TSTP Solution File: LCL492+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : LCL492+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 23:57:06 EDT 2024

% Result   : Theorem 61.24s 8.22s
% Output   : CNFRefutation 61.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  245 ( 165 unt;   0 def)
%            Number of atoms       :  365 (  78 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  215 (  95   ~;  93   |;  12   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   16 (  14 usr;  14 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;  18 con; 0-2 aty)
%            Number of variables   :  481 (  64 sgn  56   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(op_implies_or,axiom,
    ( op_implies_or
   => ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).

fof(op_and,axiom,
    ( op_and
   => ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).

fof(principia_op_implies_or,axiom,
    op_implies_or,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).

fof(hilbert_op_implies_and,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

fof(principia_op_and,axiom,
    op_and,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).

fof(op_or,axiom,
    ( op_or
   => ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).

fof(r1,axiom,
    ( r1
  <=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).

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

fof(hilbert_op_or,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).

fof(principia_r1,axiom,
    r1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).

fof(principia_modus_ponens,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).

fof(r5,axiom,
    ( r5
  <=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6)))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).

fof(principia_r5,axiom,
    r5,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).

fof(r2,axiom,
    ( r2
  <=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).

fof(r3,axiom,
    ( r3
  <=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).

fof(principia_r2,axiom,
    r2,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).

fof(r4,axiom,
    ( r4
  <=> ! [X4,X5,X6] : is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6)))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).

fof(principia_r3,axiom,
    r3,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).

fof(principia_r4,axiom,
    r4,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).

fof(op_equiv,axiom,
    ( op_equiv
   => ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).

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

fof(principia_op_equiv,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_equiv) ).

fof(substitution_of_equivalents_001,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',substitution_of_equivalents) ).

fof(hilbert_or_3,conjecture,
    or_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).

fof(or_3,axiom,
    ( or_3
  <=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).

fof(c_0_26,plain,
    ! [X123,X124] :
      ( ~ op_implies_or
      | implies(X123,X124) = or(not(X123),X124) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])]) ).

fof(c_0_27,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])])])]) ).

fof(c_0_28,plain,
    ! [X119,X120] :
      ( ~ op_and
      | and(X119,X120) = not(or(not(X119),not(X120))) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])]) ).

cnf(c_0_29,plain,
    ( implies(X1,X2) = or(not(X1),X2)
    | ~ op_implies_or ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_30,plain,
    op_implies_or,
    inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).

cnf(c_0_31,plain,
    ( implies(X1,X2) = not(and(X1,not(X2)))
    | ~ op_implies_and ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,plain,
    op_implies_and,
    inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).

cnf(c_0_33,plain,
    ( and(X1,X2) = not(or(not(X1),not(X2)))
    | ~ op_and ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_34,plain,
    or(not(X1),X2) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).

cnf(c_0_35,plain,
    op_and,
    inference(split_conjunct,[status(thm)],[principia_op_and]) ).

fof(c_0_36,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_37,plain,
    not(and(X1,not(X2))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).

cnf(c_0_38,plain,
    and(X1,X2) = not(implies(X1,not(X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).

fof(c_0_39,plain,
    ! [X95] :
      ( ( ~ r1
        | is_a_theorem(implies(or(X95,X95),X95)) )
      & ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
        | r1 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])]) ).

fof(c_0_40,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])])])])])]) ).

cnf(c_0_41,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_42,plain,
    not(not(implies(X1,not(not(X2))))) = implies(X1,X2),
    inference(rw,[status(thm)],[c_0_37,c_0_38]) ).

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

cnf(c_0_44,plain,
    ( is_a_theorem(implies(or(X1,X1),X1))
    | ~ r1 ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_45,plain,
    r1,
    inference(split_conjunct,[status(thm)],[principia_r1]) ).

cnf(c_0_46,plain,
    ( is_a_theorem(X2)
    | ~ modus_ponens
    | ~ is_a_theorem(X1)
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_47,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).

cnf(c_0_48,plain,
    or(X1,X2) = implies(not(X1),X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_38]),c_0_42]),c_0_43])]) ).

cnf(c_0_49,plain,
    is_a_theorem(implies(or(X1,X1),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).

fof(c_0_50,plain,
    ! [X111,X112,X113] :
      ( ( ~ r5
        | is_a_theorem(implies(implies(X112,X113),implies(or(X111,X112),or(X111,X113)))) )
      & ( ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))
        | r5 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])])]) ).

cnf(c_0_51,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_46,c_0_47])]) ).

cnf(c_0_52,plain,
    implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_42]),c_0_34]) ).

cnf(c_0_53,plain,
    is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
    inference(spm,[status(thm)],[c_0_49,c_0_34]) ).

