TSTP Solution File: SET806+4 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET806+4 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:40:45 EST 2010

% Result   : Theorem 1.38s
% Output   : CNFRefutation 1.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :    6
% Syntax   : Number of formulae    :  111 (  13 unt;   0 def)
%            Number of atoms       :  684 (   0 equ)
%            Maximal formula atoms :  207 (   6 avg)
%            Number of connectives :  810 ( 237   ~; 425   |; 131   &)
%                                         (   6 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   63 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   2 con; 0-2 aty)
%            Number of variables   :  251 (   1 sgn  96   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',subset) ).

fof(2,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',equal_set) ).

fof(3,axiom,
    ! [X1,X4] :
      ( equivalence(X4,X1)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => apply(X4,X3,X3) )
        & ! [X3,X5] :
            ( ( member(X3,X1)
              & member(X5,X1) )
           => ( apply(X4,X3,X5)
             => apply(X4,X5,X3) ) )
        & ! [X3,X5,X6] :
            ( ( member(X3,X1)
              & member(X5,X1)
              & member(X6,X1) )
           => ( ( apply(X4,X3,X5)
                & apply(X4,X5,X6) )
             => apply(X4,X3,X6) ) ) ) ),
    file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',equivalence) ).

fof(5,conjecture,
    ! [X7] : equivalence(equal_set_predicate,power_set(X7)),
    file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',thIII13) ).

fof(6,axiom,
    ! [X3,X5] :
      ( apply(equal_set_predicate,X3,X5)
    <=> equal_set(X3,X5) ),
    file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',rel_equal_set) ).

fof(7,negated_conjecture,
    ~ ! [X7] : equivalence(equal_set_predicate,power_set(X7)),
    inference(assume_negation,[status(cth)],[5]) ).

fof(8,plain,
    ! [X1,X4] :
      ( epred1_2(X4,X1)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => apply(X4,X3,X3) )
        & ! [X3,X5] :
            ( ( member(X3,X1)
              & member(X5,X1) )
           => ( apply(X4,X3,X5)
             => apply(X4,X5,X3) ) )
        & ! [X3,X5,X6] :
            ( ( member(X3,X1)
              & member(X5,X1)
              & member(X6,X1) )
           => ( ( apply(X4,X3,X5)
                & apply(X4,X5,X6) )
             => apply(X4,X3,X6) ) ) ) ),
    introduced(definition) ).

fof(9,plain,
    ! [X1,X4] :
      ( equivalence(X4,X1)
    <=> epred1_2(X4,X1) ),
    inference(apply_def,[status(esa)],[3,8,theory(equality)]) ).

fof(10,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(11,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ? [X7] :
            ( member(X7,X4)
            & ~ member(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[10]) ).

fof(12,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[11]) ).

fof(13,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[12]) ).

fof(14,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[13]) ).

cnf(15,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(16,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(17,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(18,plain,
    ! [X1,X2] :
      ( ( ~ equal_set(X1,X2)
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | equal_set(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(19,plain,
    ! [X3,X4] :
      ( ( ~ equal_set(X3,X4)
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | ~ equal_set(X3,X4) )
      & ( subset(X4,X3)
        | ~ equal_set(X3,X4) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(distribute,[status(thm)],[19]) ).

cnf(21,plain,
    ( equal_set(X1,X2)
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,plain,
    ( subset(X2,X1)
    | ~ equal_set(X1,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(23,plain,
    ( subset(X1,X2)
    | ~ equal_set(X1,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(24,plain,
    ! [X1,X4] :
      ( ( ~ equivalence(X4,X1)
        | epred1_2(X4,X1) )
      & ( ~ epred1_2(X4,X1)
        | equivalence(X4,X1) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(25,plain,
    ! [X5,X6] :
      ( ( ~ equivalence(X6,X5)
        | epred1_2(X6,X5) )
      & ( ~ epred1_2(X6,X5)
        | equivalence(X6,X5) ) ),
    inference(variable_rename,[status(thm)],[24]) ).

