TSTP Solution File: SET686+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET686+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 03:11:17 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  164 (  11 unt;   0 def)
%            Number of atoms       :  826 (   9 equ)
%            Maximal formula atoms :   22 (   5 avg)
%            Number of connectives : 1114 ( 452   ~; 489   |; 120   &)
%                                         (   9 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   8 con; 0-4 aty)
%            Number of variables   :  344 (  18 sgn 148   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => ! [X4] :
                  ( ilf_type(X4,set_type)
                 => inverse4(X1,X2,X3,X4) = inverse2(X3,X4) ) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p25) ).

fof(2,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,subset_type(cross_product(X1,X2)))
             => relation_like(X3) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p24) ).

fof(3,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p27) ).

fof(9,conjecture,
    ! [X1] :
      ( ( ~ empty(X1)
        & ilf_type(X1,set_type) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ! [X3] :
              ( ( ~ empty(X3)
                & ilf_type(X3,set_type) )
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X1,X3))
                 => ! [X5] :
                      ( ilf_type(X5,member_type(X1))
                     => ( member(X5,inverse4(X1,X3,X4,X2))
                      <=> ? [X6] :
                            ( ilf_type(X6,member_type(X3))
                            & member(ordered_pair(X5,X6),X4)
                            & member(X6,X2) ) ) ) ) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',prove_relset_1_53) ).

fof(15,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ilf_type(X1,binary_relation_type)
      <=> ( relation_like(X1)
          & ilf_type(X1,set_type) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p15) ).

fof(20,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,set_type)
                 => ! [X5] :
                      ( ilf_type(X5,relation_type(X1,X2))
                     => ( member(ordered_pair(X3,X4),X5)
                       => ( member(X3,X1)
                          & member(X4,X2) ) ) ) ) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p2) ).

fof(22,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,binary_relation_type)
             => ( member(X2,inverse2(X3,X1))
              <=> ? [X4] :
                    ( ilf_type(X4,set_type)
                    & member(ordered_pair(X2,X4),X3)
                    & member(X4,X1) ) ) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p1) ).

fof(24,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p7) ).

fof(26,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X1,X2)))
               => ilf_type(X3,relation_type(X1,X2)) )
            & ! [X4] :
                ( ilf_type(X4,relation_type(X1,X2))
               => ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p5) ).

fof(28,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    file('/tmp/tmpl2UB2b/sel_SET686+3.p_1',p9) ).

fof(29,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty(X1)
          & ilf_type(X1,set_type) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & ilf_type(X2,set_type) )
           => ! [X3] :
                ( ( ~ empty(X3)
                  & ilf_type(X3,set_type) )
               => ! [X4] :
                    ( ilf_type(X4,relation_type(X1,X3))
                   => ! [X5] :
                        ( ilf_type(X5,member_type(X1))
                       => ( member(X5,inverse4(X1,X3,X4,X2))
                        <=> ? [X6] :
                              ( ilf_type(X6,member_type(X3))
                              & member(ordered_pair(X5,X6),X4)
                              & member(X6,X2) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(31,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty(X1)
          & ilf_type(X1,set_type) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & ilf_type(X2,set_type) )
           => ! [X3] :
                ( ( ~ empty(X3)
                  & ilf_type(X3,set_type) )
               => ! [X4] :
                    ( ilf_type(X4,relation_type(X1,X3))
                   => ! [X5] :
                        ( ilf_type(X5,member_type(X1))
                       => ( member(X5,inverse4(X1,X3,X4,X2))
                        <=> ? [X6] :
                              ( ilf_type(X6,member_type(X3))
                              & member(ordered_pair(X5,X6),X4)
                              & member(X6,X2) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[29,theory(equality)]) ).

fof(32,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).

fof(34,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[28,theory(equality)]) ).

fof(35,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,relation_type(X1,X2))
              | ! [X4] :
                  ( ~ ilf_type(X4,set_type)
                  | inverse4(X1,X2,X3,X4) = inverse2(X3,X4) ) ) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(36,plain,
    ! [X5] :
      ( ~ ilf_type(X5,set_type)
      | ! [X6] :
          ( ~ ilf_type(X6,set_type)
          | ! [X7] :
              ( ~ ilf_type(X7,relation_type(X5,X6))
              | ! [X8] :
                  ( ~ ilf_type(X8,set_type)
                  | inverse4(X5,X6,X7,X8) = inverse2(X7,X8) ) ) ) ),
    inference(variable_rename,[status(thm)],[35]) ).

fof(37,plain,
    ! [X5,X6,X7,X8] :
      ( ~ ilf_type(X8,set_type)
      | inverse4(X5,X6,X7,X8) = inverse2(X7,X8)
      | ~ ilf_type(X7,relation_type(X5,X6))
      | ~ ilf_type(X6,set_type)
      | ~ ilf_type(X5,set_type) ),
    inference(shift_quantors,[status(thm)],[36]) ).

