TSTP Solution File: LCL507+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : LCL507+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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  : 300s
% DateTime : Sat May  4 08:27:44 EDT 2024

% Result   : Theorem 8.63s 1.51s
% Output   : CNFRefutation 8.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  129 (  54 unt;   0 def)
%            Number of atoms       :  239 (  23 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  198 (  88   ~;  87   |;  11   &)
%                                         (   7 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   13 (  11 usr;  11 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  14 con; 0-2 aty)
%            Number of variables   :  208 (  27 sgn  40   !;   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.VYpbOkQAZZ/E---3.1_1252.p',modus_ponens) ).

fof(kn3,axiom,
    ( kn3
  <=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',kn3) ).

fof(rosser_modus_ponens,axiom,
    modus_ponens,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',rosser_modus_ponens) ).

fof(rosser_kn3,axiom,
    kn3,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',rosser_kn3) ).

fof(kn1,axiom,
    ( kn1
  <=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',kn1) ).

fof(rosser_kn1,axiom,
    kn1,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',rosser_kn1) ).

fof(op_implies_and,axiom,
    ( op_implies_and
   => ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',op_implies_and) ).

fof(rosser_op_implies_and,axiom,
    op_implies_and,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',rosser_op_implies_and) ).

fof(kn2,axiom,
    ( kn2
  <=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',kn2) ).

fof(op_or,axiom,
    ( op_or
   => ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',op_or) ).

fof(rosser_kn2,axiom,
    kn2,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',rosser_kn2) ).

fof(rosser_op_or,axiom,
    op_or,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',rosser_op_or) ).

fof(r3,axiom,
    ( r3
  <=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',r3) ).

fof(substitution_of_equivalents,axiom,
    ( substitution_of_equivalents
  <=> ! [X1,X2] :
        ( is_a_theorem(equiv(X1,X2))
       => X1 = X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',substitution_of_equivalents) ).

fof(op_equiv,axiom,
    ( op_equiv
   => ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',op_equiv) ).

fof(substitution_of_equivalents_001,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',substitution_of_equivalents) ).

fof(rosser_op_equiv,axiom,
    op_equiv,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',rosser_op_equiv) ).

fof(hilbert_and_2,conjecture,
    and_2,
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',hilbert_and_2) ).

fof(and_2,axiom,
    ( and_2
  <=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p',and_2) ).

fof(c_0_19,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(fof_nnf,[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_20,plain,
    ! [X77,X78,X79] :
      ( ( ~ kn3
        | is_a_theorem(implies(implies(X77,X78),implies(not(and(X78,X79)),not(and(X79,X77))))) )
      & ( ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))
        | kn3 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])])]) ).

cnf(c_0_21,plain,
    ( is_a_theorem(X2)
    | ~ modus_ponens
    | ~ is_a_theorem(X1)
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).

cnf(c_0_23,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))
    | ~ kn3 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,plain,
    kn3,
    inference(split_conjunct,[status(thm)],[rosser_kn3]) ).

fof(c_0_25,plain,
    ! [X71] :
      ( ( ~ kn1
        | is_a_theorem(implies(X71,and(X71,X71))) )
      & ( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
        | kn1 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])]) ).

cnf(c_0_26,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_21,c_0_22])]) ).

cnf(c_0_27,plain,
    is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1))))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).

cnf(c_0_28,plain,
    ( is_a_theorem(implies(X1,and(X1,X1)))
    | ~ kn1 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,plain,
    kn1,
    inference(split_conjunct,[status(thm)],[rosser_kn1]) ).

cnf(c_0_30,plain,
    ( is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X3))))
    | ~ is_a_theorem(implies(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,plain,
    is_a_theorem(implies(X1,and(X1,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

fof(c_0_32,plain,
    ! [X121,X122] :
      ( ~ op_implies_and
      | implies(X121,X122) = not(and(X121,not(X122))) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).

cnf(c_0_33,plain,
    is_a_theorem(implies(not(and(and(X1,X1),X2)),not(and(X2,X1)))),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,plain,
    ( implies(X1,X2) = not(and(X1,not(X2)))
    | ~ op_implies_and ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_35,plain,
    op_implies_and,
    inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).

fof(c_0_36,plain,
    ! [X73,X74] :
      ( ( ~ kn2
        | is_a_theorem(implies(and(X73,X74),X73)) )
      & ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
        | kn2 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])]) ).