cnf(26,plain,
    ( equivalence(X1,X2)
    | ~ epred1_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(32,negated_conjecture,
    ? [X7] : ~ equivalence(equal_set_predicate,power_set(X7)),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(33,negated_conjecture,
    ? [X8] : ~ equivalence(equal_set_predicate,power_set(X8)),
    inference(variable_rename,[status(thm)],[32]) ).

fof(34,negated_conjecture,
    ~ equivalence(equal_set_predicate,power_set(esk2_0)),
    inference(skolemize,[status(esa)],[33]) ).

cnf(35,negated_conjecture,
    ~ equivalence(equal_set_predicate,power_set(esk2_0)),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(36,plain,
    ! [X3,X5] :
      ( ( ~ apply(equal_set_predicate,X3,X5)
        | equal_set(X3,X5) )
      & ( ~ equal_set(X3,X5)
        | apply(equal_set_predicate,X3,X5) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(37,plain,
    ! [X6,X7] :
      ( ( ~ apply(equal_set_predicate,X6,X7)
        | equal_set(X6,X7) )
      & ( ~ equal_set(X6,X7)
        | apply(equal_set_predicate,X6,X7) ) ),
    inference(variable_rename,[status(thm)],[36]) ).

cnf(38,plain,
    ( apply(equal_set_predicate,X1,X2)
    | ~ equal_set(X1,X2) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(39,plain,
    ( equal_set(X1,X2)
    | ~ apply(equal_set_predicate,X1,X2) ),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(40,plain,
    ! [X1,X4] :
      ( ( ~ epred1_2(X4,X1)
        | ( ! [X3] :
              ( ~ member(X3,X1)
              | apply(X4,X3,X3) )
          & ! [X3,X5] :
              ( ~ member(X3,X1)
              | ~ member(X5,X1)
              | ~ apply(X4,X3,X5)
              | apply(X4,X5,X3) )
          & ! [X3,X5,X6] :
              ( ~ member(X3,X1)
              | ~ member(X5,X1)
              | ~ member(X6,X1)
              | ~ apply(X4,X3,X5)
              | ~ apply(X4,X5,X6)
              | apply(X4,X3,X6) ) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ apply(X4,X3,X3) )
        | ? [X3,X5] :
            ( member(X3,X1)
            & member(X5,X1)
            & apply(X4,X3,X5)
            & ~ apply(X4,X5,X3) )
        | ? [X3,X5,X6] :
            ( member(X3,X1)
            & member(X5,X1)
            & member(X6,X1)
            & apply(X4,X3,X5)
            & apply(X4,X5,X6)
            & ~ apply(X4,X3,X6) )
        | epred1_2(X4,X1) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(41,plain,
    ! [X7,X8] :
      ( ( ~ epred1_2(X8,X7)
        | ( ! [X9] :
              ( ~ member(X9,X7)
              | apply(X8,X9,X9) )
          & ! [X10,X11] :
              ( ~ member(X10,X7)
              | ~ member(X11,X7)
              | ~ apply(X8,X10,X11)
              | apply(X8,X11,X10) )
          & ! [X12,X13,X14] :
              ( ~ member(X12,X7)
              | ~ member(X13,X7)
              | ~ member(X14,X7)
              | ~ apply(X8,X12,X13)
              | ~ apply(X8,X13,X14)
              | apply(X8,X12,X14) ) ) )
      & ( ? [X15] :
            ( member(X15,X7)
            & ~ apply(X8,X15,X15) )
        | ? [X16,X17] :
            ( member(X16,X7)
            & member(X17,X7)
            & apply(X8,X16,X17)
            & ~ apply(X8,X17,X16) )
        | ? [X18,X19,X20] :
            ( member(X18,X7)
            & member(X19,X7)
            & member(X20,X7)
            & apply(X8,X18,X19)
            & apply(X8,X19,X20)
            & ~ apply(X8,X18,X20) )
        | epred1_2(X8,X7) ) ),
    inference(variable_rename,[status(thm)],[40]) ).