cnf(38,plain,
    ( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2))
    | ~ ilf_type(X4,set_type) ),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(39,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
              | relation_like(X3) ) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(40,plain,
    ! [X4] :
      ( ~ ilf_type(X4,set_type)
      | ! [X5] :
          ( ~ ilf_type(X5,set_type)
          | ! [X6] :
              ( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
              | relation_like(X6) ) ) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,plain,
    ! [X4,X5,X6] :
      ( ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
      | relation_like(X6)
      | ~ ilf_type(X5,set_type)
      | ~ ilf_type(X4,set_type) ),
    inference(shift_quantors,[status(thm)],[40]) ).

cnf(42,plain,
    ( relation_like(X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(43,plain,
    ! [X2] : ilf_type(X2,set_type),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(44,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(77,negated_conjecture,
    ? [X1] :
      ( ~ empty(X1)
      & ilf_type(X1,set_type)
      & ? [X2] :
          ( ~ empty(X2)
          & ilf_type(X2,set_type)
          & ? [X3] :
              ( ~ empty(X3)
              & ilf_type(X3,set_type)
              & ? [X4] :
                  ( ilf_type(X4,relation_type(X1,X3))
                  & ? [X5] :
                      ( ilf_type(X5,member_type(X1))
                      & ( ~ member(X5,inverse4(X1,X3,X4,X2))
                        | ! [X6] :
                            ( ~ ilf_type(X6,member_type(X3))
                            | ~ member(ordered_pair(X5,X6),X4)
                            | ~ member(X6,X2) ) )
                      & ( member(X5,inverse4(X1,X3,X4,X2))
                        | ? [X6] :
                            ( ilf_type(X6,member_type(X3))
                            & member(ordered_pair(X5,X6),X4)
                            & member(X6,X2) ) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(78,negated_conjecture,
    ? [X7] :
      ( ~ empty(X7)
      & ilf_type(X7,set_type)
      & ? [X8] :
          ( ~ empty(X8)
          & ilf_type(X8,set_type)
          & ? [X9] :
              ( ~ empty(X9)
              & ilf_type(X9,set_type)
              & ? [X10] :
                  ( ilf_type(X10,relation_type(X7,X9))
                  & ? [X11] :
                      ( ilf_type(X11,member_type(X7))
                      & ( ~ member(X11,inverse4(X7,X9,X10,X8))
                        | ! [X12] :
                            ( ~ ilf_type(X12,member_type(X9))
                            | ~ member(ordered_pair(X11,X12),X10)
                            | ~ member(X12,X8) ) )
                      & ( member(X11,inverse4(X7,X9,X10,X8))
                        | ? [X13] :
                            ( ilf_type(X13,member_type(X9))
                            & member(ordered_pair(X11,X13),X10)
                            & member(X13,X8) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[77]) ).

fof(79,negated_conjecture,
    ( ~ empty(esk5_0)
    & ilf_type(esk5_0,set_type)
    & ~ empty(esk6_0)
    & ilf_type(esk6_0,set_type)
    & ~ empty(esk7_0)
    & ilf_type(esk7_0,set_type)
    & ilf_type(esk8_0,relation_type(esk5_0,esk7_0))
    & ilf_type(esk9_0,member_type(esk5_0))
    & ( ~ member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0))
      | ! [X12] :
          ( ~ ilf_type(X12,member_type(esk7_0))
          | ~ member(ordered_pair(esk9_0,X12),esk8_0)
          | ~ member(X12,esk6_0) ) )
    & ( member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0))
      | ( ilf_type(esk10_0,member_type(esk7_0))
        & member(ordered_pair(esk9_0,esk10_0),esk8_0)
        & member(esk10_0,esk6_0) ) ) ),
    inference(skolemize,[status(esa)],[78]) ).

fof(80,negated_conjecture,
    ! [X12] :
      ( ( ~ ilf_type(X12,member_type(esk7_0))
        | ~ member(ordered_pair(esk9_0,X12),esk8_0)
        | ~ member(X12,esk6_0)
        | ~ member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0)) )
      & ( member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0))
        | ( ilf_type(esk10_0,member_type(esk7_0))
          & member(ordered_pair(esk9_0,esk10_0),esk8_0)
          & member(esk10_0,esk6_0) ) )
      & ilf_type(esk9_0,member_type(esk5_0))
      & ilf_type(esk8_0,relation_type(esk5_0,esk7_0))
      & ~ empty(esk7_0)
      & ilf_type(esk7_0,set_type)
      & ~ empty(esk6_0)
      & ilf_type(esk6_0,set_type)
      & ~ empty(esk5_0)
      & ilf_type(esk5_0,set_type) ),
    inference(shift_quantors,[status(thm)],[79]) ).

