TSTP Solution File: LCL476+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : LCL476+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 18:12:53 EDT 2023

% Result   : Theorem 176.16s 22.74s
% Output   : CNFRefutation 176.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   98 (  45 unt;   0 def)
%            Number of atoms       :  177 (  12 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  142 (  63   ~;  62   |;   8   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   9 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  10 con; 0-2 aty)
%            Number of variables   :  186 (  33 sgn;  32   !;   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/tmp/tmp.jGxBC4UoU3/E---3.1_29758.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/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',cn1) ).

fof(luka_modus_ponens,axiom,
    modus_ponens,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',luka_modus_ponens) ).

fof(luka_cn1,axiom,
    cn1,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',luka_cn1) ).

fof(cn2,axiom,
    ( cn2
  <=> ! [X4,X5] : is_a_theorem(implies(X4,implies(not(X4),X5))) ),
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',cn2) ).

fof(luka_cn2,axiom,
    cn2,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',luka_cn2) ).

fof(cn3,axiom,
    ( cn3
  <=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',cn3) ).

fof(luka_cn3,axiom,
    cn3,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',luka_cn3) ).

fof(op_implies_or,axiom,
    ( op_implies_or
   => ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',op_implies_or) ).

fof(op_and,axiom,
    ( op_and
   => ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',op_and) ).

fof(principia_op_implies_or,axiom,
    op_implies_or,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',principia_op_implies_or) ).

fof(op_or,axiom,
    ( op_or
   => ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',op_or) ).

fof(principia_op_and,axiom,
    op_and,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',principia_op_and) ).

fof(luka_op_or,axiom,
    op_or,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',luka_op_or) ).

fof(r2,axiom,
    ( r2
  <=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',r2) ).

fof(principia_r2,conjecture,
    r2,
    file('/export/starexec/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p',principia_r2) ).

fof(c_0_16,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_17,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_18,plain,
    ( is_a_theorem(X2)
    | ~ modus_ponens
    | ~ is_a_theorem(X1)
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[luka_modus_ponens]) ).

cnf(c_0_20,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
    | ~ cn1 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    cn1,
    inference(split_conjunct,[status(thm)],[luka_cn1]) ).

fof(c_0_22,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_23,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_18,c_0_19])]) ).

cnf(c_0_24,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_20,c_0_21])]) ).

cnf(c_0_25,plain,
    ( is_a_theorem(implies(X1,implies(not(X1),X2)))
    | ~ cn2 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_26,plain,
    cn2,
    inference(split_conjunct,[status(thm)],[luka_cn2]) ).

cnf(c_0_27,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
    | ~ is_a_theorem(implies(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,plain,
    is_a_theorem(implies(X1,implies(not(X1),X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).

cnf(c_0_29,plain,
    is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_30,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_28]) ).

fof(c_0_31,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_32,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(implies(not(X1),X3),X2)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_29]) ).

cnf(c_0_33,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(not(X3),X2)))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_27,c_0_30]) ).

cnf(c_0_34,plain,
    ( is_a_theorem(implies(implies(not(X1),X1),X1))
    | ~ cn3 ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_35,plain,
    cn3,
    inference(split_conjunct,[status(thm)],[luka_cn3]) ).

cnf(c_0_36,plain,
    ( is_a_theorem(implies(X1,implies(not(X2),X3)))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,plain,
    is_a_theorem(implies(implies(not(X1),X1),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

cnf(c_0_38,plain,
    ( is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X4,X3)))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_36]) ).

cnf(c_0_39,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))),
    inference(spm,[status(thm)],[c_0_27,c_0_37]) ).

cnf(c_0_40,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(implies(not(X3),X4),X2))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_23,c_0_38]) ).

cnf(c_0_41,plain,
    ( is_a_theorem(implies(implies(not(X1),X1),X2))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_39]) ).

cnf(c_0_42,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X3,X2))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_43,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(implies(not(X2),X4),X3)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_29]) ).

cnf(c_0_44,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(not(X3),X3))
    | ~ is_a_theorem(implies(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_41]) ).