cnf(c_0_54,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))
    | ~ r5 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_55,plain,
    r5,
    inference(split_conjunct,[status(thm)],[principia_r5]) ).

cnf(c_0_56,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,not(not(X3))))
    | ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_57,plain,
    is_a_theorem(implies(or(X1,X1),not(not(X1)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_48]) ).

cnf(c_0_58,plain,
    is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).

cnf(c_0_59,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(implies(or(X2,X2),X2),X1)) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_60,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_34]) ).

fof(c_0_61,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])]) ).

fof(c_0_62,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_63,plain,
    is_a_theorem(implies(implies(X1,or(X2,X2)),implies(X1,X2))),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_64,plain,
    ( is_a_theorem(implies(X1,or(X2,X1)))
    | ~ r2 ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_65,plain,
    r2,
    inference(split_conjunct,[status(thm)],[principia_r2]) ).

fof(c_0_66,plain,
    ! [X105,X106,X107] :
      ( ( ~ r4
        | is_a_theorem(implies(or(X105,or(X106,X107)),or(X106,or(X105,X107)))) )
      & ( ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))
        | r4 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])])]) ).

cnf(c_0_67,plain,
    ( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
    | ~ r3 ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_68,plain,
    r3,
    inference(split_conjunct,[status(thm)],[principia_r3]) ).

cnf(c_0_69,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(X1,or(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_63]) ).

cnf(c_0_70,plain,
    is_a_theorem(implies(X1,or(X2,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).

cnf(c_0_71,plain,
    ( is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))
    | ~ r4 ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_72,plain,
    r4,
    inference(split_conjunct,[status(thm)],[principia_r4]) ).

fof(c_0_73,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_74,plain,
    is_a_theorem(implies(or(X1,X2),or(X2,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).

cnf(c_0_75,plain,
    is_a_theorem(implies(X1,X1)),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_76,plain,
    implies(not(not(X1)),X2) = implies(X1,X2),
    inference(spm,[status(thm)],[c_0_34,c_0_48]) ).

cnf(c_0_77,plain,
    is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).

fof(c_0_78,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])])])])])]) ).

cnf(c_0_79,plain,
    ( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
    | ~ op_equiv ),
    inference(split_conjunct,[status(thm)],[c_0_73]) ).

cnf(c_0_80,plain,
    op_equiv,
    inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).

cnf(c_0_81,plain,
    is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_74,c_0_34]) ).

cnf(c_0_82,plain,
    or(implies(X1,X2),X3) = implies(not(implies(X1,not(not(X2)))),X3),
    inference(spm,[status(thm)],[c_0_34,c_0_42]) ).

cnf(c_0_83,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_75]),c_0_76]) ).

cnf(c_0_84,plain,
    is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_34]),c_0_34]) ).

cnf(c_0_85,plain,
    ( X1 = X2
    | ~ substitution_of_equivalents
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_86,plain,
    substitution_of_equivalents,
    inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).

cnf(c_0_87,plain,
    equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).

cnf(c_0_88,plain,
    is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))),
    inference(spm,[status(thm)],[c_0_81,c_0_34]) ).

cnf(c_0_89,plain,
    or(implies(X1,not(not(X2))),X3) = or(implies(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_48,c_0_82]) ).

cnf(c_0_90,plain,
    is_a_theorem(implies(or(X1,or(X2,X2)),or(X1,X2))),
    inference(spm,[status(thm)],[c_0_59,c_0_58]) ).

cnf(c_0_91,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_74]) ).

cnf(c_0_92,plain,
    is_a_theorem(or(X1,implies(or(X1,X2),X2))),
    inference(spm,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_93,plain,
    ( X1 = X2
    | ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).

cnf(c_0_94,plain,
    ( is_a_theorem(implies(X1,not(X2)))
    | ~ is_a_theorem(implies(X2,not(X1))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_88]) ).

cnf(c_0_95,plain,
    or(or(X1,not(not(X2))),X3) = or(implies(not(X1),X2),X3),
    inference(spm,[status(thm)],[c_0_89,c_0_48]) ).

cnf(c_0_96,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(X1,or(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_90]) ).

cnf(c_0_97,plain,
    is_a_theorem(or(implies(or(X1,X2),X2),X1)),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_98,plain,
    ( X1 = X2
    | ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
    inference(rw,[status(thm)],[c_0_93,c_0_38]) ).

cnf(c_0_99,plain,
    is_a_theorem(implies(X1,not(implies(X1,not(X1))))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_49]),c_0_34]) ).

cnf(c_0_100,plain,
    is_a_theorem(implies(implies(not(X1),X2),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_74,c_0_48]) ).

cnf(c_0_101,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_70]) ).

cnf(c_0_102,plain,
    or(or(X1,not(not(X2))),X3) = or(or(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_95,c_0_48]) ).