fof(81,negated_conjecture,
    ! [X12] :
      ( ( ~ ilf_type(X12,member_type(esk7_0))
        | ~ member(ordered_pair(esk9_0,X12),esk8_0)
        | ~ member(X12,esk6_0)
        | ~ member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0)) )
      & ( ilf_type(esk10_0,member_type(esk7_0))
        | member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0)) )
      & ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
        | member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0)) )
      & ( member(esk10_0,esk6_0)
        | member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0)) )
      & ilf_type(esk9_0,member_type(esk5_0))
      & ilf_type(esk8_0,relation_type(esk5_0,esk7_0))
      & ~ empty(esk7_0)
      & ilf_type(esk7_0,set_type)
      & ~ empty(esk6_0)
      & ilf_type(esk6_0,set_type)
      & ~ empty(esk5_0)
      & ilf_type(esk5_0,set_type) ),
    inference(distribute,[status(thm)],[80]) ).

cnf(88,negated_conjecture,
    ilf_type(esk8_0,relation_type(esk5_0,esk7_0)),
    inference(split_conjunct,[status(thm)],[81]) ).

cnf(90,negated_conjecture,
    ( member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0))
    | member(esk10_0,esk6_0) ),
    inference(split_conjunct,[status(thm)],[81]) ).

cnf(91,negated_conjecture,
    ( member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0))
    | member(ordered_pair(esk9_0,esk10_0),esk8_0) ),
    inference(split_conjunct,[status(thm)],[81]) ).

cnf(92,negated_conjecture,
    ( member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0))
    | ilf_type(esk10_0,member_type(esk7_0)) ),
    inference(split_conjunct,[status(thm)],[81]) ).

cnf(93,negated_conjecture,
    ( ~ member(esk9_0,inverse4(esk5_0,esk7_0,esk8_0,esk6_0))
    | ~ member(X1,esk6_0)
    | ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ ilf_type(X1,member_type(esk7_0)) ),
    inference(split_conjunct,[status(thm)],[81]) ).

fof(113,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ( ( ~ ilf_type(X1,binary_relation_type)
          | ( relation_like(X1)
            & ilf_type(X1,set_type) ) )
        & ( ~ relation_like(X1)
          | ~ ilf_type(X1,set_type)
          | ilf_type(X1,binary_relation_type) ) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(114,plain,
    ! [X2] :
      ( ~ ilf_type(X2,set_type)
      | ( ( ~ ilf_type(X2,binary_relation_type)
          | ( relation_like(X2)
            & ilf_type(X2,set_type) ) )
        & ( ~ relation_like(X2)
          | ~ ilf_type(X2,set_type)
          | ilf_type(X2,binary_relation_type) ) ) ),
    inference(variable_rename,[status(thm)],[113]) ).

fof(115,plain,
    ! [X2] :
      ( ( relation_like(X2)
        | ~ ilf_type(X2,binary_relation_type)
        | ~ ilf_type(X2,set_type) )
      & ( ilf_type(X2,set_type)
        | ~ ilf_type(X2,binary_relation_type)
        | ~ ilf_type(X2,set_type) )
      & ( ~ relation_like(X2)
        | ~ ilf_type(X2,set_type)
        | ilf_type(X2,binary_relation_type)
        | ~ ilf_type(X2,set_type) ) ),
    inference(distribute,[status(thm)],[114]) ).

cnf(116,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ relation_like(X1) ),
    inference(split_conjunct,[status(thm)],[115]) ).

fof(142,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,set_type)
              | ! [X4] :
                  ( ~ ilf_type(X4,set_type)
                  | ! [X5] :
                      ( ~ ilf_type(X5,relation_type(X1,X2))
                      | ~ member(ordered_pair(X3,X4),X5)
                      | ( member(X3,X1)
                        & member(X4,X2) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(143,plain,
    ! [X6] :
      ( ~ ilf_type(X6,set_type)
      | ! [X7] :
          ( ~ ilf_type(X7,set_type)
          | ! [X8] :
              ( ~ ilf_type(X8,set_type)
              | ! [X9] :
                  ( ~ ilf_type(X9,set_type)
                  | ! [X10] :
                      ( ~ ilf_type(X10,relation_type(X6,X7))
                      | ~ member(ordered_pair(X8,X9),X10)
                      | ( member(X8,X6)
                        & member(X9,X7) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[142]) ).

fof(144,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ~ ilf_type(X10,relation_type(X6,X7))
      | ~ member(ordered_pair(X8,X9),X10)
      | ( member(X8,X6)
        & member(X9,X7) )
      | ~ ilf_type(X9,set_type)
      | ~ ilf_type(X8,set_type)
      | ~ ilf_type(X7,set_type)
      | ~ ilf_type(X6,set_type) ),
    inference(shift_quantors,[status(thm)],[143]) ).