cnf(c_0_45,plain,
    is_a_theorem(implies(X1,implies(X2,X2))),
    inference(spm,[status(thm)],[c_0_43,c_0_37]) ).

cnf(c_0_46,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(implies(X3,X3),X2)) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_47,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_37]) ).

cnf(c_0_48,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(not(X2),X2))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_41]) ).

cnf(c_0_49,plain,
    is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
    inference(spm,[status(thm)],[c_0_46,c_0_39]) ).

cnf(c_0_50,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_47]) ).

cnf(c_0_51,plain,
    is_a_theorem(implies(implies(implies(implies(not(X1),X1),X2),X3),implies(implies(X1,X2),X3))),
    inference(spm,[status(thm)],[c_0_27,c_0_39]) ).

cnf(c_0_52,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(implies(implies(not(X2),X2),X2),X1)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_53,plain,
    ( is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X4,X2),X3)))
    | ~ is_a_theorem(X4) ),
    inference(spm,[status(thm)],[c_0_27,c_0_50]) ).

cnf(c_0_54,plain,
    ( is_a_theorem(implies(implies(X1,X2),X3))
    | ~ is_a_theorem(implies(implies(implies(not(X1),X1),X2),X3)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_51]) ).

cnf(c_0_55,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_56,plain,
    is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))),
    inference(spm,[status(thm)],[c_0_27,c_0_24]) ).

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

cnf(c_0_58,plain,
    ( is_a_theorem(implies(implies(X1,X2),X3))
    | ~ is_a_theorem(implies(implies(implies(X2,X4),implies(X1,X4)),X3)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_56]) ).

cnf(c_0_59,plain,
    is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)),
    inference(spm,[status(thm)],[c_0_57,c_0_49]) ).

cnf(c_0_60,plain,
    is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
    | ~ is_a_theorem(implies(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_58,c_0_55]) ).

cnf(c_0_62,plain,
    is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
    inference(spm,[status(thm)],[c_0_58,c_0_60]) ).

cnf(c_0_63,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,X3))
    | ~ is_a_theorem(implies(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_61]) ).

cnf(c_0_64,plain,
    is_a_theorem(implies(X1,implies(implies(X2,X1),X1))),
    inference(spm,[status(thm)],[c_0_32,c_0_62]) ).

cnf(c_0_65,plain,
    is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(not(X1),X4),X2),X3))),
    inference(spm,[status(thm)],[c_0_27,c_0_29]) ).

cnf(c_0_66,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(implies(implies(X3,X1),X1),X2)) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_67,plain,
    ( is_a_theorem(implies(implies(implies(not(X1),X2),X3),X4))
    | ~ is_a_theorem(implies(implies(X1,X3),X4)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_65]) ).

fof(c_0_68,plain,
    ! [X123,X124] :
      ( ~ op_implies_or
      | implies(X123,X124) = or(not(X123),X124) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])]) ).

cnf(c_0_69,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_70,plain,
    is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))),
    inference(spm,[status(thm)],[c_0_58,c_0_29]) ).

fof(c_0_71,plain,
    ! [X119,X120] :
      ( ~ op_and
      | and(X119,X120) = not(or(not(X119),not(X120))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])]) ).

cnf(c_0_72,plain,
    ( implies(X1,X2) = or(not(X1),X2)
    | ~ op_implies_or ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_73,plain,
    op_implies_or,
    inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).

cnf(c_0_74,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
    inference(spm,[status(thm)],[c_0_23,c_0_60]) ).

cnf(c_0_75,plain,
    is_a_theorem(implies(not(X1),implies(X1,implies(X2,X3)))),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

fof(c_0_76,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_77,plain,
    ( and(X1,X2) = not(or(not(X1),not(X2)))
    | ~ op_and ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_78,plain,
    or(not(X1),X2) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).

cnf(c_0_79,plain,
    op_and,
    inference(split_conjunct,[status(thm)],[principia_op_and]) ).

