TSTP Solution File: SEU171+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU171+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 05:04:54 EST 2010

% Result   : Theorem 95.35s
% Output   : CNFRefutation 95.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   93 (  27 unt;   0 def)
%            Number of atoms       :  299 (  40 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  337 ( 131   ~; 122   |;  51   &)
%                                         (   9 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :  146 (   2 sgn 104   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(28,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,subset_complement(X1,X2)) = X2 ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',involutiveness_k3_subset_1) ).

fof(35,axiom,
    ! [X1,X2] :
      ( X2 = powerset(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> subset(X3,X1) ) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',d1_zfmisc_1) ).

fof(56,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',t69_enumset1) ).

fof(60,axiom,
    ! [X1,X2,X3] :
      ( subset(unordered_pair(X1,X2),X3)
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',t38_zfmisc_1) ).

fof(61,axiom,
    ! [X1] : ~ empty(powerset(X1)),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',fc1_subset_1) ).

fof(62,axiom,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',t37_zfmisc_1) ).

fof(65,axiom,
    ! [X1,X2] :
      ( ( ~ empty(X1)
       => ( element(X2,X1)
        <=> in(X2,X1) ) )
      & ( empty(X1)
       => ( element(X2,X1)
        <=> empty(X2) ) ) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',d2_subset_1) ).

fof(70,axiom,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',l28_zfmisc_1) ).

fof(72,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,X2) = set_difference(X1,X2) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',d5_subset_1) ).

fof(78,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',t6_boole) ).

fof(80,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => element(subset_complement(X1,X2),powerset(X1)) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',dt_k3_subset_1) ).

fof(85,conjecture,
    ! [X1] :
      ( X1 != empty_set
     => ! [X2] :
          ( element(X2,powerset(X1))
         => ! [X3] :
              ( element(X3,X1)
             => ( ~ in(X3,X2)
               => in(X3,subset_complement(X1,X2)) ) ) ) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',t50_subset_1) ).

fof(100,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => ! [X3] :
          ( element(X3,powerset(X1))
         => ( disjoint(X2,X3)
          <=> subset(X2,subset_complement(X1,X3)) ) ) ),
    file('/tmp/tmpeA0GWR/sel_SEU171+2.p_2',t43_subset_1) ).

fof(112,negated_conjecture,
    ~ ! [X1] :
        ( X1 != empty_set
       => ! [X2] :
            ( element(X2,powerset(X1))
           => ! [X3] :
                ( element(X3,X1)
               => ( ~ in(X3,X2)
                 => in(X3,subset_complement(X1,X2)) ) ) ) ),
    inference(assume_negation,[status(cth)],[85]) ).

fof(123,plain,
    ! [X1] : ~ empty(powerset(X1)),
    inference(fof_simplification,[status(thm)],[61,theory(equality)]) ).

fof(124,plain,
    ! [X1,X2] :
      ( ( ~ empty(X1)
       => ( element(X2,X1)
        <=> in(X2,X1) ) )
      & ( empty(X1)
       => ( element(X2,X1)
        <=> empty(X2) ) ) ),
    inference(fof_simplification,[status(thm)],[65,theory(equality)]) ).

fof(125,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    inference(fof_simplification,[status(thm)],[70,theory(equality)]) ).

fof(130,negated_conjecture,
    ~ ! [X1] :
        ( X1 != empty_set
       => ! [X2] :
            ( element(X2,powerset(X1))
           => ! [X3] :
                ( element(X3,X1)
               => ( ~ in(X3,X2)
                 => in(X3,subset_complement(X1,X2)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[112,theory(equality)]) ).

fof(216,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | subset_complement(X1,subset_complement(X1,X2)) = X2 ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(217,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | subset_complement(X3,subset_complement(X3,X4)) = X4 ),
    inference(variable_rename,[status(thm)],[216]) ).

cnf(218,plain,
    ( subset_complement(X1,subset_complement(X1,X2)) = X2
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[217]) ).

fof(246,plain,
    ! [X1,X2] :
      ( ( X2 != powerset(X1)
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | subset(X3,X1) )
            & ( ~ subset(X3,X1)
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ subset(X3,X1) )
            & ( in(X3,X2)
              | subset(X3,X1) ) )
        | X2 = powerset(X1) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(247,plain,
    ! [X4,X5] :
      ( ( X5 != powerset(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | subset(X6,X4) )
            & ( ~ subset(X6,X4)
              | in(X6,X5) ) ) )
      & ( ? [X7] :
            ( ( ~ in(X7,X5)
              | ~ subset(X7,X4) )
            & ( in(X7,X5)
              | subset(X7,X4) ) )
        | X5 = powerset(X4) ) ),
    inference(variable_rename,[status(thm)],[246]) ).

fof(248,plain,
    ! [X4,X5] :
      ( ( X5 != powerset(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | subset(X6,X4) )
            & ( ~ subset(X6,X4)
              | in(X6,X5) ) ) )
      & ( ( ( ~ in(esk6_2(X4,X5),X5)
            | ~ subset(esk6_2(X4,X5),X4) )
          & ( in(esk6_2(X4,X5),X5)
            | subset(esk6_2(X4,X5),X4) ) )
        | X5 = powerset(X4) ) ),
    inference(skolemize,[status(esa)],[247]) ).

fof(249,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ in(X6,X5)
            | subset(X6,X4) )
          & ( ~ subset(X6,X4)
            | in(X6,X5) ) )
        | X5 != powerset(X4) )
      & ( ( ( ~ in(esk6_2(X4,X5),X5)
            | ~ subset(esk6_2(X4,X5),X4) )
          & ( in(esk6_2(X4,X5),X5)
            | subset(esk6_2(X4,X5),X4) ) )
        | X5 = powerset(X4) ) ),
    inference(shift_quantors,[status(thm)],[248]) ).

