TSTP Solution File: SET681+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET681+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 03:10:49 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  139 (  13 unt;   0 def)
%            Number of atoms       :  657 (   8 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  862 ( 344   ~; 368   |;  98   &)
%                                         (   9 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   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;   7 con; 0-3 aty)
%            Number of variables   :  290 (  22 sgn 150   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1] :
      ( ( ~ empty(X1)
        & ilf_type(X1,set_type) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ! [X3] :
              ( ilf_type(X3,relation_type(X2,X1))
             => ! [X4] :
                  ( ilf_type(X4,member_type(X1))
                 => ( member(X4,range(X2,X1,X3))
                  <=> ? [X5] :
                        ( ilf_type(X5,member_type(X2))
                        & member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
    file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',prove_relset_1_48) ).

fof(5,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/tmpF7hMHH/sel_SET681+3.p_1',p26) ).

fof(10,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => range(X1,X2,X3) = range_of(X3) ) ) ),
    file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p29) ).

fof(12,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p10) ).

fof(19,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( ilf_type(X1,binary_relation_type)
      <=> ( relation_like(X1)
          & ilf_type(X1,set_type) ) ) ),
    file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p17) ).

fof(23,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p31) ).

fof(24,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,binary_relation_type)
             => ( member(ordered_pair(X1,X2),X3)
               => ( member(X1,domain_of(X3))
                  & member(X2,range_of(X3)) ) ) ) ) ),
    file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p2) ).

fof(25,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/tmpF7hMHH/sel_SET681+3.p_1',p3) ).

fof(26,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,binary_relation_type)
         => ( member(X1,range_of(X2))
          <=> ? [X3] :
                ( ilf_type(X3,set_type)
                & member(ordered_pair(X3,X1),X2) ) ) ) ),
    file('/tmp/tmpF7hMHH/sel_SET681+3.p_1',p1) ).

fof(27,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/tmpF7hMHH/sel_SET681+3.p_1',p6) ).

fof(31,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/tmpF7hMHH/sel_SET681+3.p_1',p8) ).

fof(33,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty(X1)
          & ilf_type(X1,set_type) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & ilf_type(X2,set_type) )
           => ! [X3] :
                ( ilf_type(X3,relation_type(X2,X1))
               => ! [X4] :
                    ( ilf_type(X4,member_type(X1))
                   => ( member(X4,range(X2,X1,X3))
                    <=> ? [X5] :
                          ( ilf_type(X5,member_type(X2))
                          & member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(34,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty(X1)
          & ilf_type(X1,set_type) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & ilf_type(X2,set_type) )
           => ! [X3] :
                ( ilf_type(X3,relation_type(X2,X1))
               => ! [X4] :
                    ( ilf_type(X4,member_type(X1))
                   => ( member(X4,range(X2,X1,X3))
                    <=> ? [X5] :
                          ( ilf_type(X5,member_type(X2))
                          & member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).

fof(36,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(37,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)],[31,theory(equality)]) ).

