TSTP Solution File: LCL500+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 10:11:33 EDT 2022

% Result   : Theorem 0.24s 1.41s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  112 (  54 unt;   0 def)
%            Number of atoms       :  206 (  30 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  161 (  67   ~;  65   |;  13   &)
%                                         (   9 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   17 (  15 usr;  15 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  19 con; 0-2 aty)
%            Number of variables   :  159 (   9 sgn  58   !;   0   ?)

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

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

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

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

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

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

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

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

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

fof(r2,axiom,
    ( r2
  <=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).

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

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

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

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

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

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

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

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

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

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

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

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

fof(rosser_kn2,conjecture,
    kn2,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rosser_kn2) ).

fof(kn2,axiom,
    ( kn2
  <=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).

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

fof(c_0_27,plain,
    ! [X3,X4] :
      ( ~ op_implies_or
      | implies(X3,X4) = or(not(X3),X4) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])])]) ).

fof(c_0_28,plain,
    ! [X3,X4] :
      ( ~ op_and
      | and(X3,X4) = not(or(not(X3),not(X4))) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])])]) ).

cnf(c_0_29,plain,
    ( implies(X1,X2) = or(not(X1),X2)
    | ~ op_implies_or ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

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

fof(c_0_31,plain,
    ! [X3,X4] :
      ( ~ op_implies_and
      | implies(X3,X4) = not(and(X3,not(X4))) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])])]) ).

cnf(c_0_32,plain,
    ( and(X1,X2) = not(or(not(X1),not(X2)))
    | ~ op_and ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_33,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_34,plain,
    op_and,
    inference(split_conjunct,[status(thm)],[principia_op_and]) ).

fof(c_0_35,plain,
    ! [X3,X4] :
      ( ~ op_or
      | or(X3,X4) = not(and(not(X3),not(X4))) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])])]) ).

cnf(c_0_36,plain,
    ( implies(X1,X2) = not(and(X1,not(X2)))
    | ~ op_implies_and ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_37,plain,
    and(X1,X2) = not(implies(X1,not(X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_38,plain,
    op_implies_and,
    inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).

fof(c_0_39,plain,
    ! [X3,X4] :
      ( ( ~ modus_ponens
        | ~ is_a_theorem(X3)
        | ~ is_a_theorem(implies(X3,X4))
        | is_a_theorem(X4) )
      & ( is_a_theorem(esk1_0)
        | modus_ponens )
      & ( is_a_theorem(implies(esk1_0,esk2_0))
        | modus_ponens )
      & ( ~ is_a_theorem(esk2_0)
        | modus_ponens ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])])]) ).

fof(c_0_40,plain,
    ! [X7,X8,X9] :
      ( ( ~ r4
        | is_a_theorem(implies(or(X7,or(X8,X9)),or(X8,or(X7,X9)))) )
      & ( ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))
        | r4 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])])])]) ).

cnf(c_0_41,plain,
    ( or(X1,X2) = not(and(not(X1),not(X2)))
    | ~ op_or ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,plain,
    not(not(implies(X1,not(not(X2))))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).

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

fof(c_0_44,plain,
    ! [X6,X7] :
      ( ( ~ r2
        | is_a_theorem(implies(X7,or(X6,X7))) )
      & ( ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))
        | r2 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])])]) ).

fof(c_0_45,plain,
    ! [X6,X7] :
      ( ( ~ r3
        | is_a_theorem(implies(or(X6,X7),or(X7,X6))) )
      & ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
        | r3 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])])]) ).

fof(c_0_46,plain,
    ! [X5] :
      ( ( ~ r1
        | is_a_theorem(implies(or(X5,X5),X5)) )
      & ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
        | r1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])])]) ).

cnf(c_0_47,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(X2)
    | ~ modus_ponens ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_48,plain,
    modus_ponens,
    inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).

cnf(c_0_49,plain,
    ( is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))
    | ~ r4 ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_50,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_37]),c_0_42]),c_0_43])]) ).