fof(145,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( member(X8,X6)
        | ~ member(ordered_pair(X8,X9),X10)
        | ~ ilf_type(X10,relation_type(X6,X7))
        | ~ ilf_type(X9,set_type)
        | ~ ilf_type(X8,set_type)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type) )
      & ( member(X9,X7)
        | ~ member(ordered_pair(X8,X9),X10)
        | ~ ilf_type(X10,relation_type(X6,X7))
        | ~ ilf_type(X9,set_type)
        | ~ ilf_type(X8,set_type)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type) ) ),
    inference(distribute,[status(thm)],[144]) ).

cnf(146,plain,
    ( member(X4,X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(split_conjunct,[status(thm)],[145]) ).

fof(154,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,binary_relation_type)
              | ( ( ~ member(X2,inverse2(X3,X1))
                  | ? [X4] :
                      ( ilf_type(X4,set_type)
                      & member(ordered_pair(X2,X4),X3)
                      & member(X4,X1) ) )
                & ( ! [X4] :
                      ( ~ ilf_type(X4,set_type)
                      | ~ member(ordered_pair(X2,X4),X3)
                      | ~ member(X4,X1) )
                  | member(X2,inverse2(X3,X1)) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(155,plain,
    ! [X5] :
      ( ~ ilf_type(X5,set_type)
      | ! [X6] :
          ( ~ ilf_type(X6,set_type)
          | ! [X7] :
              ( ~ ilf_type(X7,binary_relation_type)
              | ( ( ~ member(X6,inverse2(X7,X5))
                  | ? [X8] :
                      ( ilf_type(X8,set_type)
                      & member(ordered_pair(X6,X8),X7)
                      & member(X8,X5) ) )
                & ( ! [X9] :
                      ( ~ ilf_type(X9,set_type)
                      | ~ member(ordered_pair(X6,X9),X7)
                      | ~ member(X9,X5) )
                  | member(X6,inverse2(X7,X5)) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[154]) ).

fof(156,plain,
    ! [X5] :
      ( ~ ilf_type(X5,set_type)
      | ! [X6] :
          ( ~ ilf_type(X6,set_type)
          | ! [X7] :
              ( ~ ilf_type(X7,binary_relation_type)
              | ( ( ~ member(X6,inverse2(X7,X5))
                  | ( ilf_type(esk14_3(X5,X6,X7),set_type)
                    & member(ordered_pair(X6,esk14_3(X5,X6,X7)),X7)
                    & member(esk14_3(X5,X6,X7),X5) ) )
                & ( ! [X9] :
                      ( ~ ilf_type(X9,set_type)
                      | ~ member(ordered_pair(X6,X9),X7)
                      | ~ member(X9,X5) )
                  | member(X6,inverse2(X7,X5)) ) ) ) ) ),
    inference(skolemize,[status(esa)],[155]) ).

fof(157,plain,
    ! [X5,X6,X7,X9] :
      ( ( ( ~ ilf_type(X9,set_type)
          | ~ member(ordered_pair(X6,X9),X7)
          | ~ member(X9,X5)
          | member(X6,inverse2(X7,X5)) )
        & ( ~ member(X6,inverse2(X7,X5))
          | ( ilf_type(esk14_3(X5,X6,X7),set_type)
            & member(ordered_pair(X6,esk14_3(X5,X6,X7)),X7)
            & member(esk14_3(X5,X6,X7),X5) ) ) )
      | ~ ilf_type(X7,binary_relation_type)
      | ~ ilf_type(X6,set_type)
      | ~ ilf_type(X5,set_type) ),
    inference(shift_quantors,[status(thm)],[156]) ).

fof(158,plain,
    ! [X5,X6,X7,X9] :
      ( ( ~ ilf_type(X9,set_type)
        | ~ member(ordered_pair(X6,X9),X7)
        | ~ member(X9,X5)
        | member(X6,inverse2(X7,X5))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( ilf_type(esk14_3(X5,X6,X7),set_type)
        | ~ member(X6,inverse2(X7,X5))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( member(ordered_pair(X6,esk14_3(X5,X6,X7)),X7)
        | ~ member(X6,inverse2(X7,X5))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( member(esk14_3(X5,X6,X7),X5)
        | ~ member(X6,inverse2(X7,X5))
        | ~ ilf_type(X7,binary_relation_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) ) ),
    inference(distribute,[status(thm)],[157]) ).

cnf(159,plain,
    ( member(esk14_3(X1,X2,X3),X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[158]) ).

cnf(160,plain,
    ( member(ordered_pair(X2,esk14_3(X1,X2,X3)),X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[158]) ).

cnf(162,plain,
    ( member(X2,inverse2(X3,X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(X4,X1)
    | ~ member(ordered_pair(X2,X4),X3)
    | ~ ilf_type(X4,set_type) ),
    inference(split_conjunct,[status(thm)],[158]) ).