fof(39,negated_conjecture,
    ? [X1] :
      ( ~ empty(X1)
      & ilf_type(X1,set_type)
      & ? [X2] :
          ( ~ empty(X2)
          & ilf_type(X2,set_type)
          & ? [X3] :
              ( ilf_type(X3,relation_type(X2,X1))
              & ? [X4] :
                  ( ilf_type(X4,member_type(X1))
                  & ( ~ member(X4,range(X2,X1,X3))
                    | ! [X5] :
                        ( ~ ilf_type(X5,member_type(X2))
                        | ~ member(ordered_pair(X5,X4),X3) ) )
                  & ( member(X4,range(X2,X1,X3))
                    | ? [X5] :
                        ( ilf_type(X5,member_type(X2))
                        & member(ordered_pair(X5,X4),X3) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(40,negated_conjecture,
    ? [X6] :
      ( ~ empty(X6)
      & ilf_type(X6,set_type)
      & ? [X7] :
          ( ~ empty(X7)
          & ilf_type(X7,set_type)
          & ? [X8] :
              ( ilf_type(X8,relation_type(X7,X6))
              & ? [X9] :
                  ( ilf_type(X9,member_type(X6))
                  & ( ~ member(X9,range(X7,X6,X8))
                    | ! [X10] :
                        ( ~ ilf_type(X10,member_type(X7))
                        | ~ member(ordered_pair(X10,X9),X8) ) )
                  & ( member(X9,range(X7,X6,X8))
                    | ? [X11] :
                        ( ilf_type(X11,member_type(X7))
                        & member(ordered_pair(X11,X9),X8) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,negated_conjecture,
    ( ~ empty(esk1_0)
    & ilf_type(esk1_0,set_type)
    & ~ empty(esk2_0)
    & ilf_type(esk2_0,set_type)
    & ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
    & ilf_type(esk4_0,member_type(esk1_0))
    & ( ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0))
      | ! [X10] :
          ( ~ ilf_type(X10,member_type(esk2_0))
          | ~ member(ordered_pair(X10,esk4_0),esk3_0) ) )
    & ( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
      | ( ilf_type(esk5_0,member_type(esk2_0))
        & member(ordered_pair(esk5_0,esk4_0),esk3_0) ) ) ),
    inference(skolemize,[status(esa)],[40]) ).

fof(42,negated_conjecture,
    ! [X10] :
      ( ( ~ ilf_type(X10,member_type(esk2_0))
        | ~ member(ordered_pair(X10,esk4_0),esk3_0)
        | ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
      & ( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
        | ( ilf_type(esk5_0,member_type(esk2_0))
          & member(ordered_pair(esk5_0,esk4_0),esk3_0) ) )
      & ilf_type(esk4_0,member_type(esk1_0))
      & ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
      & ~ empty(esk2_0)
      & ilf_type(esk2_0,set_type)
      & ~ empty(esk1_0)
      & ilf_type(esk1_0,set_type) ),
    inference(shift_quantors,[status(thm)],[41]) ).

fof(43,negated_conjecture,
    ! [X10] :
      ( ( ~ ilf_type(X10,member_type(esk2_0))
        | ~ member(ordered_pair(X10,esk4_0),esk3_0)
        | ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
      & ( ilf_type(esk5_0,member_type(esk2_0))
        | member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
      & ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
        | member(esk4_0,range(esk2_0,esk1_0,esk3_0)) )
      & ilf_type(esk4_0,member_type(esk1_0))
      & ilf_type(esk3_0,relation_type(esk2_0,esk1_0))
      & ~ empty(esk2_0)
      & ilf_type(esk2_0,set_type)
      & ~ empty(esk1_0)
      & ilf_type(esk1_0,set_type) ),
    inference(distribute,[status(thm)],[42]) ).

cnf(48,negated_conjecture,
    ilf_type(esk3_0,relation_type(esk2_0,esk1_0)),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(50,negated_conjecture,
    ( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
    | member(ordered_pair(esk5_0,esk4_0),esk3_0) ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(51,negated_conjecture,
    ( member(esk4_0,range(esk2_0,esk1_0,esk3_0))
    | ilf_type(esk5_0,member_type(esk2_0)) ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(52,negated_conjecture,
    ( ~ member(esk4_0,range(esk2_0,esk1_0,esk3_0))
    | ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | ~ ilf_type(X1,member_type(esk2_0)) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(71,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)],[5]) ).

fof(72,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)],[71]) ).

fof(73,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)],[72]) ).

cnf(74,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)],[73]) ).

fof(103,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,relation_type(X1,X2))
              | range(X1,X2,X3) = range_of(X3) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(104,plain,
    ! [X4] :
      ( ~ ilf_type(X4,set_type)
      | ! [X5] :
          ( ~ ilf_type(X5,set_type)
          | ! [X6] :
              ( ~ ilf_type(X6,relation_type(X4,X5))
              | range(X4,X5,X6) = range_of(X6) ) ) ),
    inference(variable_rename,[status(thm)],[103]) ).