fof(c_0_37,plain,
    ! [X117,X118] :
      ( ~ op_or
      | or(X117,X118) = not(and(not(X117),not(X118))) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).

cnf(c_0_38,plain,
    ( is_a_theorem(not(and(X1,X2)))
    | ~ is_a_theorem(not(and(and(X2,X2),X1))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_33]) ).

cnf(c_0_39,plain,
    not(and(X1,not(X2))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).

cnf(c_0_40,plain,
    ( is_a_theorem(implies(and(X1,X2),X1))
    | ~ kn2 ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_41,plain,
    kn2,
    inference(split_conjunct,[status(thm)],[rosser_kn2]) ).

cnf(c_0_42,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_43,plain,
    op_or,
    inference(split_conjunct,[status(thm)],[rosser_op_or]) ).

cnf(c_0_44,plain,
    ( is_a_theorem(not(and(not(X1),X2)))
    | ~ is_a_theorem(implies(and(X2,X2),X1)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_45,plain,
    is_a_theorem(implies(and(X1,X2),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).

cnf(c_0_46,plain,
    implies(not(X1),X2) = or(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_39]),c_0_43])]) ).

cnf(c_0_47,plain,
    is_a_theorem(not(and(not(X1),X1))),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_48,plain,
    ( is_a_theorem(implies(not(and(X1,X2)),implies(X2,X3)))
    | ~ is_a_theorem(or(X3,X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_46]),c_0_39]) ).

cnf(c_0_49,plain,
    is_a_theorem(or(not(X1),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_39]),c_0_46]) ).

cnf(c_0_50,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(or(X2,X1))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_46]) ).

cnf(c_0_51,plain,
    is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_46]) ).

cnf(c_0_52,plain,
    ( is_a_theorem(implies(X1,not(X2)))
    | ~ is_a_theorem(not(and(X2,X1))) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_53,plain,
    ( is_a_theorem(implies(not(X1),not(X2)))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_52,c_0_39]) ).

cnf(c_0_54,plain,
    is_a_theorem(implies(not(X1),not(and(X1,X2)))),
    inference(spm,[status(thm)],[c_0_53,c_0_45]) ).

cnf(c_0_55,plain,
    is_a_theorem(implies(not(X1),implies(X1,X2))),
    inference(spm,[status(thm)],[c_0_54,c_0_39]) ).

cnf(c_0_56,plain,
    is_a_theorem(or(and(X1,X1),not(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_31]),c_0_46]) ).

cnf(c_0_57,plain,
    is_a_theorem(or(and(implies(X1,X2),X3),implies(X3,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_55]),c_0_39]),c_0_46]) ).

cnf(c_0_58,plain,
    or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_46,c_0_39]) ).

cnf(c_0_59,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),not(and(not(X3),X1))))),
    inference(spm,[status(thm)],[c_0_27,c_0_39]) ).

cnf(c_0_60,plain,
    ( is_a_theorem(not(X1))
    | ~ is_a_theorem(not(and(X1,X1))) ),
    inference(spm,[status(thm)],[c_0_50,c_0_56]) ).

cnf(c_0_61,plain,
    is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_46]),c_0_58]) ).

cnf(c_0_62,plain,
    ( is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X3))))
    | ~ is_a_theorem(implies(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_59]) ).

cnf(c_0_63,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(not(not(X1))) ),
    inference(spm,[status(thm)],[c_0_50,c_0_49]) ).

cnf(c_0_64,plain,
    ( is_a_theorem(not(not(X1)))
    | ~ is_a_theorem(or(X1,X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_39]),c_0_46]) ).

cnf(c_0_65,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_61]) ).

cnf(c_0_66,plain,
    is_a_theorem(implies(implies(implies(X1,X2),X3),implies(not(X3),X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_55]),c_0_39]) ).

cnf(c_0_67,plain,
    is_a_theorem(implies(X1,not(not(X1)))),
    inference(spm,[status(thm)],[c_0_52,c_0_47]) ).

fof(c_0_68,plain,
    ! [X101,X102] :
      ( ( ~ r3
        | is_a_theorem(implies(or(X101,X102),or(X102,X101))) )
      & ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
        | r3 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])]) ).