cnf(c_0_103,plain,
    is_a_theorem(implies(or(X1,implies(X2,X3)),implies(X2,or(X1,X3)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_34]),c_0_34]) ).

cnf(c_0_104,plain,
    is_a_theorem(or(implies(or(or(X1,X1),X2),X2),X1)),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_105,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(not(X3),X1),or(X3,X2)))),
    inference(spm,[status(thm)],[c_0_58,c_0_48]) ).

cnf(c_0_106,plain,
    is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_34]),c_0_34]) ).

cnf(c_0_107,plain,
    ( X1 = not(not(X2))
    | ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_76]),c_0_52]) ).

cnf(c_0_108,plain,
    ( is_a_theorem(not(implies(X1,not(X1))))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_99]) ).

cnf(c_0_109,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(implies(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_100]) ).

cnf(c_0_110,plain,
    is_a_theorem(implies(X1,implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_70,c_0_34]) ).

cnf(c_0_111,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_91,c_0_101]) ).

cnf(c_0_112,plain,
    or(or(X1,X2),X3) = implies(not(or(X1,not(not(X2)))),X3),
    inference(spm,[status(thm)],[c_0_48,c_0_102]) ).

cnf(c_0_113,plain,
    implies(not(implies(X1,not(not(X2)))),X3) = implies(not(implies(X1,X2)),X3),
    inference(spm,[status(thm)],[c_0_76,c_0_42]) ).

cnf(c_0_114,plain,
    ( is_a_theorem(implies(X1,or(X2,X3)))
    | ~ is_a_theorem(or(X2,implies(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_103]) ).

cnf(c_0_115,plain,
    is_a_theorem(or(X1,implies(or(or(X1,X1),X2),X2))),
    inference(spm,[status(thm)],[c_0_91,c_0_104]) ).

cnf(c_0_116,plain,
    is_a_theorem(implies(implies(not(X1),X2),or(X1,X2))),
    inference(spm,[status(thm)],[c_0_83,c_0_105]) ).

cnf(c_0_117,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(X2,implies(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_106]) ).

cnf(c_0_118,plain,
    is_a_theorem(implies(or(X1,not(X2)),implies(X2,not(not(X1))))),
    inference(spm,[status(thm)],[c_0_88,c_0_48]) ).

cnf(c_0_119,plain,
    not(not(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_75])]) ).

cnf(c_0_120,plain,
    is_a_theorem(or(implies(X1,not(X2)),X2)),
    inference(spm,[status(thm)],[c_0_109,c_0_110]) ).

cnf(c_0_121,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_111,c_0_48]) ).

cnf(c_0_122,plain,
    or(or(X1,X2),X3) = implies(not(implies(not(X1),X2)),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_48]),c_0_113]) ).

cnf(c_0_123,plain,
    is_a_theorem(implies(or(or(X1,X1),X2),or(X1,X2))),
    inference(spm,[status(thm)],[c_0_114,c_0_115]) ).

cnf(c_0_124,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(implies(not(X1),X2)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_116]) ).

cnf(c_0_125,plain,
    is_a_theorem(implies(X1,implies(or(X2,not(X1)),X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]) ).

cnf(c_0_126,plain,
    is_a_theorem(or(implies(X1,X2),not(X2))),
    inference(spm,[status(thm)],[c_0_120,c_0_89]) ).

cnf(c_0_127,plain,
    ( is_a_theorem(or(or(X1,X2),X3))
    | ~ is_a_theorem(implies(not(X1),X2)) ),
    inference(spm,[status(thm)],[c_0_121,c_0_122]) ).

cnf(c_0_128,plain,
    is_a_theorem(implies(not(X1),implies(or(X1,X2),X2))),
    inference(spm,[status(thm)],[c_0_92,c_0_48]) ).

cnf(c_0_129,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(or(X1,X1),X2)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_123]) ).

cnf(c_0_130,plain,
    is_a_theorem(or(X1,implies(or(X2,X1),X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_119]) ).

cnf(c_0_131,plain,
    is_a_theorem(or(implies(X1,X2),not(not(not(X2))))),
    inference(spm,[status(thm)],[c_0_126,c_0_89]) ).

cnf(c_0_132,plain,
    ( is_a_theorem(implies(or(X1,X2),or(X1,X3)))
    | ~ is_a_theorem(implies(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_58]) ).

cnf(c_0_133,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(or(X2,not(X1))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_81]) ).

cnf(c_0_134,plain,
    is_a_theorem(or(or(X1,implies(or(X1,X2),X2)),X3)),
    inference(spm,[status(thm)],[c_0_127,c_0_128]) ).

cnf(c_0_135,plain,
    is_a_theorem(or(X1,implies(or(X2,or(X1,X1)),X2))),
    inference(spm,[status(thm)],[c_0_129,c_0_130]) ).