fof(105,plain,
    ! [X4,X5,X6] :
      ( ~ ilf_type(X6,relation_type(X4,X5))
      | range(X4,X5,X6) = range_of(X6)
      | ~ ilf_type(X5,set_type)
      | ~ ilf_type(X4,set_type) ),
    inference(shift_quantors,[status(thm)],[104]) ).

cnf(106,plain,
    ( range(X1,X2,X3) = range_of(X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[105]) ).

fof(111,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)],[36]) ).

fof(112,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)],[111]) ).

fof(113,plain,
    ! [X3] :
      ( ~ ilf_type(X3,set_type)
      | ( ( ~ empty(X3)
          | ! [X4] :
              ( ~ ilf_type(X4,set_type)
              | ~ member(X4,X3) ) )
        & ( ( ilf_type(esk12_1(X3),set_type)
            & member(esk12_1(X3),X3) )
          | empty(X3) ) ) ),
    inference(skolemize,[status(esa)],[112]) ).

fof(114,plain,
    ! [X3,X4] :
      ( ( ( ~ ilf_type(X4,set_type)
          | ~ member(X4,X3)
          | ~ empty(X3) )
        & ( ( ilf_type(esk12_1(X3),set_type)
            & member(esk12_1(X3),X3) )
          | empty(X3) ) )
      | ~ ilf_type(X3,set_type) ),
    inference(shift_quantors,[status(thm)],[113]) ).

fof(115,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X4,set_type)
        | ~ member(X4,X3)
        | ~ empty(X3)
        | ~ ilf_type(X3,set_type) )
      & ( ilf_type(esk12_1(X3),set_type)
        | empty(X3)
        | ~ ilf_type(X3,set_type) )
      & ( member(esk12_1(X3),X3)
        | empty(X3)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[114]) ).

cnf(118,plain,
    ( ~ ilf_type(X1,set_type)
    | ~ empty(X1)
    | ~ member(X2,X1)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[115]) ).

fof(140,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)],[19]) ).

fof(141,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)],[140]) ).

fof(142,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)],[141]) ).

cnf(143,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)],[142]) ).

fof(159,plain,
    ! [X2] : ilf_type(X2,set_type),
    inference(variable_rename,[status(thm)],[23]) ).

cnf(160,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[159]) ).

fof(161,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,binary_relation_type)
              | ~ member(ordered_pair(X1,X2),X3)
              | ( member(X1,domain_of(X3))
                & member(X2,range_of(X3)) ) ) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(162,plain,
    ! [X4] :
      ( ~ ilf_type(X4,set_type)
      | ! [X5] :
          ( ~ ilf_type(X5,set_type)
          | ! [X6] :
              ( ~ ilf_type(X6,binary_relation_type)
              | ~ member(ordered_pair(X4,X5),X6)
              | ( member(X4,domain_of(X6))
                & member(X5,range_of(X6)) ) ) ) ),
    inference(variable_rename,[status(thm)],[161]) ).

fof(163,plain,
    ! [X4,X5,X6] :
      ( ~ ilf_type(X6,binary_relation_type)
      | ~ member(ordered_pair(X4,X5),X6)
      | ( member(X4,domain_of(X6))
        & member(X5,range_of(X6)) )
      | ~ ilf_type(X5,set_type)
      | ~ ilf_type(X4,set_type) ),
    inference(shift_quantors,[status(thm)],[162]) ).

fof(164,plain,
    ! [X4,X5,X6] :
      ( ( member(X4,domain_of(X6))
        | ~ member(ordered_pair(X4,X5),X6)
        | ~ ilf_type(X6,binary_relation_type)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( member(X5,range_of(X6))
        | ~ member(ordered_pair(X4,X5),X6)
        | ~ ilf_type(X6,binary_relation_type)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) ) ),
    inference(distribute,[status(thm)],[163]) ).

cnf(165,plain,
    ( member(X2,range_of(X3))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(ordered_pair(X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[164]) ).

fof(167,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)],[25]) ).

fof(168,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)],[167]) ).

fof(169,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)],[168]) ).

fof(170,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)],[169]) ).

cnf(172,plain,
    ( member(X3,X1)
    | ~ 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)],[170]) ).

