TSTP Solution File: LCL454+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : LCL454+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n012.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 10:11:18 EDT 2022

% Result   : Theorem 0.21s 1.39s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  103 (  52 unt;   0 def)
%            Number of atoms       :  189 (  36 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  147 (  61   ~;  59   |;  12   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   16 (  14 usr;  14 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  14 con; 0-2 aty)
%            Number of variables   :  127 (   6 sgn  48   !;   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/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).

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

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

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

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

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

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

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

fof(and_2,axiom,
    ( and_2
  <=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).

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

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

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

fof(hilbert_and_2,axiom,
    and_2,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).

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

fof(principia_op_implies_or,axiom,
    op_implies_or,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',principia_op_implies_or) ).

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

fof(hilbert_and_1,axiom,
    and_1,
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).

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

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

fof(principia_op_and,axiom,
    op_and,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',principia_op_and) ).

fof(principia_r1,conjecture,
    r1,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',principia_r1) ).

fof(r1,axiom,
    ( r1
  <=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).

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

fof(c_0_25,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_26,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_27,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(X2)
    | ~ modus_ponens ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_28,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).

cnf(c_0_29,plain,
    ( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
    | ~ and_3 ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_30,plain,
    and_3,
    inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).

cnf(c_0_31,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_27,c_0_28])]) ).

cnf(c_0_32,plain,
    is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).

fof(c_0_33,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])])])])]) ).

fof(c_0_34,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_35,plain,
    ( is_a_theorem(implies(X1,and(X2,X1)))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,plain,
    ( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
    | ~ op_equiv ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_37,plain,
    op_equiv,
    inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).

fof(c_0_38,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])])])])])]) ).

cnf(c_0_39,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2))
    | ~ substitution_of_equivalents ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

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

cnf(c_0_41,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_35]) ).

cnf(c_0_42,plain,
    and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).

fof(c_0_43,plain,
    ! [X3,X4] :
      ( ( ~ and_2
        | is_a_theorem(implies(and(X3,X4),X4)) )
      & ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
        | and_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)],[and_2])])])])])]) ).

fof(c_0_44,plain,
    ! [X3,X4] :
      ( ~ op_implies_or
      | implies(X3,X4) = or(not(X3),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_or])])])])]) ).

fof(c_0_45,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_46,plain,
    ( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
    | ~ implies_2 ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_47,plain,
    implies_2,
    inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).

cnf(c_0_48,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).

cnf(c_0_49,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_41,c_0_42]) ).

cnf(c_0_50,plain,
    ( is_a_theorem(implies(and(X1,X2),X2))
    | ~ and_2 ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_51,plain,
    and_2,
    inference(split_conjunct,[status(thm)],[hilbert_and_2]) ).

fof(c_0_52,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_53,plain,
    ( implies(X1,X2) = or(not(X1),X2)
    | ~ op_implies_or ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_54,plain,
    op_implies_or,
    inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).

cnf(c_0_55,plain,
    ( implies(X1,X2) = not(and(X1,not(X2)))
    | ~ op_implies_and ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_56,plain,
    op_implies_and,
    inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).

cnf(c_0_57,plain,
    is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).

cnf(c_0_58,plain,
    ( X1 = X2
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_59,plain,
    is_a_theorem(implies(and(X1,X2),X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).

cnf(c_0_60,plain,
    ( is_a_theorem(implies(and(X1,X2),X1))
    | ~ and_1 ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_61,plain,
    and_1,
    inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).

cnf(c_0_62,plain,
    or(not(X1),X2) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]) ).

cnf(c_0_63,plain,
    not(and(X1,not(X2))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).

cnf(c_0_64,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
    inference(spm,[status(thm)],[c_0_31,c_0_57]) ).

fof(c_0_65,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])])])])]) ).

fof(c_0_66,plain,
    ! [X3,X4] :
      ( ~ op_and
      | and(X3,X4) = not(or(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_and])])])])]) ).

cnf(c_0_67,plain,
    ( and(X1,X2) = X2
    | ~ is_a_theorem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_35]),c_0_59])]) ).

cnf(c_0_68,plain,
    is_a_theorem(implies(and(X1,X2),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).

cnf(c_0_69,plain,
    implies(and(X1,not(X2)),X3) = or(implies(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_70,plain,
    is_a_theorem(implies(X1,and(X1,X1))),
    inference(spm,[status(thm)],[c_0_64,c_0_32]) ).

cnf(c_0_71,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_72,plain,
    op_or,
    inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).

cnf(c_0_73,plain,
    ( and(X1,X2) = not(or(not(X1),not(X2)))
    | ~ op_and ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

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

cnf(c_0_75,plain,
    ( is_a_theorem(implies(X1,X1))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_59,c_0_67]) ).

cnf(c_0_76,plain,
    is_a_theorem(or(implies(X1,X2),X1)),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_77,plain,
    and(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_70]),c_0_68])]) ).