cnf(c_0_136,plain,
    is_a_theorem(or(or(X1,X2),not(not(not(X2))))),
    inference(spm,[status(thm)],[c_0_131,c_0_48]) ).

cnf(c_0_137,plain,
    is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
    inference(spm,[status(thm)],[c_0_74,c_0_34]) ).

cnf(c_0_138,plain,
    is_a_theorem(or(implies(not(X1),or(X2,not(X1))),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_70]),c_0_48]) ).

cnf(c_0_139,plain,
    ( is_a_theorem(implies(or(X1,X2),X1))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_69,c_0_132]) ).

cnf(c_0_140,plain,
    is_a_theorem(implies(X1,or(X2,implies(or(X2,X3),X3)))),
    inference(spm,[status(thm)],[c_0_133,c_0_134]) ).

cnf(c_0_141,plain,
    is_a_theorem(implies(or(X1,or(X2,X2)),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_114,c_0_135]) ).

cnf(c_0_142,plain,
    is_a_theorem(implies(not(or(X1,X2)),not(not(not(X2))))),
    inference(spm,[status(thm)],[c_0_136,c_0_48]) ).

cnf(c_0_143,plain,
    is_a_theorem(implies(or(X1,X2),implies(not(X2),X1))),
    inference(spm,[status(thm)],[c_0_74,c_0_48]) ).

cnf(c_0_144,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(or(X2,X1))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_48]) ).

cnf(c_0_145,plain,
    ( is_a_theorem(or(X1,not(X2)))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_137]) ).

cnf(c_0_146,plain,
    is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
    inference(spm,[status(thm)],[c_0_83,c_0_106]) ).

cnf(c_0_147,plain,
    is_a_theorem(or(implies(X1,or(X2,X1)),X3)),
    inference(spm,[status(thm)],[c_0_138,c_0_119]) ).

cnf(c_0_148,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_139]) ).

cnf(c_0_149,plain,
    is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_34]),c_0_34]) ).

cnf(c_0_150,plain,
    ( is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(or(X2,or(X1,X1))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_141]) ).

cnf(c_0_151,plain,
    is_a_theorem(or(or(or(X1,X2),not(X2)),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_142]),c_0_119]) ).

cnf(c_0_152,plain,
    is_a_theorem(implies(implies(X1,X2),implies(not(X2),not(X1)))),
    inference(spm,[status(thm)],[c_0_143,c_0_34]) ).

cnf(c_0_153,plain,
    ( is_a_theorem(not(X1))
    | ~ is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_144,c_0_145]) ).

cnf(c_0_154,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_146]) ).

cnf(c_0_155,plain,
    is_a_theorem(implies(X1,implies(X2,or(X3,X2)))),
    inference(spm,[status(thm)],[c_0_133,c_0_147]) ).

cnf(c_0_156,plain,
    ( is_a_theorem(implies(or(X1,X2),X2))
    | ~ is_a_theorem(implies(X1,implies(or(X1,X2),X2))) ),
    inference(spm,[status(thm)],[c_0_148,c_0_97]) ).

cnf(c_0_157,plain,
    is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X3),X3)))),
    inference(spm,[status(thm)],[c_0_117,c_0_149]) ).

cnf(c_0_158,plain,
    ( is_a_theorem(or(X1,or(X2,X3)))
    | ~ is_a_theorem(or(X2,or(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_77]) ).

cnf(c_0_159,plain,
    is_a_theorem(or(X1,or(or(X2,X3),not(X3)))),
    inference(spm,[status(thm)],[c_0_150,c_0_151]) ).

cnf(c_0_160,plain,
    ( is_a_theorem(implies(not(X1),not(X2)))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_152]) ).

cnf(c_0_161,plain,
    ( is_a_theorem(not(implies(X1,X2)))
    | ~ is_a_theorem(not(X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_153,c_0_154]) ).

cnf(c_0_162,plain,
    is_a_theorem(implies(X1,implies(X2,or(X3,X1)))),
    inference(spm,[status(thm)],[c_0_117,c_0_155]) ).

cnf(c_0_163,plain,
    is_a_theorem(implies(or(X1,implies(implies(X1,X2),X2)),implies(implies(X1,X2),X2))),
    inference(spm,[status(thm)],[c_0_156,c_0_157]) ).

cnf(c_0_164,plain,
    is_a_theorem(or(or(X1,X2),or(X3,not(X2)))),
    inference(spm,[status(thm)],[c_0_158,c_0_159]) ).

cnf(c_0_165,plain,
    is_a_theorem(implies(not(or(X1,X2)),not(or(X2,X1)))),
    inference(spm,[status(thm)],[c_0_160,c_0_74]) ).