fof(173,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,binary_relation_type)
          | ( ( ~ member(X1,range_of(X2))
              | ? [X3] :
                  ( ilf_type(X3,set_type)
                  & member(ordered_pair(X3,X1),X2) ) )
            & ( ! [X3] :
                  ( ~ ilf_type(X3,set_type)
                  | ~ member(ordered_pair(X3,X1),X2) )
              | member(X1,range_of(X2)) ) ) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(174,plain,
    ! [X4] :
      ( ~ ilf_type(X4,set_type)
      | ! [X5] :
          ( ~ ilf_type(X5,binary_relation_type)
          | ( ( ~ member(X4,range_of(X5))
              | ? [X6] :
                  ( ilf_type(X6,set_type)
                  & member(ordered_pair(X6,X4),X5) ) )
            & ( ! [X7] :
                  ( ~ ilf_type(X7,set_type)
                  | ~ member(ordered_pair(X7,X4),X5) )
              | member(X4,range_of(X5)) ) ) ) ),
    inference(variable_rename,[status(thm)],[173]) ).

fof(175,plain,
    ! [X4] :
      ( ~ ilf_type(X4,set_type)
      | ! [X5] :
          ( ~ ilf_type(X5,binary_relation_type)
          | ( ( ~ member(X4,range_of(X5))
              | ( ilf_type(esk14_2(X4,X5),set_type)
                & member(ordered_pair(esk14_2(X4,X5),X4),X5) ) )
            & ( ! [X7] :
                  ( ~ ilf_type(X7,set_type)
                  | ~ member(ordered_pair(X7,X4),X5) )
              | member(X4,range_of(X5)) ) ) ) ),
    inference(skolemize,[status(esa)],[174]) ).

fof(176,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ ilf_type(X7,set_type)
          | ~ member(ordered_pair(X7,X4),X5)
          | member(X4,range_of(X5)) )
        & ( ~ member(X4,range_of(X5))
          | ( ilf_type(esk14_2(X4,X5),set_type)
            & member(ordered_pair(esk14_2(X4,X5),X4),X5) ) ) )
      | ~ ilf_type(X5,binary_relation_type)
      | ~ ilf_type(X4,set_type) ),
    inference(shift_quantors,[status(thm)],[175]) ).

fof(177,plain,
    ! [X4,X5,X7] :
      ( ( ~ ilf_type(X7,set_type)
        | ~ member(ordered_pair(X7,X4),X5)
        | member(X4,range_of(X5))
        | ~ ilf_type(X5,binary_relation_type)
        | ~ ilf_type(X4,set_type) )
      & ( ilf_type(esk14_2(X4,X5),set_type)
        | ~ member(X4,range_of(X5))
        | ~ ilf_type(X5,binary_relation_type)
        | ~ ilf_type(X4,set_type) )
      & ( member(ordered_pair(esk14_2(X4,X5),X4),X5)
        | ~ member(X4,range_of(X5))
        | ~ ilf_type(X5,binary_relation_type)
        | ~ ilf_type(X4,set_type) ) ),
    inference(distribute,[status(thm)],[176]) ).

cnf(178,plain,
    ( member(ordered_pair(esk14_2(X1,X2),X1),X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,binary_relation_type)
    | ~ member(X1,range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[177]) ).

fof(181,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)],[27]) ).

fof(182,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)],[181]) ).

fof(183,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)],[182]) ).

fof(184,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)],[183]) ).

cnf(186,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)],[184]) ).

fof(202,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)],[37]) ).

fof(203,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)],[202]) ).

fof(204,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)],[203]) ).

fof(205,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)],[204]) ).

cnf(206,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)],[205]) ).

cnf(224,negated_conjecture,
    ( ilf_type(esk5_0,member_type(esk2_0))
    | ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | ~ ilf_type(X1,member_type(esk2_0)) ),
    inference(spm,[status(thm)],[52,51,theory(equality)]) ).

cnf(225,negated_conjecture,
    ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | ~ ilf_type(X1,member_type(esk2_0)) ),
    inference(spm,[status(thm)],[52,50,theory(equality)]) ).