cnf(c_0_51,plain,
    r4,
    inference(split_conjunct,[status(thm)],[principia_r4]) ).

cnf(c_0_52,plain,
    ( is_a_theorem(implies(X1,or(X2,X1)))
    | ~ r2 ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_53,plain,
    r2,
    inference(split_conjunct,[status(thm)],[principia_r2]) ).

fof(c_0_54,plain,
    ! [X7,X8,X9] :
      ( ( ~ r5
        | is_a_theorem(implies(implies(X8,X9),implies(or(X7,X8),or(X7,X9)))) )
      & ( ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))
        | r5 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])])])]) ).

cnf(c_0_55,plain,
    ( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
    | ~ r3 ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_56,plain,
    r3,
    inference(split_conjunct,[status(thm)],[principia_r3]) ).

cnf(c_0_57,plain,
    ( is_a_theorem(implies(or(X1,X1),X1))
    | ~ r1 ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_58,plain,
    r1,
    inference(split_conjunct,[status(thm)],[principia_r1]) ).

cnf(c_0_59,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_47,c_0_48])]) ).

cnf(c_0_60,plain,
    is_a_theorem(implies(implies(not(X1),implies(not(X2),X3)),implies(not(X2),implies(not(X1),X3)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_51])]) ).

cnf(c_0_61,plain,
    is_a_theorem(implies(X1,implies(not(X2),X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_50]),c_0_53])]) ).

cnf(c_0_62,plain,
    implies(not(not(X1)),X2) = implies(X1,X2),
    inference(rw,[status(thm)],[c_0_33,c_0_50]) ).

cnf(c_0_63,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))
    | ~ r5 ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_64,plain,
    r5,
    inference(split_conjunct,[status(thm)],[principia_r5]) ).

fof(c_0_65,plain,
    ! [X3,X4] :
      ( ( ~ substitution_of_equivalents
        | ~ is_a_theorem(equiv(X3,X4))
        | X3 = X4 )
      & ( is_a_theorem(equiv(esk3_0,esk4_0))
        | substitution_of_equivalents )
      & ( esk3_0 != esk4_0
        | substitution_of_equivalents ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])])]) ).

fof(c_0_66,plain,
    ! [X3,X4] :
      ( ~ op_equiv
      | equiv(X3,X4) = and(implies(X3,X4),implies(X4,X3)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])])]) ).

cnf(c_0_67,plain,
    is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_50]),c_0_50]),c_0_56])]) ).

cnf(c_0_68,plain,
    is_a_theorem(implies(implies(not(X1),X1),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_50]),c_0_58])]) ).

cnf(c_0_69,plain,
    ( is_a_theorem(implies(not(X1),implies(not(X2),X3)))
    | ~ is_a_theorem(implies(not(X2),implies(not(X1),X3))) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_70,plain,
    is_a_theorem(implies(X1,implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_71,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(not(X3),X1),implies(not(X3),X2)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_50]),c_0_50]),c_0_64])]) ).

cnf(c_0_72,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2))
    | ~ substitution_of_equivalents ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

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

cnf(c_0_74,plain,
    ( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
    | ~ op_equiv ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_75,plain,
    op_equiv,
    inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).

cnf(c_0_76,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(implies(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_67]) ).

cnf(c_0_77,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(implies(not(X1),X1)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_68]) ).

cnf(c_0_78,plain,
    is_a_theorem(implies(not(X1),implies(not(X2),not(X2)))),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_79,plain,
    ( is_a_theorem(implies(implies(not(X1),X2),implies(not(X1),X3)))
    | ~ is_a_theorem(implies(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_71]) ).

cnf(c_0_80,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).

cnf(c_0_81,plain,
    equiv(X1,X2) = not(implies(implies(X1,X2),not(implies(X2,X1)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_37]),c_0_75])]) ).

cnf(c_0_82,plain,
    implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_62,c_0_42]) ).

cnf(c_0_83,plain,
    ( is_a_theorem(implies(not(X1),not(X2)))
    | ~ is_a_theorem(implies(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_76,c_0_62]) ).