fof(168,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( empty(X2)
          | ~ ilf_type(X2,set_type)
          | ( ( ~ ilf_type(X1,member_type(X2))
              | member(X1,X2) )
            & ( ~ member(X1,X2)
              | ilf_type(X1,member_type(X2)) ) ) ) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(169,plain,
    ! [X3] :
      ( ~ ilf_type(X3,set_type)
      | ! [X4] :
          ( empty(X4)
          | ~ ilf_type(X4,set_type)
          | ( ( ~ ilf_type(X3,member_type(X4))
              | member(X3,X4) )
            & ( ~ member(X3,X4)
              | ilf_type(X3,member_type(X4)) ) ) ) ),
    inference(variable_rename,[status(thm)],[168]) ).

fof(170,plain,
    ! [X3,X4] :
      ( empty(X4)
      | ~ ilf_type(X4,set_type)
      | ( ( ~ ilf_type(X3,member_type(X4))
          | member(X3,X4) )
        & ( ~ member(X3,X4)
          | ilf_type(X3,member_type(X4)) ) )
      | ~ ilf_type(X3,set_type) ),
    inference(shift_quantors,[status(thm)],[169]) ).

fof(171,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X3,member_type(X4))
        | member(X3,X4)
        | empty(X4)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( ~ member(X3,X4)
        | ilf_type(X3,member_type(X4))
        | empty(X4)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[170]) ).

cnf(172,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[171]) ).

fof(178,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ( ! [X3] :
                ( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
                | ilf_type(X3,relation_type(X1,X2)) )
            & ! [X4] :
                ( ~ ilf_type(X4,relation_type(X1,X2))
                | ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(179,plain,
    ! [X5] :
      ( ~ ilf_type(X5,set_type)
      | ! [X6] :
          ( ~ ilf_type(X6,set_type)
          | ( ! [X7] :
                ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
                | ilf_type(X7,relation_type(X5,X6)) )
            & ! [X8] :
                ( ~ ilf_type(X8,relation_type(X5,X6))
                | ilf_type(X8,subset_type(cross_product(X5,X6))) ) ) ) ),
    inference(variable_rename,[status(thm)],[178]) ).

fof(180,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ~ ilf_type(X8,relation_type(X5,X6))
          | ilf_type(X8,subset_type(cross_product(X5,X6))) )
        & ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
          | ilf_type(X7,relation_type(X5,X6)) ) )
      | ~ ilf_type(X6,set_type)
      | ~ ilf_type(X5,set_type) ),
    inference(shift_quantors,[status(thm)],[179]) ).

fof(181,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ ilf_type(X8,relation_type(X5,X6))
        | ilf_type(X8,subset_type(cross_product(X5,X6)))
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
        | ilf_type(X7,relation_type(X5,X6))
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) ) ),
    inference(distribute,[status(thm)],[180]) ).

cnf(183,plain,
    ( ilf_type(X3,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[181]) ).

fof(188,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ( ( ~ empty(X1)
          | ! [X2] :
              ( ~ ilf_type(X2,set_type)
              | ~ member(X2,X1) ) )
        & ( ? [X2] :
              ( ilf_type(X2,set_type)
              & member(X2,X1) )
          | empty(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(189,plain,
    ! [X3] :
      ( ~ ilf_type(X3,set_type)
      | ( ( ~ empty(X3)
          | ! [X4] :
              ( ~ ilf_type(X4,set_type)
              | ~ member(X4,X3) ) )
        & ( ? [X5] :
              ( ilf_type(X5,set_type)
              & member(X5,X3) )
          | empty(X3) ) ) ),
    inference(variable_rename,[status(thm)],[188]) ).

fof(190,plain,
    ! [X3] :
      ( ~ ilf_type(X3,set_type)
      | ( ( ~ empty(X3)
          | ! [X4] :
              ( ~ ilf_type(X4,set_type)
              | ~ member(X4,X3) ) )
        & ( ( ilf_type(esk17_1(X3),set_type)
            & member(esk17_1(X3),X3) )
          | empty(X3) ) ) ),
    inference(skolemize,[status(esa)],[189]) ).

fof(191,plain,
    ! [X3,X4] :
      ( ( ( ~ ilf_type(X4,set_type)
          | ~ member(X4,X3)
          | ~ empty(X3) )
        & ( ( ilf_type(esk17_1(X3),set_type)
            & member(esk17_1(X3),X3) )
          | empty(X3) ) )
      | ~ ilf_type(X3,set_type) ),
    inference(shift_quantors,[status(thm)],[190]) ).

fof(192,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X4,set_type)
        | ~ member(X4,X3)
        | ~ empty(X3)
        | ~ ilf_type(X3,set_type) )
      & ( ilf_type(esk17_1(X3),set_type)
        | empty(X3)
        | ~ ilf_type(X3,set_type) )
      & ( member(esk17_1(X3),X3)
        | empty(X3)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[191]) ).

cnf(195,plain,
    ( ~ ilf_type(X1,set_type)
    | ~ empty(X1)
    | ~ member(X2,X1)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[192]) ).