cnf(c_0_166,plain,
    ( X1 = X2
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_161]),c_0_119]) ).

cnf(c_0_167,plain,
    is_a_theorem(implies(or(X1,or(X2,X1)),or(X2,X1))),
    inference(spm,[status(thm)],[c_0_156,c_0_162]) ).

cnf(c_0_168,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(or(X1,implies(implies(X1,X2),X2))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_163]) ).

cnf(c_0_169,plain,
    is_a_theorem(or(or(X1,X2),implies(X3,not(X2)))),
    inference(spm,[status(thm)],[c_0_164,c_0_34]) ).

cnf(c_0_170,plain,
    is_a_theorem(implies(or(X1,X2),not(not(or(X2,X1))))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_165]),c_0_76]) ).

cnf(c_0_171,plain,
    or(X1,or(X2,X1)) = or(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_70])]) ).

cnf(c_0_172,plain,
    or(X1,X2) = or(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_74]),c_0_74])]) ).

cnf(c_0_173,plain,
    is_a_theorem(implies(not(implies(X1,X2)),not(not(not(X2))))),
    inference(spm,[status(thm)],[c_0_131,c_0_48]) ).

cnf(c_0_174,plain,
    is_a_theorem(implies(implies(or(X1,X2),not(X2)),not(X2))),
    inference(spm,[status(thm)],[c_0_168,c_0_169]) ).

cnf(c_0_175,plain,
    is_a_theorem(implies(or(X1,not(X2)),not(not(implies(X2,X1))))),
    inference(spm,[status(thm)],[c_0_170,c_0_34]) ).

cnf(c_0_176,plain,
    or(X1,or(X1,X2)) = or(X1,X2),
    inference(spm,[status(thm)],[c_0_171,c_0_172]) ).

cnf(c_0_177,plain,
    or(X1,or(X2,X3)) = or(X2,or(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_77]),c_0_77])]) ).

cnf(c_0_178,plain,
    is_a_theorem(or(or(implies(X1,X2),not(X2)),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_173]),c_0_119]) ).

cnf(c_0_179,plain,
    implies(or(X1,not(not(X2))),X3) = implies(implies(not(X1),X2),X3),
    inference(spm,[status(thm)],[c_0_52,c_0_48]) ).

cnf(c_0_180,plain,
    implies(or(X1,X2),not(X2)) = not(X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_174]),c_0_110])]) ).

cnf(c_0_181,plain,
    or(X1,not(X2)) = implies(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_175]),c_0_119]),c_0_76]),c_0_137])]) ).

cnf(c_0_182,plain,
    or(X1,or(X2,or(X1,X3))) = or(X2,or(X1,X3)),
    inference(spm,[status(thm)],[c_0_176,c_0_177]) ).

cnf(c_0_183,plain,
    is_a_theorem(or(X1,or(implies(X2,X3),not(X3)))),
    inference(spm,[status(thm)],[c_0_150,c_0_178]) ).

cnf(c_0_184,plain,
    is_a_theorem(implies(X1,or(X2,not(not(X1))))),
    inference(spm,[status(thm)],[c_0_70,c_0_76]) ).

cnf(c_0_185,plain,
    implies(or(X1,not(not(X2))),X3) = implies(or(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_179,c_0_48]) ).

cnf(c_0_186,plain,
    not(not(or(X1,not(not(X2))))) = implies(not(X1),X2),
    inference(spm,[status(thm)],[c_0_42,c_0_48]) ).

cnf(c_0_187,plain,
    implies(implies(X1,X2),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_119]),c_0_181]) ).

cnf(c_0_188,plain,
    implies(X1,or(X2,implies(X1,X3))) = or(X2,implies(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_182]),c_0_34]),c_0_34]) ).

cnf(c_0_189,plain,
    is_a_theorem(or(implies(X1,X2),or(X3,not(X2)))),
    inference(spm,[status(thm)],[c_0_158,c_0_183]) ).

cnf(c_0_190,plain,
    is_a_theorem(implies(or(X1,X2),or(X3,implies(not(X1),X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]) ).

cnf(c_0_191,plain,
    implies(or(X1,implies(X2,X3)),X2) = X2,
    inference(spm,[status(thm)],[c_0_187,c_0_188]) ).

cnf(c_0_192,plain,
    implies(or(X1,X2),not(X1)) = not(X1),
    inference(spm,[status(thm)],[c_0_180,c_0_172]) ).

cnf(c_0_193,plain,
    is_a_theorem(or(implies(X1,X2),implies(X3,not(X2)))),
    inference(spm,[status(thm)],[c_0_189,c_0_34]) ).

cnf(c_0_194,plain,
    ( is_a_theorem(or(X1,implies(not(X2),X3)))
    | ~ is_a_theorem(or(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_190]) ).