cnf(228,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1)
    | $false
    | ~ ilf_type(X1,set_type) ),
    inference(rw,[status(thm)],[118,160,theory(equality)]) ).

cnf(229,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[228,160,theory(equality)]) ).

cnf(230,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[229,theory(equality)]) ).

cnf(242,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1)
    | $false ),
    inference(rw,[status(thm)],[143,160,theory(equality)]) ).

cnf(243,plain,
    ( ilf_type(X1,binary_relation_type)
    | ~ relation_like(X1) ),
    inference(cn,[status(thm)],[242,theory(equality)]) ).

cnf(273,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ member(X1,X2)
    | $false
    | ~ ilf_type(X1,set_type) ),
    inference(rw,[status(thm)],[206,160,theory(equality)]) ).

cnf(274,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ member(X1,X2)
    | $false
    | $false ),
    inference(rw,[status(thm)],[273,160,theory(equality)]) ).

cnf(275,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(cn,[status(thm)],[274,theory(equality)]) ).

cnf(276,plain,
    ( ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[275,230]) ).

cnf(297,plain,
    ( relation_like(X3)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(rw,[status(thm)],[74,160,theory(equality)]) ).

cnf(298,plain,
    ( relation_like(X3)
    | $false
    | $false
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(rw,[status(thm)],[297,160,theory(equality)]) ).

cnf(299,plain,
    ( relation_like(X3)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(cn,[status(thm)],[298,theory(equality)]) ).

cnf(343,plain,
    ( member(X2,range_of(X3))
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ member(ordered_pair(X1,X2),X3) ),
    inference(rw,[status(thm)],[165,160,theory(equality)]) ).

cnf(344,plain,
    ( member(X2,range_of(X3))
    | ~ ilf_type(X3,binary_relation_type)
    | $false
    | $false
    | ~ member(ordered_pair(X1,X2),X3) ),
    inference(rw,[status(thm)],[343,160,theory(equality)]) ).

cnf(345,plain,
    ( member(X2,range_of(X3))
    | ~ ilf_type(X3,binary_relation_type)
    | ~ member(ordered_pair(X1,X2),X3) ),
    inference(cn,[status(thm)],[344,theory(equality)]) ).

cnf(352,plain,
    ( range(X1,X2,X3) = range_of(X3)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[106,160,theory(equality)]) ).

cnf(353,plain,
    ( range(X1,X2,X3) = range_of(X3)
    | $false
    | $false
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[352,160,theory(equality)]) ).

cnf(354,plain,
    ( range(X1,X2,X3) = range_of(X3)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(cn,[status(thm)],[353,theory(equality)]) ).

cnf(355,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | ilf_type(esk5_0,member_type(esk2_0))
    | ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[51,354,theory(equality)]) ).

cnf(356,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[50,354,theory(equality)]) ).

cnf(357,negated_conjecture,
    ( ~ member(esk4_0,range_of(esk3_0))
    | ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | ~ ilf_type(X1,member_type(esk2_0))
    | ~ ilf_type(esk3_0,relation_type(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[52,354,theory(equality)]) ).

cnf(358,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | ilf_type(esk5_0,member_type(esk2_0))
    | $false ),
    inference(rw,[status(thm)],[355,48,theory(equality)]) ).

cnf(359,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | ilf_type(esk5_0,member_type(esk2_0)) ),
    inference(cn,[status(thm)],[358,theory(equality)]) ).

cnf(360,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | $false ),
    inference(rw,[status(thm)],[356,48,theory(equality)]) ).

cnf(361,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | member(ordered_pair(esk5_0,esk4_0),esk3_0) ),
    inference(cn,[status(thm)],[360,theory(equality)]) ).

cnf(362,negated_conjecture,
    ( ~ member(esk4_0,range_of(esk3_0))
    | ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | ~ ilf_type(X1,member_type(esk2_0))
    | $false ),
    inference(rw,[status(thm)],[357,48,theory(equality)]) ).