cnf(c_0_78,plain,
    implies(not(X1),X2) = or(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_63]),c_0_72])]) ).

cnf(c_0_79,plain,
    not(implies(X1,not(X2))) = and(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_62]),c_0_74])]) ).

cnf(c_0_80,plain,
    is_a_theorem(implies(X1,X1)),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

fof(c_0_81,negated_conjecture,
    ~ r1,
    inference(assume_negation,[status(cth)],[principia_r1]) ).

cnf(c_0_82,plain,
    not(not(X1)) = or(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_77]),c_0_78]) ).

cnf(c_0_83,plain,
    not(or(X1,not(X2))) = and(not(X1),X2),
    inference(spm,[status(thm)],[c_0_79,c_0_78]) ).

cnf(c_0_84,plain,
    is_a_theorem(or(X1,not(X1))),
    inference(spm,[status(thm)],[c_0_80,c_0_78]) ).

fof(c_0_85,plain,
    ! [X5] :
      ( ( ~ r1
        | is_a_theorem(implies(or(X5,X5),X5)) )
      & ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
        | r1 ) ),
    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)],[r1])])])])])]) ).

fof(c_0_86,negated_conjecture,
    ~ r1,
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_87,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_88,plain,
    not(or(X1,X1)) = implies(X1,not(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_82]),c_0_62]) ).

cnf(c_0_89,plain,
    and(not(not(X1)),X2) = and(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_62]),c_0_79]) ).

cnf(c_0_90,plain,
    is_a_theorem(implies(X1,not(not(X1)))),
    inference(spm,[status(thm)],[c_0_84,c_0_62]) ).

cnf(c_0_91,plain,
    ( r1
    | ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_92,negated_conjecture,
    ~ r1,
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_93,plain,
    ( is_a_theorem(implies(implies(not(X1),X1),X1))
    | ~ cn3 ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

cnf(c_0_94,plain,
    ( cn3
    | ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

cnf(c_0_95,plain,
    or(X1,not(not(X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_88]),c_0_78]),c_0_89]),c_0_77]) ).

cnf(c_0_96,plain,
    not(not(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_90]),c_0_78]),c_0_62]),c_0_80])]) ).

cnf(c_0_97,plain,
    ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)),
    inference(sr,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_98,plain,
    ( is_a_theorem(implies(or(X1,X1),X1))
    | ~ cn3 ),
    inference(rw,[status(thm)],[c_0_93,c_0_78]) ).

cnf(c_0_99,plain,
    ( cn3
    | ~ is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)) ),
    inference(rw,[status(thm)],[c_0_94,c_0_78]) ).