cnf(c_0_80,plain,
    is_a_theorem(implies(not(not(implies(X1,X2))),implies(X1,X2))),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_81,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_82,plain,
    and(X1,X2) = not(implies(X1,not(X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).

cnf(c_0_83,plain,
    op_or,
    inference(split_conjunct,[status(thm)],[luka_op_or]) ).

cnf(c_0_84,plain,
    is_a_theorem(implies(not(not(implies(not(X1),X1))),X1)),
    inference(spm,[status(thm)],[c_0_74,c_0_80]) ).

cnf(c_0_85,plain,
    not(not(implies(not(X1),not(not(X2))))) = or(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).

cnf(c_0_86,plain,
    is_a_theorem(implies(implies(not(X1),X1),not(not(X1)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_78]) ).

cnf(c_0_87,plain,
    is_a_theorem(implies(X1,not(not(X1)))),
    inference(spm,[status(thm)],[c_0_32,c_0_86]) ).

fof(c_0_88,plain,
    ! [X97,X98] :
      ( ( ~ r2
        | is_a_theorem(implies(X98,or(X97,X98))) )
      & ( ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))
        | r2 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])]) ).

fof(c_0_89,negated_conjecture,
    ~ r2,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[principia_r2])]) ).

cnf(c_0_90,plain,
    is_a_theorem(implies(X1,not(not(implies(X2,X1))))),
    inference(spm,[status(thm)],[c_0_69,c_0_87]) ).

cnf(c_0_91,plain,
    ( r2
    | ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_88]) ).

cnf(c_0_92,negated_conjecture,
    ~ r2,
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_93,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(not(not(X1)),X2)) ),
    inference(spm,[status(thm)],[c_0_63,c_0_87]) ).

cnf(c_0_94,plain,
    is_a_theorem(implies(not(not(X1)),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_90,c_0_85]) ).