cnf(212,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0)) ),
    inference(spm,[status(thm)],[93,90,theory(equality)]) ).

cnf(213,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0)) ),
    inference(spm,[status(thm)],[93,92,theory(equality)]) ).

cnf(214,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0)) ),
    inference(spm,[status(thm)],[93,91,theory(equality)]) ).

cnf(215,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1)
    | $false
    | ~ ilf_type(X1,set_type) ),
    inference(rw,[status(thm)],[195,44,theory(equality)]) ).

cnf(216,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[215,44,theory(equality)]) ).

cnf(217,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[216,theory(equality)]) ).

cnf(230,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1)
    | $false ),
    inference(rw,[status(thm)],[116,44,theory(equality)]) ).

cnf(231,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1) ),
    inference(cn,[status(thm)],[230,theory(equality)]) ).

cnf(264,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ member(X1,X2)
    | $false
    | ~ ilf_type(X1,set_type) ),
    inference(rw,[status(thm)],[172,44,theory(equality)]) ).

cnf(265,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ member(X1,X2)
    | $false
    | $false ),
    inference(rw,[status(thm)],[264,44,theory(equality)]) ).

cnf(266,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(cn,[status(thm)],[265,theory(equality)]) ).

cnf(267,plain,
    ( ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[266,217]) ).

cnf(292,plain,
    ( relation_like(X3)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(rw,[status(thm)],[42,44,theory(equality)]) ).

cnf(293,plain,
    ( relation_like(X3)
    | $false
    | $false
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(rw,[status(thm)],[292,44,theory(equality)]) ).

cnf(294,plain,
    ( relation_like(X3)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(cn,[status(thm)],[293,theory(equality)]) ).

cnf(328,plain,
    ( ilf_type(X3,subset_type(cross_product(X1,X2)))
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[183,44,theory(equality)]) ).

cnf(329,plain,
    ( ilf_type(X3,subset_type(cross_product(X1,X2)))
    | $false
    | $false
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[328,44,theory(equality)]) ).

cnf(330,plain,
    ( ilf_type(X3,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(cn,[status(thm)],[329,theory(equality)]) ).

cnf(331,plain,
    ( relation_like(X1)
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(spm,[status(thm)],[294,330,theory(equality)]) ).

cnf(336,plain,
    ( member(X4,X2)
    | $false
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(rw,[status(thm)],[146,44,theory(equality)]) ).

cnf(337,plain,
    ( member(X4,X2)
    | $false
    | $false
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(rw,[status(thm)],[336,44,theory(equality)]) ).

cnf(338,plain,
    ( member(X4,X2)
    | $false
    | $false
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(rw,[status(thm)],[337,44,theory(equality)]) ).

cnf(339,plain,
    ( member(X4,X2)
    | $false
    | $false
    | $false
    | $false
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(rw,[status(thm)],[338,44,theory(equality)]) ).

cnf(340,plain,
    ( member(X4,X2)
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(cn,[status(thm)],[339,theory(equality)]) ).

cnf(341,negated_conjecture,
    ( member(X1,esk7_0)
    | ~ member(ordered_pair(X2,X1),esk8_0) ),
    inference(spm,[status(thm)],[340,88,theory(equality)]) ).

cnf(383,plain,
    ( member(esk14_3(X1,X2,X3),X1)
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(rw,[status(thm)],[159,44,theory(equality)]) ).

cnf(384,plain,
    ( member(esk14_3(X1,X2,X3),X1)
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | $false
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(rw,[status(thm)],[383,44,theory(equality)]) ).

cnf(385,plain,
    ( member(esk14_3(X1,X2,X3),X1)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(cn,[status(thm)],[384,theory(equality)]) ).

cnf(388,plain,
    ( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
    | $false
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[38,44,theory(equality)]) ).

cnf(389,plain,
    ( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
    | $false
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[388,44,theory(equality)]) ).

cnf(390,plain,
    ( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
    | $false
    | $false
    | $false
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[389,44,theory(equality)]) ).

cnf(391,plain,
    ( inverse4(X1,X2,X3,X4) = inverse2(X3,X4)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(cn,[status(thm)],[390,theory(equality)]) ).

cnf(392,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | member(esk10_0,esk6_0)
    | ~ ilf_type(esk8_0,relation_type(esk5_0,esk7_0)) ),
    inference(spm,[status(thm)],[90,391,theory(equality)]) ).

cnf(393,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | ilf_type(esk10_0,member_type(esk7_0))
    | ~ ilf_type(esk8_0,relation_type(esk5_0,esk7_0)) ),
    inference(spm,[status(thm)],[92,391,theory(equality)]) ).

cnf(394,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ ilf_type(esk8_0,relation_type(esk5_0,esk7_0)) ),
    inference(spm,[status(thm)],[91,391,theory(equality)]) ).

cnf(395,negated_conjecture,
    ( ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0))
    | ~ ilf_type(esk8_0,relation_type(esk5_0,esk7_0)) ),
    inference(spm,[status(thm)],[93,391,theory(equality)]) ).