cnf(c_0_195,plain,
    is_a_theorem(implies(or(X1,X2),not(not(implies(not(X2),X1))))),
    inference(spm,[status(thm)],[c_0_170,c_0_48]) ).

cnf(c_0_196,plain,
    or(X1,implies(implies(X1,X2),X2)) = implies(implies(X1,X2),X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_163]),c_0_70])]) ).

cnf(c_0_197,plain,
    or(X1,implies(X2,X3)) = implies(X2,or(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_103]),c_0_84])]) ).

cnf(c_0_198,plain,
    implies(implies(X1,X2),or(X1,X3)) = or(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_181]) ).

cnf(c_0_199,plain,
    is_a_theorem(implies(or(X1,implies(X2,X1)),implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_167,c_0_34]) ).

cnf(c_0_200,plain,
    is_a_theorem(implies(implies(implies(X1,X2),not(X2)),not(X2))),
    inference(spm,[status(thm)],[c_0_168,c_0_193]) ).

cnf(c_0_201,plain,
    is_a_theorem(or(X1,or(implies(or(X2,X3),X3),X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_97]),c_0_48]) ).

cnf(c_0_202,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(not(not(X2)))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_76]) ).

cnf(c_0_203,plain,
    ( is_a_theorem(not(not(X1)))
    | ~ is_a_theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_57]) ).

fof(c_0_204,negated_conjecture,
    ~ or_3,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_or_3])]) ).

cnf(c_0_205,plain,
    is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
    inference(spm,[status(thm)],[c_0_83,c_0_146]) ).

cnf(c_0_206,plain,
    is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(not(not(X1)))))),
    inference(spm,[status(thm)],[c_0_88,c_0_76]) ).

cnf(c_0_207,plain,
    implies(not(X1),X2) = or(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_195]),c_0_119]),c_0_76]),c_0_100])]) ).

cnf(c_0_208,plain,
    or(X1,X2) = implies(implies(X1,X2),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_198]) ).

cnf(c_0_209,plain,
    is_a_theorem(implies(implies(not(X1),implies(X2,X1)),implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_199,c_0_48]) ).

cnf(c_0_210,plain,
    implies(implies(X1,X2),not(X2)) = not(X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_200]),c_0_110])]) ).

cnf(c_0_211,plain,
    is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_81,c_0_48]) ).

cnf(c_0_212,plain,
    is_a_theorem(or(implies(or(X1,X2),X2),or(X3,X1))),
    inference(spm,[status(thm)],[c_0_158,c_0_201]) ).

cnf(c_0_213,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(or(X2,X2)) ),
    inference(spm,[status(thm)],[c_0_202,c_0_203]) ).

fof(c_0_214,plain,
    ! [X53,X54,X55] :
      ( ( ~ or_3
        | is_a_theorem(implies(implies(X53,X55),implies(implies(X54,X55),implies(or(X53,X54),X55)))) )
      & ( ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0))))
        | or_3 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_3])])])])]) ).

fof(c_0_215,negated_conjecture,
    ~ or_3,
    inference(fof_nnf,[status(thm)],[c_0_204]) ).

cnf(c_0_216,plain,
    implies(implies(X1,X1),X2) = X2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_205]),c_0_110])]) ).

cnf(c_0_217,plain,
    implies(X1,not(X2)) = implies(X2,not(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_206]),c_0_119]),c_0_52]),c_0_88])]) ).

cnf(c_0_218,plain,
    implies(not(X1),X2) = implies(implies(X2,X1),X1),
    inference(rw,[status(thm)],[c_0_207,c_0_208]) ).

cnf(c_0_219,plain,
    implies(not(X1),implies(X2,X1)) = implies(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_209]),c_0_110])]) ).

cnf(c_0_220,plain,
    implies(implies(X1,X2),implies(X3,X1)) = implies(X3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_210]),c_0_181]) ).

cnf(c_0_221,plain,
    implies(X1,X2) = implies(not(X2),not(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_211]),c_0_152])]) ).

cnf(c_0_222,plain,
    implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_106]),c_0_106])]) ).

cnf(c_0_223,plain,
    is_a_theorem(or(implies(or(X1,X2),X2),implies(X3,X1))),
    inference(spm,[status(thm)],[c_0_212,c_0_34]) ).

cnf(c_0_224,plain,
    ( is_a_theorem(implies(implies(X1,X2),X2))
    | ~ is_a_theorem(or(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_213,c_0_146]) ).

cnf(c_0_225,plain,
    is_a_theorem(or(implies(X1,implies(X2,X1)),X3)),
    inference(spm,[status(thm)],[c_0_147,c_0_34]) ).