cnf(c_0_69,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_70,plain,
    is_a_theorem(or(implies(not(X1),X2),implies(X2,X3))),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_71,plain,
    ( is_a_theorem(not(and(X1,X2)))
    | ~ is_a_theorem(not(X1)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_54]) ).

cnf(c_0_72,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(not(X1)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_55]) ).

cnf(c_0_73,plain,
    ( is_a_theorem(not(not(X1)))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_67]) ).

cnf(c_0_74,plain,
    ( r3
    | ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

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

cnf(c_0_76,plain,
    ( is_a_theorem(not(and(X1,X2)))
    | ~ is_a_theorem(not(and(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_38,c_0_71]) ).

cnf(c_0_77,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_78,plain,
    ( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
    | ~ r3 ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_79,plain,
    ( r3
    | ~ is_a_theorem(implies(implies(not(esk48_0),esk49_0),or(esk49_0,esk48_0))) ),
    inference(rw,[status(thm)],[c_0_74,c_0_46]) ).

cnf(c_0_80,plain,
    is_a_theorem(or(and(not(X1),X2),implies(X2,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_75]),c_0_39]),c_0_46]) ).

cnf(c_0_81,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(or(X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_39]),c_0_39]),c_0_46]) ).

cnf(c_0_82,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_46]) ).

cnf(c_0_83,plain,
    ( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
    | ~ is_a_theorem(implies(implies(not(esk48_0),esk49_0),or(esk49_0,esk48_0))) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_84,plain,
    is_a_theorem(implies(implies(not(X1),X2),or(X2,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_46]),c_0_58]) ).

cnf(c_0_85,plain,
    ( is_a_theorem(implies(not(and(X1,X2)),implies(X2,X3)))
    | ~ is_a_theorem(implies(not(X3),X1)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_46]) ).

cnf(c_0_86,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_87,plain,
    is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_46]),c_0_58]) ).

cnf(c_0_88,plain,
    ( is_a_theorem(implies(implies(X1,X2),X3))
    | ~ is_a_theorem(and(X1,not(X2))) ),
    inference(spm,[status(thm)],[c_0_77,c_0_39]) ).

cnf(c_0_89,plain,
    ( is_a_theorem(and(X1,X1))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_31]) ).

cnf(c_0_90,plain,
    is_a_theorem(implies(or(X1,X2),or(X2,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).

cnf(c_0_91,plain,
    ( is_a_theorem(implies(not(and(X1,X2)),implies(X2,X3)))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_92,plain,
    ( is_a_theorem(or(X1,not(X2)))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_87]) ).

cnf(c_0_93,plain,
    ( is_a_theorem(implies(or(X1,X1),X2))
    | ~ is_a_theorem(not(X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_46]) ).

fof(c_0_94,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(fof_nnf,[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_95,plain,
    ! [X125,X126] :
      ( ~ op_equiv
      | equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).

cnf(c_0_96,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_90]) ).

cnf(c_0_97,plain,
    ( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_91,c_0_46]) ).

cnf(c_0_98,plain,
    ( is_a_theorem(not(X1))
    | ~ is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_50,c_0_92]) ).

cnf(c_0_99,plain,
    ( is_a_theorem(not(X1))
    | ~ is_a_theorem(implies(X1,not(X1))) ),
    inference(spm,[status(thm)],[c_0_69,c_0_92]) ).

cnf(c_0_100,plain,
    ( is_a_theorem(implies(or(not(X1),not(X1)),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_93,c_0_73]) ).

cnf(c_0_101,plain,
    ( X1 = X2
    | ~ substitution_of_equivalents
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_102,plain,
    substitution_of_equivalents,
    inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).

cnf(c_0_103,plain,
    ( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
    | ~ op_equiv ),
    inference(split_conjunct,[status(thm)],[c_0_95]) ).

cnf(c_0_104,plain,
    op_equiv,
    inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).

cnf(c_0_105,plain,
    ( is_a_theorem(or(implies(X1,X2),and(X3,X1)))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_106,plain,
    ( is_a_theorem(not(implies(X1,X2)))
    | ~ is_a_theorem(not(or(X2,not(X1)))) ),
    inference(spm,[status(thm)],[c_0_98,c_0_87]) ).

cnf(c_0_107,plain,
    ( is_a_theorem(not(or(not(X1),not(X1))))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_108,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).

cnf(c_0_109,plain,
    equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).

cnf(c_0_110,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(not(implies(X2,X3)))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_105]) ).