fof(42,plain,
    ! [X7,X8] :
      ( ( ~ epred1_2(X8,X7)
        | ( ! [X9] :
              ( ~ member(X9,X7)
              | apply(X8,X9,X9) )
          & ! [X10,X11] :
              ( ~ member(X10,X7)
              | ~ member(X11,X7)
              | ~ apply(X8,X10,X11)
              | apply(X8,X11,X10) )
          & ! [X12,X13,X14] :
              ( ~ member(X12,X7)
              | ~ member(X13,X7)
              | ~ member(X14,X7)
              | ~ apply(X8,X12,X13)
              | ~ apply(X8,X13,X14)
              | apply(X8,X12,X14) ) ) )
      & ( ( member(esk3_2(X7,X8),X7)
          & ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8)) )
        | ( member(esk4_2(X7,X8),X7)
          & member(esk5_2(X7,X8),X7)
          & apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
          & ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8)) )
        | ( member(esk6_2(X7,X8),X7)
          & member(esk7_2(X7,X8),X7)
          & member(esk8_2(X7,X8),X7)
          & apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
          & apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
          & ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8)) )
        | epred1_2(X8,X7) ) ),
    inference(skolemize,[status(esa)],[41]) ).

fof(43,plain,
    ! [X7,X8,X9,X10,X11,X12,X13,X14] :
      ( ( ( ( ~ member(X12,X7)
            | ~ member(X13,X7)
            | ~ member(X14,X7)
            | ~ apply(X8,X12,X13)
            | ~ apply(X8,X13,X14)
            | apply(X8,X12,X14) )
          & ( ~ member(X10,X7)
            | ~ member(X11,X7)
            | ~ apply(X8,X10,X11)
            | apply(X8,X11,X10) )
          & ( ~ member(X9,X7)
            | apply(X8,X9,X9) ) )
        | ~ epred1_2(X8,X7) )
      & ( ( member(esk3_2(X7,X8),X7)
          & ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8)) )
        | ( member(esk4_2(X7,X8),X7)
          & member(esk5_2(X7,X8),X7)
          & apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
          & ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8)) )
        | ( member(esk6_2(X7,X8),X7)
          & member(esk7_2(X7,X8),X7)
          & member(esk8_2(X7,X8),X7)
          & apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
          & apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
          & ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8)) )
        | epred1_2(X8,X7) ) ),
    inference(shift_quantors,[status(thm)],[42]) ).

fof(44,plain,
    ! [X7,X8,X9,X10,X11,X12,X13,X14] :
      ( ( ~ member(X12,X7)
        | ~ member(X13,X7)
        | ~ member(X14,X7)
        | ~ apply(X8,X12,X13)
        | ~ apply(X8,X13,X14)
        | apply(X8,X12,X14)
        | ~ epred1_2(X8,X7) )
      & ( ~ member(X10,X7)
        | ~ member(X11,X7)
        | ~ apply(X8,X10,X11)
        | apply(X8,X11,X10)
        | ~ epred1_2(X8,X7) )
      & ( ~ member(X9,X7)
        | apply(X8,X9,X9)
        | ~ epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | member(esk4_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | member(esk4_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | member(esk4_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | member(esk4_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | member(esk4_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | member(esk4_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | member(esk5_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | member(esk5_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | member(esk5_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | member(esk5_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | member(esk5_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | member(esk5_2(X7,X8),X7)
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | member(esk3_2(X7,X8),X7)
        | epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | member(esk4_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | member(esk4_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | member(esk4_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | member(esk4_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | member(esk4_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | member(esk4_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | member(esk5_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | member(esk5_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | member(esk5_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | member(esk5_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | member(esk5_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | member(esk5_2(X7,X8),X7)
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk6_2(X7,X8),X7)
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk7_2(X7,X8),X7)
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( member(esk8_2(X7,X8),X7)
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) )
      & ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
        | ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
        | ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
        | epred1_2(X8,X7) ) ),
    inference(distribute,[status(thm)],[43]) ).