cnf(c_0_84,plain,
    is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
    inference(spm,[status(thm)],[c_0_68,c_0_62]) ).

cnf(c_0_85,plain,
    is_a_theorem(implies(not(X1),not(X1))),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

fof(c_0_86,negated_conjecture,
    ~ kn2,
    inference(assume_negation,[status(cth)],[rosser_kn2]) ).

cnf(c_0_87,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(implies(not(X1),X3))
    | ~ is_a_theorem(implies(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_79]) ).

cnf(c_0_88,plain,
    ( X1 = X2
    | ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
    inference(rw,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_89,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_59,c_0_82]) ).

cnf(c_0_90,plain,
    is_a_theorem(implies(X1,not(implies(X1,not(X1))))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_62]) ).

cnf(c_0_91,plain,
    is_a_theorem(implies(X1,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_85]),c_0_62]) ).

fof(c_0_92,plain,
    ! [X6,X7] :
      ( ( ~ kn2
        | is_a_theorem(implies(and(X6,X7),X6)) )
      & ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
        | kn2 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])])]) ).

fof(c_0_93,negated_conjecture,
    ~ kn2,
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_94,plain,
    ! [X3,X4] :
      ( ( ~ and_1
        | is_a_theorem(implies(and(X3,X4),X3)) )
      & ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
        | and_1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])])]) ).

cnf(c_0_95,plain,
    ( is_a_theorem(implies(not(X1),X2))
    | ~ is_a_theorem(implies(implies(X3,not(X1)),X2)) ),
    inference(spm,[status(thm)],[c_0_87,c_0_70]) ).

cnf(c_0_96,plain,
    is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_67,c_0_62]) ).

cnf(c_0_97,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_88,c_0_62]),c_0_82]) ).

cnf(c_0_98,plain,
    ( is_a_theorem(not(implies(implies(X1,X2),not(implies(X1,X2)))))
    | ~ is_a_theorem(implies(X1,not(not(X2)))) ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_99,plain,
    is_a_theorem(implies(X1,not(not(X1)))),
    inference(spm,[status(thm)],[c_0_91,c_0_62]) ).

cnf(c_0_100,plain,
    ( kn2
    | ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_92]) ).

cnf(c_0_101,negated_conjecture,
    ~ kn2,
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_102,plain,
    ( is_a_theorem(implies(and(X1,X2),X1))
    | ~ and_1 ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_103,plain,
    ( and_1
    | ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_104,plain,
    is_a_theorem(implies(not(X1),implies(X1,X2))),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_105,plain,
    not(not(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99])]) ).

cnf(c_0_106,plain,
    ~ is_a_theorem(implies(not(implies(esk34_0,not(esk35_0))),esk34_0)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_37]),c_0_101]) ).

cnf(c_0_107,plain,
    ( is_a_theorem(implies(not(implies(X1,not(X2))),X1))
    | ~ and_1 ),
    inference(rw,[status(thm)],[c_0_102,c_0_37]) ).

cnf(c_0_108,plain,
    ( and_1
    | ~ is_a_theorem(implies(not(implies(esk14_0,not(esk15_0))),esk14_0)) ),
    inference(rw,[status(thm)],[c_0_103,c_0_37]) ).

cnf(c_0_109,plain,
    is_a_theorem(implies(not(implies(X1,X2)),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_104]),c_0_105]) ).

cnf(c_0_110,plain,
    ~ and_1,
    inference(spm,[status(thm)],[c_0_106,c_0_107]) ).