cnf(363,negated_conjecture,
    ( ~ member(esk4_0,range_of(esk3_0))
    | ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | ~ ilf_type(X1,member_type(esk2_0)) ),
    inference(cn,[status(thm)],[362,theory(equality)]) ).

cnf(364,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)],[186,160,theory(equality)]) ).

cnf(365,plain,
    ( ilf_type(X3,subset_type(cross_product(X1,X2)))
    | $false
    | $false
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[364,160,theory(equality)]) ).

cnf(366,plain,
    ( ilf_type(X3,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(cn,[status(thm)],[365,theory(equality)]) ).

cnf(367,plain,
    ( relation_like(X1)
    | ~ ilf_type(X1,relation_type(X2,X3)) ),
    inference(spm,[status(thm)],[299,366,theory(equality)]) ).

cnf(378,plain,
    ( member(ordered_pair(esk14_2(X1,X2),X1),X2)
    | ~ ilf_type(X2,binary_relation_type)
    | $false
    | ~ member(X1,range_of(X2)) ),
    inference(rw,[status(thm)],[178,160,theory(equality)]) ).

cnf(379,plain,
    ( member(ordered_pair(esk14_2(X1,X2),X1),X2)
    | ~ ilf_type(X2,binary_relation_type)
    | ~ member(X1,range_of(X2)) ),
    inference(cn,[status(thm)],[378,theory(equality)]) ).

cnf(410,plain,
    ( member(X3,X1)
    | $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)],[172,160,theory(equality)]) ).

cnf(411,plain,
    ( member(X3,X1)
    | $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)],[410,160,theory(equality)]) ).

cnf(412,plain,
    ( member(X3,X1)
    | $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)],[411,160,theory(equality)]) ).

cnf(413,plain,
    ( member(X3,X1)
    | $false
    | $false
    | $false
    | $false
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(rw,[status(thm)],[412,160,theory(equality)]) ).

cnf(414,plain,
    ( member(X3,X1)
    | ~ ilf_type(X5,relation_type(X1,X2))
    | ~ member(ordered_pair(X3,X4),X5) ),
    inference(cn,[status(thm)],[413,theory(equality)]) ).

cnf(415,negated_conjecture,
    ( member(X1,esk2_0)
    | ~ member(ordered_pair(X1,X2),esk3_0) ),
    inference(spm,[status(thm)],[414,48,theory(equality)]) ).

cnf(452,negated_conjecture,
    ( ilf_type(esk5_0,member_type(esk2_0))
    | ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
    | ~ member(esk4_0,range_of(esk3_0))
    | ~ ilf_type(esk3_0,binary_relation_type) ),
    inference(spm,[status(thm)],[224,379,theory(equality)]) ).

cnf(458,negated_conjecture,
    ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
    | ~ member(esk4_0,range_of(esk3_0))
    | ~ ilf_type(esk3_0,binary_relation_type) ),
    inference(spm,[status(thm)],[225,379,theory(equality)]) ).

cnf(461,negated_conjecture,
    ( member(esk14_2(X1,esk3_0),esk2_0)
    | ~ member(X1,range_of(esk3_0))
    | ~ ilf_type(esk3_0,binary_relation_type) ),
    inference(spm,[status(thm)],[415,379,theory(equality)]) ).

cnf(481,negated_conjecture,
    ( ilf_type(esk5_0,member_type(esk2_0))
    | ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
    | ~ ilf_type(esk3_0,binary_relation_type) ),
    inference(csr,[status(thm)],[452,359]) ).

cnf(482,negated_conjecture,
    ( ilf_type(esk5_0,member_type(esk2_0))
    | ~ ilf_type(esk3_0,binary_relation_type)
    | ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[481,276,theory(equality)]) ).

cnf(483,negated_conjecture,
    ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ ilf_type(esk14_2(esk4_0,esk3_0),member_type(esk2_0))
    | ~ ilf_type(esk3_0,binary_relation_type) ),
    inference(csr,[status(thm)],[458,361]) ).

cnf(484,negated_conjecture,
    ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ ilf_type(esk3_0,binary_relation_type)
    | ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[483,276,theory(equality)]) ).