cnf(c_0_100,plain,
    or(X1,X1) = X1,
    inference(rw,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_101,plain,
    ~ cn3,
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_102,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_80])]),c_0_101]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL454+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : run_ET %s %d
% 0.11/0.33  % Computer : n012.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Mon Jul  4 06:06:31 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.21/1.39  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.39  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.39  # Preprocessing time       : 0.008 s
% 0.21/1.39  
% 0.21/1.39  # Failure: Out of unprocessed clauses!
% 0.21/1.39  # OLD status GaveUp
% 0.21/1.39  # Parsed axioms                        : 53
% 0.21/1.39  # Removed by relevancy pruning/SinE    : 51
% 0.21/1.39  # Initial clauses                      : 3
% 0.21/1.39  # Removed in clause preprocessing      : 0
% 0.21/1.39  # Initial clauses in saturation        : 3
% 0.21/1.39  # Processed clauses                    : 3
% 0.21/1.39  # ...of these trivial                  : 0
% 0.21/1.39  # ...subsumed                          : 1
% 0.21/1.39  # ...remaining for further processing  : 2
% 0.21/1.39  # Other redundant clauses eliminated   : 0
% 0.21/1.39  # Clauses deleted for lack of memory   : 0
% 0.21/1.39  # Backward-subsumed                    : 0
% 0.21/1.39  # Backward-rewritten                   : 0
% 0.21/1.39  # Generated clauses                    : 0
% 0.21/1.39  # ...of the previous two non-trivial   : 0
% 0.21/1.39  # Contextual simplify-reflections      : 0
% 0.21/1.39  # Paramodulations                      : 0
% 0.21/1.39  # Factorizations                       : 0
% 0.21/1.39  # Equation resolutions                 : 0
% 0.21/1.39  # Current number of processed clauses  : 2
% 0.21/1.39  #    Positive orientable unit clauses  : 0
% 0.21/1.39  #    Positive unorientable unit clauses: 0
% 0.21/1.39  #    Negative unit clauses             : 2
% 0.21/1.39  #    Non-unit-clauses                  : 0
% 0.21/1.39  # Current number of unprocessed clauses: 0
% 0.21/1.39  # ...number of literals in the above   : 0
% 0.21/1.39  # Current number of archived formulas  : 0
% 0.21/1.39  # Current number of archived clauses   : 0
% 0.21/1.39  # Clause-clause subsumption calls (NU) : 0
% 0.21/1.39  # Rec. Clause-clause subsumption calls : 0
% 0.21/1.39  # Non-unit clause-clause subsumptions  : 0
% 0.21/1.39  # Unit Clause-clause subsumption calls : 0
% 0.21/1.39  # Rewrite failures with RHS unbound    : 0
% 0.21/1.39  # BW rewrite match attempts            : 0
% 0.21/1.39  # BW rewrite match successes           : 0
% 0.21/1.39  # Condensation attempts                : 0
% 0.21/1.39  # Condensation successes               : 0
% 0.21/1.39  # Termbank termtop insertions          : 484
% 0.21/1.39  
% 0.21/1.39  # -------------------------------------------------
% 0.21/1.39  # User time                : 0.006 s
% 0.21/1.39  # System time              : 0.002 s
% 0.21/1.39  # Total time               : 0.008 s
% 0.21/1.39  # Maximum resident set size: 2732 pages
% 0.21/1.39  # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.21/1.39  # Preprocessing time       : 0.019 s
% 0.21/1.39  
% 0.21/1.39  # Proof found!
% 0.21/1.39  # SZS status Theorem
% 0.21/1.39  # SZS output start CNFRefutation
% See solution above
% 0.21/1.39  # Proof object total steps             : 103
% 0.21/1.39  # Proof object clause steps            : 63
% 0.21/1.39  # Proof object formula steps           : 40
% 0.21/1.39  # Proof object conjectures             : 4
% 0.21/1.39  # Proof object clause conjectures      : 1
% 0.21/1.39  # Proof object formula conjectures     : 3
% 0.21/1.39  # Proof object initial clauses used    : 26
% 0.21/1.39  # Proof object initial formulas used   : 25
% 0.21/1.39  # Proof object generating inferences   : 21
% 0.21/1.39  # Proof object simplifying inferences  : 46
% 0.21/1.39  # Training examples: 0 positive, 0 negative
% 0.21/1.39  # Parsed axioms                        : 53
% 0.21/1.39  # Removed by relevancy pruning/SinE    : 0
% 0.21/1.39  # Initial clauses                      : 82
% 0.21/1.39  # Removed in clause preprocessing      : 0
% 0.21/1.39  # Initial clauses in saturation        : 82
% 0.21/1.39  # Processed clauses                    : 1852
% 0.21/1.39  # ...of these trivial                  : 62
% 0.21/1.39  # ...subsumed                          : 1255
% 0.21/1.39  # ...remaining for further processing  : 535
% 0.21/1.39  # Other redundant clauses eliminated   : 0
% 0.21/1.39  # Clauses deleted for lack of memory   : 0
% 0.21/1.39  # Backward-subsumed                    : 35
% 0.21/1.39  # Backward-rewritten                   : 173
% 0.21/1.39  # Generated clauses                    : 16345
% 0.21/1.39  # ...of the previous two non-trivial   : 15224
% 0.21/1.39  # Contextual simplify-reflections      : 408
% 0.21/1.39  # Paramodulations                      : 16345
% 0.21/1.39  # Factorizations                       : 0
% 0.21/1.39  # Equation resolutions                 : 0
% 0.21/1.39  # Current number of processed clauses  : 327
% 0.21/1.39  #    Positive orientable unit clauses  : 110
% 0.21/1.39  #    Positive unorientable unit clauses: 2
% 0.21/1.39  #    Negative unit clauses             : 5
% 0.21/1.39  #    Non-unit-clauses                  : 210
% 0.21/1.39  # Current number of unprocessed clauses: 8662
% 0.21/1.39  # ...number of literals in the above   : 14527
% 0.21/1.39  # Current number of archived formulas  : 0
% 0.21/1.39  # Current number of archived clauses   : 208
% 0.21/1.39  # Clause-clause subsumption calls (NU) : 20756
% 0.21/1.39  # Rec. Clause-clause subsumption calls : 20260
% 0.21/1.39  # Non-unit clause-clause subsumptions  : 1664
% 0.21/1.39  # Unit Clause-clause subsumption calls : 521
% 0.21/1.39  # Rewrite failures with RHS unbound    : 18
% 0.21/1.39  # BW rewrite match attempts            : 856
% 0.21/1.39  # BW rewrite match successes           : 100
% 0.21/1.39  # Condensation attempts                : 0
% 0.21/1.39  # Condensation successes               : 0
% 0.21/1.39  # Termbank termtop insertions          : 198555
% 0.21/1.39  
% 0.21/1.39  # -------------------------------------------------
% 0.21/1.39  # User time                : 0.211 s
% 0.21/1.39  # System time              : 0.010 s
% 0.21/1.39  # Total time               : 0.221 s
% 0.21/1.39  # Maximum resident set size: 13364 pages
%------------------------------------------------------------------------------