cnf(45,plain,
    ( epred1_2(X1,X2)
    | ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
    | ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1))
    | ~ apply(X1,esk6_2(X2,X1),esk8_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(46,plain,
    ( epred1_2(X1,X2)
    | apply(X1,esk7_2(X2,X1),esk8_2(X2,X1))
    | ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
    | ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(47,plain,
    ( epred1_2(X1,X2)
    | apply(X1,esk6_2(X2,X1),esk7_2(X2,X1))
    | ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
    | ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(51,plain,
    ( epred1_2(X1,X2)
    | apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
    | ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
    | ~ apply(X1,esk6_2(X2,X1),esk8_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(52,plain,
    ( epred1_2(X1,X2)
    | apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
    | apply(X1,esk7_2(X2,X1),esk8_2(X2,X1))
    | ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(53,plain,
    ( epred1_2(X1,X2)
    | apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
    | apply(X1,esk6_2(X2,X1),esk7_2(X2,X1))
    | ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(96,negated_conjecture,
    ~ epred1_2(equal_set_predicate,power_set(esk2_0)),
    inference(spm,[status(thm)],[35,26,theory(equality)]) ).

cnf(100,plain,
    ( subset(X1,X2)
    | ~ apply(equal_set_predicate,X2,X1) ),
    inference(spm,[status(thm)],[22,39,theory(equality)]) ).

cnf(101,plain,
    ( subset(X1,X2)
    | ~ apply(equal_set_predicate,X1,X2) ),
    inference(spm,[status(thm)],[23,39,theory(equality)]) ).

cnf(104,plain,
    subset(X1,X1),
    inference(spm,[status(thm)],[15,16,theory(equality)]) ).

cnf(107,plain,
    ( apply(equal_set_predicate,X1,X2)
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[38,21,theory(equality)]) ).

cnf(159,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ apply(equal_set_predicate,X2,X3) ),
    inference(spm,[status(thm)],[17,100,theory(equality)]) ).

cnf(160,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ apply(equal_set_predicate,X3,X2) ),
    inference(spm,[status(thm)],[17,101,theory(equality)]) ).

cnf(166,plain,
    ( apply(equal_set_predicate,X1,X1)
    | ~ subset(X1,X1) ),
    inference(spm,[status(thm)],[107,104,theory(equality)]) ).

cnf(168,plain,
    ( apply(equal_set_predicate,X1,X2)
    | ~ subset(X1,X2)
    | ~ apply(equal_set_predicate,X2,X1) ),
    inference(spm,[status(thm)],[107,101,theory(equality)]) ).

cnf(170,plain,
    ( apply(equal_set_predicate,X1,X1)
    | $false ),
    inference(rw,[status(thm)],[166,104,theory(equality)]) ).

cnf(171,plain,
    apply(equal_set_predicate,X1,X1),
    inference(cn,[status(thm)],[170,theory(equality)]) ).

cnf(182,plain,
    ( apply(equal_set_predicate,X1,X2)
    | ~ apply(equal_set_predicate,X2,X1) ),
    inference(csr,[status(thm)],[168,100]) ).

cnf(251,plain,
    ( member(X1,esk6_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[159,53,theory(equality)]) ).

cnf(252,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk8_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[159,52,theory(equality)]) ).

cnf(253,plain,
    ( member(X1,esk6_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[159,47,theory(equality)]) ).

cnf(254,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk8_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[159,46,theory(equality)]) ).

cnf(269,plain,
    ( member(X1,esk6_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | $false ),
    inference(rw,[status(thm)],[251,171,theory(equality)]) ).

cnf(270,plain,
    ( member(X1,esk6_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk7_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[269,theory(equality)]) ).