cnf(c_0_95,plain,
    ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))),
    inference(sr,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_96,plain,
    is_a_theorem(implies(X1,or(X2,X1))),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_97,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : LCL476+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n009.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   : 2400
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Oct  2 12:26:44 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.jGxBC4UoU3/E---3.1_29758.p
% 176.16/22.74  # Version: 3.1pre001
% 176.16/22.74  # Preprocessing class: FSMSSLSSSSSNFFN.
% 176.16/22.74  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 176.16/22.74  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 176.16/22.74  # Starting new_bool_3 with 300s (1) cores
% 176.16/22.74  # Starting new_bool_1 with 300s (1) cores
% 176.16/22.74  # Starting sh5l with 300s (1) cores
% 176.16/22.74  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 29836 completed with status 0
% 176.16/22.74  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 176.16/22.74  # Preprocessing class: FSMSSLSSSSSNFFN.
% 176.16/22.74  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 176.16/22.74  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 176.16/22.74  # No SInE strategy applied
% 176.16/22.74  # Search class: FGUSF-FFMM21-MFFFFFNN
% 176.16/22.74  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 176.16/22.74  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 176.16/22.74  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 176.16/22.74  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 176.16/22.74  # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 176.16/22.74  # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 176.16/22.74  # G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 29850 completed with status 0
% 176.16/22.74  # Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 176.16/22.74  # Preprocessing class: FSMSSLSSSSSNFFN.
% 176.16/22.74  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 176.16/22.74  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 176.16/22.74  # No SInE strategy applied
% 176.16/22.74  # Search class: FGUSF-FFMM21-MFFFFFNN
% 176.16/22.74  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 176.16/22.74  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 176.16/22.74  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 176.16/22.74  # Preprocessing time       : 0.002 s
% 176.16/22.74  # Presaturation interreduction done
% 176.16/22.74  
% 176.16/22.74  # Proof found!
% 176.16/22.74  # SZS status Theorem
% 176.16/22.74  # SZS output start CNFRefutation
% See solution above
% 176.16/22.74  # Parsed axioms                        : 43
% 176.16/22.74  # Removed by relevancy pruning/SinE    : 0
% 176.16/22.74  # Initial clauses                      : 72
% 176.16/22.74  # Removed in clause preprocessing      : 0
% 176.16/22.74  # Initial clauses in saturation        : 72
% 176.16/22.74  # Processed clauses                    : 27173
% 176.16/22.74  # ...of these trivial                  : 853
% 176.16/22.74  # ...subsumed                          : 22854
% 176.16/22.74  # ...remaining for further processing  : 3466
% 176.16/22.74  # Other redundant clauses eliminated   : 0
% 176.16/22.74  # Clauses deleted for lack of memory   : 0
% 176.16/22.74  # Backward-subsumed                    : 140
% 176.16/22.74  # Backward-rewritten                   : 228
% 176.16/22.74  # Generated clauses                    : 1084003
% 176.16/22.74  # ...of the previous two non-redundant : 1017774
% 176.16/22.74  # ...aggressively subsumed             : 0
% 176.16/22.74  # Contextual simplify-reflections      : 0
% 176.16/22.74  # Paramodulations                      : 1084003
% 176.16/22.74  # Factorizations                       : 0
% 176.16/22.74  # NegExts                              : 0
% 176.16/22.74  # Equation resolutions                 : 0
% 176.16/22.74  # Total rewrite steps                  : 239141
% 176.16/22.74  # Propositional unsat checks           : 0
% 176.16/22.74  #    Propositional check models        : 0
% 176.16/22.74  #    Propositional check unsatisfiable : 0
% 176.16/22.74  #    Propositional clauses             : 0
% 176.16/22.74  #    Propositional clauses after purity: 0
% 176.16/22.74  #    Propositional unsat core size     : 0
% 176.16/22.74  #    Propositional preprocessing time  : 0.000
% 176.16/22.74  #    Propositional encoding time       : 0.000
% 176.16/22.74  #    Propositional solver time         : 0.000
% 176.16/22.74  #    Success case prop preproc time    : 0.000
% 176.16/22.74  #    Success case prop encoding time   : 0.000
% 176.16/22.74  #    Success case prop solver time     : 0.000
% 176.16/22.74  # Current number of processed clauses  : 3037
% 176.16/22.74  #    Positive orientable unit clauses  : 1290
% 176.16/22.74  #    Positive unorientable unit clauses: 55
% 176.16/22.74  #    Negative unit clauses             : 5
% 176.16/22.74  #    Non-unit-clauses                  : 1687
% 176.16/22.74  # Current number of unprocessed clauses: 940196
% 176.16/22.74  # ...number of literals in the above   : 1530328
% 176.16/22.74  # Current number of archived formulas  : 0
% 176.16/22.74  # Current number of archived clauses   : 429
% 176.16/22.74  # Clause-clause subsumption calls (NU) : 1177991
% 176.16/22.74  # Rec. Clause-clause subsumption calls : 1176894
% 176.16/22.74  # Non-unit clause-clause subsumptions  : 22982
% 176.16/22.74  # Unit Clause-clause subsumption calls : 120386
% 176.16/22.74  # Rewrite failures with RHS unbound    : 0
% 176.16/22.74  # BW rewrite match attempts            : 325068
% 176.16/22.74  # BW rewrite match successes           : 263
% 176.16/22.74  # Condensation attempts                : 0
% 176.16/22.74  # Condensation successes               : 0
% 176.16/22.74  # Termbank termtop insertions          : 34085010
% 176.16/22.74  
% 176.16/22.74  # -------------------------------------------------
% 176.16/22.74  # User time                : 21.136 s
% 176.16/22.74  # System time              : 0.722 s
% 176.16/22.74  # Total time               : 21.857 s
% 176.16/22.74  # Maximum resident set size: 2000 pages
% 176.16/22.74  
% 176.16/22.74  # -------------------------------------------------
% 176.16/22.74  # User time                : 105.662 s
% 176.16/22.74  # System time              : 3.822 s
% 176.16/22.74  # Total time               : 109.485 s
% 176.16/22.74  # Maximum resident set size: 1724 pages
% 176.16/22.74  % E---3.1 exiting
% 176.16/22.74  % E---3.1 exiting
%------------------------------------------------------------------------------