cnf(c_0_226,plain,
    ( or_3
    | ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0)))) ),
    inference(split_conjunct,[status(thm)],[c_0_214]) ).

cnf(c_0_227,negated_conjecture,
    ~ or_3,
    inference(split_conjunct,[status(thm)],[c_0_215]) ).

cnf(c_0_228,plain,
    implies(X1,not(implies(X2,X2))) = not(X1),
    inference(spm,[status(thm)],[c_0_216,c_0_217]) ).

cnf(c_0_229,plain,
    implies(implies(not(X1),X2),X1) = implies(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_218]),c_0_219]) ).

cnf(c_0_230,plain,
    implies(X1,implies(implies(not(X1),X2),X3)) = implies(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_222]) ).

cnf(c_0_231,plain,
    is_a_theorem(implies(implies(implies(or(X1,X2),X2),X1),X1)),
    inference(spm,[status(thm)],[c_0_168,c_0_223]) ).

cnf(c_0_232,plain,
    is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)),
    inference(spm,[status(thm)],[c_0_224,c_0_225]) ).

cnf(c_0_233,plain,
    ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(implies(not(esk24_0),esk25_0),esk26_0)))),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_226,c_0_48]),c_0_227]) ).

cnf(c_0_234,plain,
    implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_208]),c_0_208]) ).

cnf(c_0_235,plain,
    implies(implies(X1,X2),X2) = implies(not(X1),X2),
    inference(rw,[status(thm)],[c_0_48,c_0_208]) ).

cnf(c_0_236,plain,
    not(implies(X1,not(implies(X2,X2)))) = X1,
    inference(spm,[status(thm)],[c_0_119,c_0_228]) ).

cnf(c_0_237,plain,
    implies(implies(implies(X1,X2),X3),X1) = implies(X3,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_229]),c_0_119]) ).

cnf(c_0_238,plain,
    implies(implies(or(X1,X2),X2),X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_231]),c_0_110])]) ).

cnf(c_0_239,plain,
    implies(implies(X1,implies(X2,X1)),X3) = X3,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_232]),c_0_110])]) ).

cnf(c_0_240,plain,
    implies(implies(X1,not(X2)),not(X2)) = implies(X2,X1),
    inference(rw,[status(thm)],[c_0_181,c_0_208]) ).

cnf(c_0_241,plain,
    ~ is_a_theorem(implies(not(esk26_0),implies(esk24_0,implies(implies(esk24_0,esk26_0),esk25_0)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_222]),c_0_228]),c_0_234]),c_0_235]),c_0_222]),c_0_235]),c_0_236]),c_0_222]),c_0_222]) ).

cnf(c_0_242,plain,
    implies(X1,implies(implies(X1,X2),X3)) = implies(X2,implies(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_208]),c_0_234]),c_0_239]),c_0_208]),c_0_234]),c_0_239]),c_0_222]) ).

cnf(c_0_243,plain,
    implies(X1,implies(not(X1),X2)) = implies(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_187]),c_0_221]) ).