cnf(397,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | member(esk10_0,esk6_0)
    | $false ),
    inference(rw,[status(thm)],[392,88,theory(equality)]) ).

cnf(398,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | member(esk10_0,esk6_0) ),
    inference(cn,[status(thm)],[397,theory(equality)]) ).

cnf(399,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | ilf_type(esk10_0,member_type(esk7_0))
    | $false ),
    inference(rw,[status(thm)],[393,88,theory(equality)]) ).

cnf(400,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | ilf_type(esk10_0,member_type(esk7_0)) ),
    inference(cn,[status(thm)],[399,theory(equality)]) ).

cnf(401,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | $false ),
    inference(rw,[status(thm)],[394,88,theory(equality)]) ).

cnf(402,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,esk6_0))
    | member(ordered_pair(esk9_0,esk10_0),esk8_0) ),
    inference(cn,[status(thm)],[401,theory(equality)]) ).

cnf(403,negated_conjecture,
    ( ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0))
    | $false ),
    inference(rw,[status(thm)],[395,88,theory(equality)]) ).

cnf(404,negated_conjecture,
    ( ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0)) ),
    inference(cn,[status(thm)],[403,theory(equality)]) ).

cnf(405,plain,
    ( member(X2,inverse2(X3,X1))
    | ~ member(X4,X1)
    | $false
    | ~ ilf_type(X3,binary_relation_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ member(ordered_pair(X2,X4),X3) ),
    inference(rw,[status(thm)],[162,44,theory(equality)]) ).

cnf(406,plain,
    ( member(X2,inverse2(X3,X1))
    | ~ member(X4,X1)
    | $false
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ member(ordered_pair(X2,X4),X3) ),
    inference(rw,[status(thm)],[405,44,theory(equality)]) ).

cnf(407,plain,
    ( member(X2,inverse2(X3,X1))
    | ~ member(X4,X1)
    | $false
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | $false
    | ~ member(ordered_pair(X2,X4),X3) ),
    inference(rw,[status(thm)],[406,44,theory(equality)]) ).

cnf(408,plain,
    ( member(X2,inverse2(X3,X1))
    | ~ member(X4,X1)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(ordered_pair(X2,X4),X3) ),
    inference(cn,[status(thm)],[407,theory(equality)]) ).

cnf(417,plain,
    ( member(ordered_pair(X2,esk14_3(X1,X2,X3)),X3)
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(rw,[status(thm)],[160,44,theory(equality)]) ).

cnf(418,plain,
    ( member(ordered_pair(X2,esk14_3(X1,X2,X3)),X3)
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | $false
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(rw,[status(thm)],[417,44,theory(equality)]) ).

cnf(419,plain,
    ( member(ordered_pair(X2,esk14_3(X1,X2,X3)),X3)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(X2,inverse2(X3,X1)) ),
    inference(cn,[status(thm)],[418,theory(equality)]) ).

cnf(434,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[212,419,theory(equality)]) ).

cnf(441,negated_conjecture,
    ( member(esk14_3(X1,X2,esk8_0),esk7_0)
    | ~ member(X2,inverse2(esk8_0,X1))
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[341,419,theory(equality)]) ).

cnf(447,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[213,419,theory(equality)]) ).

cnf(448,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[214,419,theory(equality)]) ).

cnf(455,negated_conjecture,
    relation_like(esk8_0),
    inference(spm,[status(thm)],[331,88,theory(equality)]) ).

cnf(457,negated_conjecture,
    ilf_type(esk8_0,binary_relation_type),
    inference(spm,[status(thm)],[231,455,theory(equality)]) ).

cnf(616,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | $false ),
    inference(rw,[status(thm)],[434,457,theory(equality)]) ).

cnf(617,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1)) ),
    inference(cn,[status(thm)],[616,theory(equality)]) ).

cnf(618,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk7_0) ),
    inference(spm,[status(thm)],[617,267,theory(equality)]) ).

cnf(619,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[618,385,theory(equality)]) ).

cnf(620,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | $false ),
    inference(rw,[status(thm)],[619,457,theory(equality)]) ).

cnf(621,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0)) ),
    inference(cn,[status(thm)],[620,theory(equality)]) ).

cnf(622,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0) ),
    inference(csr,[status(thm)],[621,398]) ).

cnf(623,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | $false ),
    inference(rw,[status(thm)],[447,457,theory(equality)]) ).

cnf(624,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1)) ),
    inference(cn,[status(thm)],[623,theory(equality)]) ).

cnf(625,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk7_0) ),
    inference(spm,[status(thm)],[624,267,theory(equality)]) ).

cnf(626,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[625,385,theory(equality)]) ).

cnf(627,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | $false ),
    inference(rw,[status(thm)],[626,457,theory(equality)]) ).

