_93,c_0_44]) ).

cnf(c_0_101,plain,
    or(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_44]),c_0_62])]) ).

cnf(c_0_102,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(or(X2,X2)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_95]) ).

cnf(c_0_103,plain,
    is_a_theorem(or(or(implies(X1,X1),X2),X3)),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

fof(c_0_104,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])])])]) ).

fof(c_0_105,negated_conjecture,
    ~ implies_1,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_1])]) ).

cnf(c_0_106,plain,
    ( is_a_theorem(implies(or(X1,X2),implies(X3,or(X1,X4))))
    | ~ is_a_theorem(implies(X3,implies(X2,X4))) ),
    inference(spm,[status(thm)],[c_0_98,c_0_81]) ).

cnf(c_0_107,plain,
    or(X1,not(implies(X2,X2))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_101]) ).

cnf(c_0_108,plain,
    is_a_theorem(implies(X1,or(implies(X2,X2),X3))),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_109,plain,
    ( implies_1
    | ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_110,negated_conjecture,
    ~ implies_1,
    inference(split_conjunct,[status(thm)],[c_0_105]) ).

cnf(c_0_111,plain,
    is_a_theorem(implies(X1,implies(X2,or(X1,X3)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_39]),c_0_108])]) ).

cnf(c_0_112,plain,
    ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0))),
    inference(sr,[status(thm)],[c_0_109,c_0_110]) ).

cnf(c_0_113,plain,
    is_a_theorem(implies(X1,implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_111,c_0_107]) ).

cnf(c_0_114,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : LCL463+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n026.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 2400
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Mon Oct  2 13:20:29 EDT 2023
% 0.10/0.31  % CPUTime    : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ozNvhHwgtY/E---3.1_32534.p
% 120.75/16.13  # Version: 3.1pre001
% 120.75/16.13  # Preprocessing class: FSMSSLSSSSSNFFN.
% 120.75/16.13  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 120.75/16.13  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 120.75/16.13  # Starting new_bool_3 with 300s (1) cores
% 120.75/16.13  # Starting new_bool_1 with 300s (1) cores
% 120.75/16.13  # Starting sh5l with 300s (1) cores
% 120.75/16.13  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 32612 completed with status 0
% 120.75/16.13  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 120.75/16.13  # Preprocessing class: FSMSSLSSSSSNFFN.
% 120.75/16.13  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 120.75/16.13  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 120.75/16.13  # No SInE strategy applied
% 120.75/16.13  # Search class: FGUSF-FFMM21-MFFFFFNN
% 120.75/16.13  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 120.75/16.13  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 120.75/16.13  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 120.75/16.13  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 120.75/16.13  # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 120.75/16.13  # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 120.75/16.13  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 32622 completed with status 0
% 120.75/16.13  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 120.75/16.13  # Preprocessing class: FSMSSLSSSSSNFFN.
% 120.75/16.13  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 120.75/16.13  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 120.75/16.13  # No SInE strategy applied
% 120.75/16.13  # Search class: FGUSF-FFMM21-MFFFFFNN
% 120.75/16.13  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 120.75/16.13  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 120.75/16.13  # Preprocessing time       : 0.001 s
% 120.75/16.13  # Presaturation interreduction done
% 120.75/16.13  
% 120.75/16.13  # Proof found!
% 120.75/16.13  # SZS status Theorem
% 120.75/16.13  # SZS output start CNFRefutation
% See solution above
% 120.75/16.13  # Parsed axioms                        : 43
% 120.75/16.13  # Removed by relevancy pruning/SinE    : 0
% 120.75/16.13  # Initial clauses                      : 72
% 120.75/16.13  # Removed in clause preprocessing      : 0
% 120.75/16.13  # Initial clauses in saturation        : 72
% 120.75/16.13  # Processed clauses                    : 57815
% 120.75/16.13  # ...of these trivial                  : 1264
% 120.75/16.13  # ...subsumed                          : 49501
% 120.75/16.13  # ...remaining for further processing  : 7050
% 120.75/16.13  # Other redundant clauses eliminated   : 0
% 120.75/16.13  # Clauses deleted for lack of memory   : 0
% 120.75/16.13  # Backward-subsumed                    : 714
% 120.75/16.13  # Backward-rewritten                   : 326
% 120.75/16.13  # Generated clauses                    : 997157
% 120.75/16.13  # ...of the previous two non-redundant : 878294
% 120.75/16.13  # ...aggressively subsumed             : 0
% 120.75/16.13  # Contextual simplify-reflections      : 8
% 120.75/16.13  # Paramodulations                      : 997157
% 120.75/16.13  # Factorizations                       : 0
% 120.75/16.13  # NegExts                              : 0
% 120.75/16.13  # Equation resolutions                 : 0
% 120.75/16.13  # Total rewrite steps                  : 538933
% 120.75/16.13  # Propositional unsat checks           : 1
% 120.75/16.13  #    Propositional check models        : 0
% 120.75/16.13  #    Propositional check unsatisfiable : 0
% 120.75/16.13  #    Propositional clauses             : 0
% 120.75/16.13  #    Propositional clauses after purity: 0
% 120.75/16.13  #    Propositional unsat core size     : 0
% 120.75/16.13  #    Propositional preprocessing time  : 0.000
% 120.75/16.13  #    Propositional encoding time       : 0.793
% 120.75/16.13  #    Propositional solver time         : 0.324
% 120.75/16.13  #    Success case prop preproc time    : 0.000
% 120.75/16.13  #    Success case prop encoding time   : 0.000
% 120.75/16.13  #    Success case prop solver time     : 0.000
% 120.75/16.13  # Current number of processed clauses  : 5950
% 120.75/16.13  #    Positive orientable unit clauses  : 441
% 120.75/16.13  #    Positive unorientable unit clauses: 2
% 120.75/16.13  #    Negative unit clauses             : 5
% 120.75/16.13  #    Non-unit-clauses                  : 5502
% 120.75/16.13  # Current number of unprocessed clauses: 814384
% 120.75/16.13  # ...number of literals in the above   : 2012880
% 120.75/16.13  # Current number of archived formulas  : 0
% 120.75/16.13  # Current number of archived clauses   : 1100
% 120.75/16.13  # Clause-clause subsumption calls (NU) : 1718895
% 120.75/16.13  # Rec. Clause-clause subsumption calls : 1548262
% 120.75/16.13  # Non-unit clause-clause subsumptions  : 48210
% 120.75/16.13  # Unit Clause-clause subsumption calls : 23599
% 120.75/16.13  # Rewrite failures with RHS unbound    : 0
% 120.75/16.13  # BW rewrite match attempts            : 33276
% 120.75/16.13  # BW rewrite match successes           : 148
% 120.75/16.13  # Condensation attempts                : 0
% 120.75/16.13  # Condensation successes               : 0
% 120.75/16.13  # Termbank termtop insertions          : 17971243
% 120.75/16.13  
% 120.75/16.13  # -------------------------------------------------
% 120.75/16.13  # User time                : 13.663 s
% 120.75/16.13  # System time              : 0.479 s
% 120.75/16.13  # Total time               : 14.143 s
% 120.75/16.13  # Maximum resident set size: 1992 pages
% 120.75/16.13  
% 120.75/16.13  # -------------------------------------------------
% 120.75/16.13  # User time                : 70.997 s
% 120.75/16.13  # System time              : 2.527 s
% 120.75/16.13  # Total time               : 73.524 s
% 120.75/16.13  # Maximum resident set size: 1724 pages
% 120.75/16.13  % E---3.1 exiting
% 120.75/16.13  % E---3.1 exiting
%------------------------------------------------------------------------------