cnf(271,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk8_2(X2,equal_set_predicate))
    | $false ),
    inference(rw,[status(thm)],[252,171,theory(equality)]) ).

cnf(272,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk8_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[271,theory(equality)]) ).

cnf(273,plain,
    ( member(X1,esk6_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | $false
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(rw,[status(thm)],[253,171,theory(equality)]) ).

cnf(274,plain,
    ( member(X1,esk6_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[273,theory(equality)]) ).

cnf(275,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk8_2(X2,equal_set_predicate))
    | $false
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(rw,[status(thm)],[254,171,theory(equality)]) ).

cnf(276,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk8_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[275,theory(equality)]) ).

cnf(300,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk6_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[160,53,theory(equality)]) ).

cnf(301,plain,
    ( member(X1,esk8_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[160,52,theory(equality)]) ).

cnf(302,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk6_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[160,47,theory(equality)]) ).

cnf(303,plain,
    ( member(X1,esk8_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[160,46,theory(equality)]) ).

cnf(318,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk6_2(X2,equal_set_predicate))
    | $false ),
    inference(rw,[status(thm)],[300,171,theory(equality)]) ).

cnf(319,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk6_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[318,theory(equality)]) ).

cnf(320,plain,
    ( member(X1,esk8_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | $false ),
    inference(rw,[status(thm)],[301,171,theory(equality)]) ).

cnf(321,plain,
    ( member(X1,esk8_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
    | ~ member(X1,esk7_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[320,theory(equality)]) ).

cnf(322,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk6_2(X2,equal_set_predicate))
    | $false
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(rw,[status(thm)],[302,171,theory(equality)]) ).

cnf(323,plain,
    ( member(X1,esk7_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk6_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[322,theory(equality)]) ).

cnf(324,plain,
    ( member(X1,esk8_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | $false
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(rw,[status(thm)],[303,171,theory(equality)]) ).

cnf(325,plain,
    ( member(X1,esk8_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(X1,esk7_2(X2,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
    inference(cn,[status(thm)],[324,theory(equality)]) ).

cnf(2233,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
    | member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
    | subset(esk8_2(X1,equal_set_predicate),X2) ),
    inference(spm,[status(thm)],[272,16,theory(equality)]) ).

cnf(2403,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
    | member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
    | subset(esk8_2(X1,equal_set_predicate),X2) ),
    inference(spm,[status(thm)],[270,2233,theory(equality)]) ).

cnf(2525,plain,
    ( subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
    | epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[15,2403,theory(equality)]) ).

cnf(2532,plain,
    ( apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
    | epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
    | ~ subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[107,2525,theory(equality)]) ).

cnf(2568,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
    | member(esk1_2(esk6_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
    | subset(esk6_2(X1,equal_set_predicate),X2) ),
    inference(spm,[status(thm)],[319,16,theory(equality)]) ).

cnf(2709,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
    | member(esk1_2(esk6_2(X1,equal_set_predicate),X2),esk8_2(X1,equal_set_predicate))
    | subset(esk6_2(X1,equal_set_predicate),X2) ),
    inference(spm,[status(thm)],[321,2568,theory(equality)]) ).

cnf(2878,plain,
    ( subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
    | epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[15,2709,theory(equality)]) ).

cnf(14914,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
    inference(csr,[status(thm)],[2532,2878]) ).

cnf(14923,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk3_2(X1,equal_set_predicate),esk3_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[51,14914,theory(equality)]) ).

cnf(14934,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
    | $false ),
    inference(rw,[status(thm)],[14923,171,theory(equality)]) ).

cnf(14935,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
    inference(cn,[status(thm)],[14934,theory(equality)]) ).

cnf(14970,plain,
    ( apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
    | epred1_2(equal_set_predicate,X1) ),
    inference(spm,[status(thm)],[182,14935,theory(equality)]) ).