cnf(c_0_111,plain,
    ( is_a_theorem(not(implies(X1,not(X1))))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_106,c_0_107]) ).

cnf(c_0_112,plain,
    ( X1 = X2
    | ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
    inference(rw,[status(thm)],[c_0_108,c_0_109]) ).

cnf(c_0_113,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(X1)
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_110,c_0_111]) ).

cnf(c_0_114,plain,
    ( X1 = X2
    | ~ is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_112,c_0_113]) ).

fof(c_0_115,negated_conjecture,
    ~ and_2,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_and_2])]) ).

cnf(c_0_116,plain,
    is_a_theorem(implies(implies(and(X1,X1),X2),not(and(not(X2),X1)))),
    inference(spm,[status(thm)],[c_0_33,c_0_39]) ).

cnf(c_0_117,plain,
    not(not(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_67]),c_0_46]),c_0_49])]) ).

fof(c_0_118,plain,
    ! [X37,X38] :
      ( ( ~ and_2
        | is_a_theorem(implies(and(X37,X38),X38)) )
      & ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
        | and_2 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])])]) ).

fof(c_0_119,negated_conjecture,
    ~ and_2,
    inference(fof_nnf,[status(thm)],[c_0_115]) ).

cnf(c_0_120,plain,
    is_a_theorem(or(not(and(not(X1),X2)),and(X2,X2))),
    inference(spm,[status(thm)],[c_0_65,c_0_116]) ).

cnf(c_0_121,plain,
    or(not(X1),X2) = implies(X1,X2),
    inference(spm,[status(thm)],[c_0_46,c_0_117]) ).

cnf(c_0_122,plain,
    and(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_31]),c_0_45])]) ).

cnf(c_0_123,plain,
    ( and_2
    | ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_118]) ).

cnf(c_0_124,negated_conjecture,
    ~ and_2,
    inference(split_conjunct,[status(thm)],[c_0_119]) ).

cnf(c_0_125,plain,
    is_a_theorem(implies(and(not(X1),X2),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121]),c_0_122]) ).

cnf(c_0_126,plain,
    ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)),
    inference(sr,[status(thm)],[c_0_123,c_0_124]) ).

cnf(c_0_127,plain,
    is_a_theorem(implies(and(X1,X2),X2)),
    inference(spm,[status(thm)],[c_0_125,c_0_117]) ).