cnf(497,negated_conjecture,
    relation_like(esk3_0),
    inference(spm,[status(thm)],[367,48,theory(equality)]) ).

cnf(510,negated_conjecture,
    ilf_type(esk3_0,binary_relation_type),
    inference(spm,[status(thm)],[243,497,theory(equality)]) ).

cnf(513,negated_conjecture,
    ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ member(esk14_2(esk4_0,esk3_0),esk2_0)
    | $false ),
    inference(rw,[status(thm)],[484,510,theory(equality)]) ).

cnf(514,negated_conjecture,
    ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
    inference(cn,[status(thm)],[513,theory(equality)]) ).

cnf(517,negated_conjecture,
    ( ilf_type(esk5_0,member_type(esk2_0))
    | ~ member(esk14_2(esk4_0,esk3_0),esk2_0)
    | $false ),
    inference(rw,[status(thm)],[482,510,theory(equality)]) ).

cnf(518,negated_conjecture,
    ( ilf_type(esk5_0,member_type(esk2_0))
    | ~ member(esk14_2(esk4_0,esk3_0),esk2_0) ),
    inference(cn,[status(thm)],[517,theory(equality)]) ).

cnf(592,negated_conjecture,
    ( member(esk14_2(X1,esk3_0),esk2_0)
    | ~ member(X1,range_of(esk3_0))
    | $false ),
    inference(rw,[status(thm)],[461,510,theory(equality)]) ).

cnf(593,negated_conjecture,
    ( member(esk14_2(X1,esk3_0),esk2_0)
    | ~ member(X1,range_of(esk3_0)) ),
    inference(cn,[status(thm)],[592,theory(equality)]) ).

cnf(595,negated_conjecture,
    ( ilf_type(esk5_0,member_type(esk2_0))
    | ~ member(esk4_0,range_of(esk3_0)) ),
    inference(spm,[status(thm)],[518,593,theory(equality)]) ).

cnf(596,negated_conjecture,
    ( member(ordered_pair(esk5_0,esk4_0),esk3_0)
    | ~ member(esk4_0,range_of(esk3_0)) ),
    inference(spm,[status(thm)],[514,593,theory(equality)]) ).

cnf(597,negated_conjecture,
    ilf_type(esk5_0,member_type(esk2_0)),
    inference(csr,[status(thm)],[595,359]) ).

cnf(610,negated_conjecture,
    member(ordered_pair(esk5_0,esk4_0),esk3_0),
    inference(csr,[status(thm)],[596,361]) ).

cnf(612,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | ~ ilf_type(esk3_0,binary_relation_type) ),
    inference(spm,[status(thm)],[345,610,theory(equality)]) ).

cnf(623,negated_conjecture,
    ( member(esk4_0,range_of(esk3_0))
    | $false ),
    inference(rw,[status(thm)],[612,510,theory(equality)]) ).

cnf(624,negated_conjecture,
    member(esk4_0,range_of(esk3_0)),
    inference(cn,[status(thm)],[623,theory(equality)]) ).

cnf(632,negated_conjecture,
    ( ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | $false
    | ~ ilf_type(X1,member_type(esk2_0)) ),
    inference(rw,[status(thm)],[363,624,theory(equality)]) ).

cnf(633,negated_conjecture,
    ( ~ member(ordered_pair(X1,esk4_0),esk3_0)
    | ~ ilf_type(X1,member_type(esk2_0)) ),
    inference(cn,[status(thm)],[632,theory(equality)]) ).

cnf(647,negated_conjecture,
    ~ ilf_type(esk5_0,member_type(esk2_0)),
    inference(spm,[status(thm)],[633,610,theory(equality)]) ).

cnf(649,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[647,597,theory(equality)]) ).

cnf(650,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[649,theory(equality)]) ).

cnf(651,negated_conjecture,
    $false,
    650,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET681+3.p
% --creating new selector for []
% -running prover on /tmp/tmpF7hMHH/sel_SET681+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET681+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET681+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET681+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
% 
%------------------------------------------------------------------------------