cnf(628,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0)) ),
    inference(cn,[status(thm)],[627,theory(equality)]) ).

cnf(629,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0) ),
    inference(csr,[status(thm)],[628,400]) ).

cnf(630,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | $false ),
    inference(rw,[status(thm)],[448,457,theory(equality)]) ).

cnf(631,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ ilf_type(esk14_3(X1,esk9_0,esk8_0),member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,X1)) ),
    inference(cn,[status(thm)],[630,theory(equality)]) ).

cnf(632,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk6_0)
    | ~ member(esk9_0,inverse2(esk8_0,X1))
    | ~ member(esk14_3(X1,esk9_0,esk8_0),esk7_0) ),
    inference(spm,[status(thm)],[631,267,theory(equality)]) ).

cnf(633,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[632,385,theory(equality)]) ).

cnf(634,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0))
    | $false ),
    inference(rw,[status(thm)],[633,457,theory(equality)]) ).

cnf(635,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0)) ),
    inference(cn,[status(thm)],[634,theory(equality)]) ).

cnf(636,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk14_3(esk6_0,esk9_0,esk8_0),esk7_0) ),
    inference(csr,[status(thm)],[635,402]) ).

cnf(694,negated_conjecture,
    ( member(esk14_3(X1,X2,esk8_0),esk7_0)
    | ~ member(X2,inverse2(esk8_0,X1))
    | $false ),
    inference(rw,[status(thm)],[441,457,theory(equality)]) ).

cnf(695,negated_conjecture,
    ( member(esk14_3(X1,X2,esk8_0),esk7_0)
    | ~ member(X2,inverse2(esk8_0,X1)) ),
    inference(cn,[status(thm)],[694,theory(equality)]) ).

cnf(697,negated_conjecture,
    ( member(esk10_0,esk6_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0)) ),
    inference(spm,[status(thm)],[622,695,theory(equality)]) ).

cnf(698,negated_conjecture,
    ( ilf_type(esk10_0,member_type(esk7_0))
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0)) ),
    inference(spm,[status(thm)],[629,695,theory(equality)]) ).

cnf(699,negated_conjecture,
    ( member(ordered_pair(esk9_0,esk10_0),esk8_0)
    | ~ member(esk9_0,inverse2(esk8_0,esk6_0)) ),
    inference(spm,[status(thm)],[636,695,theory(equality)]) ).

cnf(700,negated_conjecture,
    member(esk10_0,esk6_0),
    inference(csr,[status(thm)],[697,398]) ).

cnf(711,negated_conjecture,
    ilf_type(esk10_0,member_type(esk7_0)),
    inference(csr,[status(thm)],[698,400]) ).

cnf(725,negated_conjecture,
    member(ordered_pair(esk9_0,esk10_0),esk8_0),
    inference(csr,[status(thm)],[699,402]) ).

cnf(727,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,X1))
    | ~ member(esk10_0,X1)
    | ~ ilf_type(esk8_0,binary_relation_type) ),
    inference(spm,[status(thm)],[408,725,theory(equality)]) ).

cnf(738,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,X1))
    | ~ member(esk10_0,X1)
    | $false ),
    inference(rw,[status(thm)],[727,457,theory(equality)]) ).

cnf(739,negated_conjecture,
    ( member(esk9_0,inverse2(esk8_0,X1))
    | ~ member(esk10_0,X1) ),
    inference(cn,[status(thm)],[738,theory(equality)]) ).

cnf(753,negated_conjecture,
    ( ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0))
    | ~ member(esk10_0,esk6_0) ),
    inference(spm,[status(thm)],[404,739,theory(equality)]) ).

cnf(757,negated_conjecture,
    ( ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0))
    | $false ),
    inference(rw,[status(thm)],[753,700,theory(equality)]) ).

cnf(758,negated_conjecture,
    ( ~ member(ordered_pair(esk9_0,X1),esk8_0)
    | ~ member(X1,esk6_0)
    | ~ ilf_type(X1,member_type(esk7_0)) ),
    inference(cn,[status(thm)],[757,theory(equality)]) ).

cnf(766,negated_conjecture,
    ( ~ member(esk10_0,esk6_0)
    | ~ ilf_type(esk10_0,member_type(esk7_0)) ),
    inference(spm,[status(thm)],[758,725,theory(equality)]) ).

cnf(768,negated_conjecture,
    ( $false
    | ~ ilf_type(esk10_0,member_type(esk7_0)) ),
    inference(rw,[status(thm)],[766,700,theory(equality)]) ).

cnf(769,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[768,711,theory(equality)]) ).

cnf(770,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[769,theory(equality)]) ).

cnf(771,negated_conjecture,
    $false,
    770,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET686+3.p
% --creating new selector for []
% -running prover on /tmp/tmpl2UB2b/sel_SET686+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET686+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET686+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET686+3.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
% 
%------------------------------------------------------------------------------