cnf(c_0_128,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : LCL507+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.10  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n002.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Fri May  3 09:23:42 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.14/0.40  Running first-order model finding
% 0.14/0.40  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.VYpbOkQAZZ/E---3.1_1252.p
% 8.63/1.51  # Version: 3.1.0
% 8.63/1.51  # Preprocessing class: FSMSSLSSSSSNFFN.
% 8.63/1.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.63/1.51  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 8.63/1.51  # Starting new_bool_3 with 300s (1) cores
% 8.63/1.51  # Starting new_bool_1 with 300s (1) cores
% 8.63/1.51  # Starting sh5l with 300s (1) cores
% 8.63/1.51  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1334 completed with status 0
% 8.63/1.51  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 8.63/1.51  # Preprocessing class: FSMSSLSSSSSNFFN.
% 8.63/1.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.63/1.51  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 8.63/1.51  # No SInE strategy applied
% 8.63/1.51  # Search class: FGUSF-FFMM21-MFFFFFNN
% 8.63/1.51  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.63/1.51  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 8.63/1.51  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 8.63/1.51  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 8.63/1.51  # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.63/1.51  # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 8.63/1.51  # G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 1346 completed with status 0
% 8.63/1.51  # Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 8.63/1.51  # Preprocessing class: FSMSSLSSSSSNFFN.
% 8.63/1.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.63/1.51  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 8.63/1.51  # No SInE strategy applied
% 8.63/1.51  # Search class: FGUSF-FFMM21-MFFFFFNN
% 8.63/1.51  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.63/1.51  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 8.63/1.51  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 8.63/1.51  # Preprocessing time       : 0.002 s
% 8.63/1.51  # Presaturation interreduction done
% 8.63/1.51  
% 8.63/1.51  # Proof found!
% 8.63/1.51  # SZS status Theorem
% 8.63/1.51  # SZS output start CNFRefutation
% See solution above
% 8.63/1.51  # Parsed axioms                        : 43
% 8.63/1.51  # Removed by relevancy pruning/SinE    : 0
% 8.63/1.51  # Initial clauses                      : 72
% 8.63/1.51  # Removed in clause preprocessing      : 0
% 8.63/1.51  # Initial clauses in saturation        : 72
% 8.63/1.51  # Processed clauses                    : 5440
% 8.63/1.51  # ...of these trivial                  : 196
% 8.63/1.51  # ...subsumed                          : 4017
% 8.63/1.51  # ...remaining for further processing  : 1227
% 8.63/1.51  # Other redundant clauses eliminated   : 0
% 8.63/1.51  # Clauses deleted for lack of memory   : 0
% 8.63/1.51  # Backward-subsumed                    : 15
% 8.63/1.51  # Backward-rewritten                   : 262
% 8.63/1.51  # Generated clauses                    : 86809
% 8.63/1.51  # ...of the previous two non-redundant : 82359
% 8.63/1.51  # ...aggressively subsumed             : 0
% 8.63/1.51  # Contextual simplify-reflections      : 0
% 8.63/1.51  # Paramodulations                      : 86809
% 8.63/1.51  # Factorizations                       : 0
% 8.63/1.51  # NegExts                              : 0
% 8.63/1.51  # Equation resolutions                 : 0
% 8.63/1.51  # Disequality decompositions           : 0
% 8.63/1.51  # Total rewrite steps                  : 17895
% 8.63/1.51  # ...of those cached                   : 14169
% 8.63/1.51  # Propositional unsat checks           : 0
% 8.63/1.51  #    Propositional check models        : 0
% 8.63/1.51  #    Propositional check unsatisfiable : 0
% 8.63/1.51  #    Propositional clauses             : 0
% 8.63/1.51  #    Propositional clauses after purity: 0
% 8.63/1.51  #    Propositional unsat core size     : 0
% 8.63/1.51  #    Propositional preprocessing time  : 0.000
% 8.63/1.51  #    Propositional encoding time       : 0.000
% 8.63/1.51  #    Propositional solver time         : 0.000
% 8.63/1.51  #    Success case prop preproc time    : 0.000
% 8.63/1.51  #    Success case prop encoding time   : 0.000
% 8.63/1.51  #    Success case prop solver time     : 0.000
% 8.63/1.51  # Current number of processed clauses  : 892
% 8.63/1.51  #    Positive orientable unit clauses  : 379
% 8.63/1.51  #    Positive unorientable unit clauses: 28
% 8.63/1.51  #    Negative unit clauses             : 4
% 8.63/1.51  #    Non-unit-clauses                  : 481
% 8.63/1.51  # Current number of unprocessed clauses: 74432
% 8.63/1.51  # ...number of literals in the above   : 115699
% 8.63/1.51  # Current number of archived formulas  : 0
% 8.63/1.51  # Current number of archived clauses   : 335
% 8.63/1.51  # Clause-clause subsumption calls (NU) : 96029
% 8.63/1.51  # Rec. Clause-clause subsumption calls : 95929
% 8.63/1.51  # Non-unit clause-clause subsumptions  : 4008
% 8.63/1.51  # Unit Clause-clause subsumption calls : 7236
% 8.63/1.51  # Rewrite failures with RHS unbound    : 22
% 8.63/1.51  # BW rewrite match attempts            : 11787
% 8.63/1.51  # BW rewrite match successes           : 579
% 8.63/1.51  # Condensation attempts                : 0
% 8.63/1.51  # Condensation successes               : 0
% 8.63/1.51  # Termbank termtop insertions          : 1218374
% 8.63/1.51  # Search garbage collected termcells   : 1095
% 8.63/1.51  
% 8.63/1.51  # -------------------------------------------------
% 8.63/1.51  # User time                : 1.024 s
% 8.63/1.51  # System time              : 0.052 s
% 8.63/1.51  # Total time               : 1.076 s
% 8.63/1.51  # Maximum resident set size: 1940 pages
% 8.63/1.51  
% 8.63/1.51  # -------------------------------------------------
% 8.63/1.51  # User time                : 5.143 s
% 8.63/1.51  # System time              : 0.214 s
% 8.63/1.51  # Total time               : 5.358 s
% 8.63/1.51  # Maximum resident set size: 1732 pages
% 8.63/1.51  % E---3.1 exiting
%------------------------------------------------------------------------------