cnf(14986,plain,
    ( epred1_2(equal_set_predicate,X1)
    | member(X2,esk6_2(X1,equal_set_predicate))
    | ~ member(X2,esk7_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[274,14970,theory(equality)]) ).

cnf(14988,plain,
    ( epred1_2(equal_set_predicate,X1)
    | member(X2,esk7_2(X1,equal_set_predicate))
    | ~ member(X2,esk8_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[276,14970,theory(equality)]) ).

cnf(14990,plain,
    ( epred1_2(equal_set_predicate,X1)
    | member(X2,esk7_2(X1,equal_set_predicate))
    | ~ member(X2,esk6_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[323,14970,theory(equality)]) ).

cnf(14991,plain,
    ( epred1_2(equal_set_predicate,X1)
    | member(X2,esk8_2(X1,equal_set_predicate))
    | ~ member(X2,esk7_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[325,14970,theory(equality)]) ).

cnf(15276,plain,
    ( epred1_2(equal_set_predicate,X1)
    | member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
    | subset(esk8_2(X1,equal_set_predicate),X2) ),
    inference(spm,[status(thm)],[14988,16,theory(equality)]) ).

cnf(15439,plain,
    ( subset(X1,esk8_2(X2,equal_set_predicate))
    | epred1_2(equal_set_predicate,X2)
    | ~ member(esk1_2(X1,esk8_2(X2,equal_set_predicate)),esk7_2(X2,equal_set_predicate)) ),
    inference(spm,[status(thm)],[15,14991,theory(equality)]) ).

cnf(15863,plain,
    ( epred1_2(equal_set_predicate,X1)
    | member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
    | subset(esk8_2(X1,equal_set_predicate),X2) ),
    inference(spm,[status(thm)],[14986,15276,theory(equality)]) ).

cnf(16219,plain,
    ( epred1_2(equal_set_predicate,X1)
    | subset(X2,esk8_2(X1,equal_set_predicate))
    | ~ member(esk1_2(X2,esk8_2(X1,equal_set_predicate)),esk6_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[15439,14990,theory(equality)]) ).

cnf(16279,plain,
    ( subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
    | epred1_2(equal_set_predicate,X1) ),
    inference(spm,[status(thm)],[15,15863,theory(equality)]) ).

cnf(16300,plain,
    ( apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
    | epred1_2(equal_set_predicate,X1)
    | ~ subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[107,16279,theory(equality)]) ).

cnf(16589,plain,
    ( epred1_2(equal_set_predicate,X1)
    | subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[16219,16,theory(equality)]) ).

cnf(18201,plain,
    ( epred1_2(equal_set_predicate,X1)
    | apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
    inference(csr,[status(thm)],[16300,16589]) ).

cnf(18211,plain,
    ( epred1_2(equal_set_predicate,X1)
    | ~ apply(equal_set_predicate,esk3_2(X1,equal_set_predicate),esk3_2(X1,equal_set_predicate))
    | ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
    inference(spm,[status(thm)],[45,18201,theory(equality)]) ).

cnf(18225,plain,
    ( epred1_2(equal_set_predicate,X1)
    | $false
    | ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
    inference(rw,[status(thm)],[18211,171,theory(equality)]) ).

cnf(18226,plain,
    ( epred1_2(equal_set_predicate,X1)
    | ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
    inference(cn,[status(thm)],[18225,theory(equality)]) ).

cnf(18240,plain,
    epred1_2(equal_set_predicate,X1),
    inference(csr,[status(thm)],[18226,14970]) ).

cnf(18242,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[96,18240,theory(equality)]) ).

cnf(18243,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[18242,theory(equality)]) ).

cnf(18244,negated_conjecture,
    $false,
    18243,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET806+4.p
% --creating new selector for [SET006+0.ax, SET006+2.ax]
% -running prover on /tmp/tmpsfS2ZG/sel_SET806+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET806+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET806+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET806+4.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------