cnf(c_0_111,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]),c_0_110]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul  4 06:36:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.24/1.41  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.24/1.41  # Preprocessing time       : 0.019 s
% 0.24/1.41  
% 0.24/1.41  # Proof found!
% 0.24/1.41  # SZS status Theorem
% 0.24/1.41  # SZS output start CNFRefutation
% See solution above
% 0.24/1.41  # Proof object total steps             : 112
% 0.24/1.41  # Proof object clause steps            : 69
% 0.24/1.41  # Proof object formula steps           : 43
% 0.24/1.41  # Proof object conjectures             : 4
% 0.24/1.41  # Proof object clause conjectures      : 1
% 0.24/1.41  # Proof object formula conjectures     : 3
% 0.24/1.41  # Proof object initial clauses used    : 28
% 0.24/1.41  # Proof object initial formulas used   : 27
% 0.24/1.41  # Proof object generating inferences   : 23
% 0.24/1.41  # Proof object simplifying inferences  : 54
% 0.24/1.41  # Training examples: 0 positive, 0 negative
% 0.24/1.41  # Parsed axioms                        : 45
% 0.24/1.41  # Removed by relevancy pruning/SinE    : 0
% 0.24/1.41  # Initial clauses                      : 74
% 0.24/1.41  # Removed in clause preprocessing      : 0
% 0.24/1.41  # Initial clauses in saturation        : 74
% 0.24/1.41  # Processed clauses                    : 5891
% 0.24/1.41  # ...of these trivial                  : 453
% 0.24/1.41  # ...subsumed                          : 4089
% 0.24/1.41  # ...remaining for further processing  : 1349
% 0.24/1.41  # Other redundant clauses eliminated   : 0
% 0.24/1.41  # Clauses deleted for lack of memory   : 0
% 0.24/1.41  # Backward-subsumed                    : 52
% 0.24/1.41  # Backward-rewritten                   : 712
% 0.24/1.41  # Generated clauses                    : 98121
% 0.24/1.41  # ...of the previous two non-trivial   : 64291
% 0.24/1.41  # Contextual simplify-reflections      : 1494
% 0.24/1.41  # Paramodulations                      : 98105
% 0.24/1.41  # Factorizations                       : 0
% 0.24/1.41  # Equation resolutions                 : 0
% 0.24/1.41  # Current number of processed clauses  : 577
% 0.24/1.41  #    Positive orientable unit clauses  : 153
% 0.24/1.41  #    Positive unorientable unit clauses: 0
% 0.24/1.41  #    Negative unit clauses             : 37
% 0.24/1.41  #    Non-unit-clauses                  : 387
% 0.24/1.41  # Current number of unprocessed clauses: 23361
% 0.24/1.41  # ...number of literals in the above   : 82307
% 0.24/1.41  # Current number of archived formulas  : 0
% 0.24/1.41  # Current number of archived clauses   : 764
% 0.24/1.41  # Clause-clause subsumption calls (NU) : 231695
% 0.24/1.41  # Rec. Clause-clause subsumption calls : 216617
% 0.24/1.41  # Non-unit clause-clause subsumptions  : 4086
% 0.24/1.41  # Unit Clause-clause subsumption calls : 16827
% 0.24/1.41  # Rewrite failures with RHS unbound    : 0
% 0.24/1.41  # BW rewrite match attempts            : 40071
% 0.24/1.41  # BW rewrite match successes           : 655
% 0.24/1.41  # Condensation attempts                : 0
% 0.24/1.41  # Condensation successes               : 0
% 0.24/1.41  # Termbank termtop insertions          : 1428884
% 0.24/1.41  
% 0.24/1.41  # -------------------------------------------------
% 0.24/1.41  # User time                : 0.908 s
% 0.24/1.41  # System time              : 0.045 s
% 0.24/1.41  # Total time               : 0.953 s
% 0.24/1.41  # Maximum resident set size: 45292 pages
% 0.24/23.42  eprover: CPU time limit exceeded, terminating
% 0.24/23.43  eprover: CPU time limit exceeded, terminating
% 0.24/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44  eprover: No such file or directory
% 0.24/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44  eprover: No such file or directory
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: CPU time limit exceeded, terminating
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48  eprover: No such file or directory
% 0.24/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.49  eprover: No such file or directory
% 0.24/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49  eprover: No such file or directory
% 0.24/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
% 0.24/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.51  eprover: No such file or directory
% 0.24/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.51  eprover: No such file or directory
% 0.24/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.51  eprover: No such file or directory
%------------------------------------------------------------------------------