cnf(c_0_244,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_222]),c_0_243]),c_0_75])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : LCL492+1 : TPTP v8.2.0. Released v3.3.0.
% 0.07/0.16  % Command    : run_E %s %d THM
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Mon May 20 00:58:38 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.24/0.47  Running first-order model finding
% 0.24/0.47  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 61.24/8.22  # Version: 3.1.0
% 61.24/8.22  # Preprocessing class: FSMSSLSSSSSNFFN.
% 61.24/8.22  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.24/8.22  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 61.24/8.22  # Starting new_bool_3 with 300s (1) cores
% 61.24/8.22  # Starting new_bool_1 with 300s (1) cores
% 61.24/8.22  # Starting sh5l with 300s (1) cores
% 61.24/8.22  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 8175 completed with status 0
% 61.24/8.22  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 61.24/8.22  # Preprocessing class: FSMSSLSSSSSNFFN.
% 61.24/8.22  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.24/8.22  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 61.24/8.22  # No SInE strategy applied
% 61.24/8.22  # Search class: FGUSF-FFMM21-MFFFFFNN
% 61.24/8.22  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 61.24/8.22  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 61.24/8.22  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 61.24/8.22  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 61.24/8.22  # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 61.24/8.22  # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 61.24/8.22  # U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 8189 completed with status 0
% 61.24/8.22  # Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 61.24/8.22  # Preprocessing class: FSMSSLSSSSSNFFN.
% 61.24/8.22  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 61.24/8.22  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 61.24/8.22  # No SInE strategy applied
% 61.24/8.22  # Search class: FGUSF-FFMM21-MFFFFFNN
% 61.24/8.22  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 61.24/8.22  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 61.24/8.22  # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 61.24/8.22  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 61.24/8.22  # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 61.24/8.22  # Preprocessing time       : 0.002 s
% 61.24/8.22  # Presaturation interreduction done
% 61.24/8.22  
% 61.24/8.22  # Proof found!
% 61.24/8.22  # SZS status Theorem
% 61.24/8.22  # SZS output start CNFRefutation
% See solution above
% 61.57/8.22  # Parsed axioms                        : 45
% 61.57/8.22  # Removed by relevancy pruning/SinE    : 0
% 61.57/8.22  # Initial clauses                      : 74
% 61.57/8.22  # Removed in clause preprocessing      : 0
% 61.57/8.22  # Initial clauses in saturation        : 74
% 61.57/8.22  # Processed clauses                    : 17189
% 61.57/8.22  # ...of these trivial                  : 3936
% 61.57/8.22  # ...subsumed                          : 10875
% 61.57/8.22  # ...remaining for further processing  : 2377
% 61.57/8.22  # Other redundant clauses eliminated   : 0
% 61.57/8.22  # Clauses deleted for lack of memory   : 0
% 61.57/8.22  # Backward-subsumed                    : 14
% 61.57/8.22  # Backward-rewritten                   : 1105
% 61.57/8.22  # Generated clauses                    : 477105
% 61.57/8.22  # ...of the previous two non-redundant : 301798
% 61.57/8.22  # ...aggressively subsumed             : 0
% 61.57/8.22  # Contextual simplify-reflections      : 1
% 61.57/8.22  # Paramodulations                      : 477105
% 61.57/8.22  # Factorizations                       : 0
% 61.57/8.22  # NegExts                              : 0
% 61.57/8.22  # Equation resolutions                 : 0
% 61.57/8.22  # Disequality decompositions           : 0
% 61.57/8.22  # Total rewrite steps                  : 1156323
% 61.57/8.22  # ...of those cached                   : 1076532
% 61.57/8.22  # Propositional unsat checks           : 0
% 61.57/8.22  #    Propositional check models        : 0
% 61.57/8.22  #    Propositional check unsatisfiable : 0
% 61.57/8.22  #    Propositional clauses             : 0
% 61.57/8.22  #    Propositional clauses after purity: 0
% 61.57/8.22  #    Propositional unsat core size     : 0
% 61.57/8.22  #    Propositional preprocessing time  : 0.000
% 61.57/8.22  #    Propositional encoding time       : 0.000
% 61.57/8.22  #    Propositional solver time         : 0.000
% 61.57/8.22  #    Success case prop preproc time    : 0.000
% 61.57/8.22  #    Success case prop encoding time   : 0.000
% 61.57/8.22  #    Success case prop solver time     : 0.000
% 61.57/8.22  # Current number of processed clauses  : 1197
% 61.57/8.22  #    Positive orientable unit clauses  : 873
% 61.57/8.22  #    Positive unorientable unit clauses: 31
% 61.57/8.22  #    Negative unit clauses             : 24
% 61.57/8.22  #    Non-unit-clauses                  : 269
% 61.57/8.22  # Current number of unprocessed clauses: 280319
% 61.57/8.22  # ...number of literals in the above   : 349055
% 61.57/8.22  # Current number of archived formulas  : 0
% 61.57/8.22  # Current number of archived clauses   : 1180
% 61.57/8.22  # Clause-clause subsumption calls (NU) : 115538
% 61.57/8.22  # Rec. Clause-clause subsumption calls : 114731
% 61.57/8.22  # Non-unit clause-clause subsumptions  : 6357
% 61.57/8.22  # Unit Clause-clause subsumption calls : 19428
% 61.57/8.22  # Rewrite failures with RHS unbound    : 0
% 61.57/8.22  # BW rewrite match attempts            : 134158
% 61.57/8.22  # BW rewrite match successes           : 4693
% 61.57/8.22  # Condensation attempts                : 0
% 61.57/8.22  # Condensation successes               : 0
% 61.57/8.22  # Termbank termtop insertions          : 9423128
% 61.57/8.22  # Search garbage collected termcells   : 1095
% 61.57/8.22  
% 61.57/8.22  # -------------------------------------------------
% 61.57/8.22  # User time                : 7.371 s
% 61.57/8.22  # System time              : 0.225 s
% 61.57/8.22  # Total time               : 7.596 s
% 61.57/8.22  # Maximum resident set size: 1992 pages
% 61.57/8.22  
% 61.57/8.22  # -------------------------------------------------
% 61.57/8.22  # User time                : 36.532 s
% 61.57/8.22  # System time              : 1.488 s
% 61.57/8.22  # Total time               : 38.020 s
% 61.57/8.22  # Maximum resident set size: 1744 pages
% 61.57/8.22  % E---3.1 exiting
%------------------------------------------------------------------------------