fof(250,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X5)
        | subset(X6,X4)
        | X5 != powerset(X4) )
      & ( ~ subset(X6,X4)
        | in(X6,X5)
        | X5 != powerset(X4) )
      & ( ~ in(esk6_2(X4,X5),X5)
        | ~ subset(esk6_2(X4,X5),X4)
        | X5 = powerset(X4) )
      & ( in(esk6_2(X4,X5),X5)
        | subset(esk6_2(X4,X5),X4)
        | X5 = powerset(X4) ) ),
    inference(distribute,[status(thm)],[249]) ).

cnf(253,plain,
    ( in(X3,X1)
    | X1 != powerset(X2)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[250]) ).

fof(323,plain,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[56]) ).

cnf(324,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[323]) ).

fof(332,plain,
    ! [X1,X2,X3] :
      ( ( ~ subset(unordered_pair(X1,X2),X3)
        | ( in(X1,X3)
          & in(X2,X3) ) )
      & ( ~ in(X1,X3)
        | ~ in(X2,X3)
        | subset(unordered_pair(X1,X2),X3) ) ),
    inference(fof_nnf,[status(thm)],[60]) ).

fof(333,plain,
    ! [X4,X5,X6] :
      ( ( ~ subset(unordered_pair(X4,X5),X6)
        | ( in(X4,X6)
          & in(X5,X6) ) )
      & ( ~ in(X4,X6)
        | ~ in(X5,X6)
        | subset(unordered_pair(X4,X5),X6) ) ),
    inference(variable_rename,[status(thm)],[332]) ).

fof(334,plain,
    ! [X4,X5,X6] :
      ( ( in(X4,X6)
        | ~ subset(unordered_pair(X4,X5),X6) )
      & ( in(X5,X6)
        | ~ subset(unordered_pair(X4,X5),X6) )
      & ( ~ in(X4,X6)
        | ~ in(X5,X6)
        | subset(unordered_pair(X4,X5),X6) ) ),
    inference(distribute,[status(thm)],[333]) ).

cnf(336,plain,
    ( in(X2,X3)
    | ~ subset(unordered_pair(X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[334]) ).

fof(338,plain,
    ! [X2] : ~ empty(powerset(X2)),
    inference(variable_rename,[status(thm)],[123]) ).

cnf(339,plain,
    ~ empty(powerset(X1)),
    inference(split_conjunct,[status(thm)],[338]) ).

fof(340,plain,
    ! [X1,X2] :
      ( ( ~ subset(singleton(X1),X2)
        | in(X1,X2) )
      & ( ~ in(X1,X2)
        | subset(singleton(X1),X2) ) ),
    inference(fof_nnf,[status(thm)],[62]) ).

fof(341,plain,
    ! [X3,X4] :
      ( ( ~ subset(singleton(X3),X4)
        | in(X3,X4) )
      & ( ~ in(X3,X4)
        | subset(singleton(X3),X4) ) ),
    inference(variable_rename,[status(thm)],[340]) ).

cnf(342,plain,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[341]) ).

fof(350,plain,
    ! [X1,X2] :
      ( ( empty(X1)
        | ( ( ~ element(X2,X1)
            | in(X2,X1) )
          & ( ~ in(X2,X1)
            | element(X2,X1) ) ) )
      & ( ~ empty(X1)
        | ( ( ~ element(X2,X1)
            | empty(X2) )
          & ( ~ empty(X2)
            | element(X2,X1) ) ) ) ),
    inference(fof_nnf,[status(thm)],[124]) ).

fof(351,plain,
    ! [X3,X4] :
      ( ( empty(X3)
        | ( ( ~ element(X4,X3)
            | in(X4,X3) )
          & ( ~ in(X4,X3)
            | element(X4,X3) ) ) )
      & ( ~ empty(X3)
        | ( ( ~ element(X4,X3)
            | empty(X4) )
          & ( ~ empty(X4)
            | element(X4,X3) ) ) ) ),
    inference(variable_rename,[status(thm)],[350]) ).

fof(352,plain,
    ! [X3,X4] :
      ( ( ~ element(X4,X3)
        | in(X4,X3)
        | empty(X3) )
      & ( ~ in(X4,X3)
        | element(X4,X3)
        | empty(X3) )
      & ( ~ element(X4,X3)
        | empty(X4)
        | ~ empty(X3) )
      & ( ~ empty(X4)
        | element(X4,X3)
        | ~ empty(X3) ) ),
    inference(distribute,[status(thm)],[351]) ).

cnf(355,plain,
    ( empty(X1)
    | element(X2,X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[352]) ).

cnf(356,plain,
    ( empty(X1)
    | in(X2,X1)
    | ~ element(X2,X1) ),
    inference(split_conjunct,[status(thm)],[352]) ).

fof(366,plain,
    ! [X1,X2] :
      ( in(X1,X2)
      | disjoint(singleton(X1),X2) ),
    inference(fof_nnf,[status(thm)],[125]) ).

fof(367,plain,
    ! [X3,X4] :
      ( in(X3,X4)
      | disjoint(singleton(X3),X4) ),
    inference(variable_rename,[status(thm)],[366]) ).

cnf(368,plain,
    ( disjoint(singleton(X1),X2)
    | in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[367]) ).

fof(375,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | subset_complement(X1,X2) = set_difference(X1,X2) ),
    inference(fof_nnf,[status(thm)],[72]) ).

fof(376,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | subset_complement(X3,X4) = set_difference(X3,X4) ),
    inference(variable_rename,[status(thm)],[375]) ).

cnf(377,plain,
    ( subset_complement(X1,X2) = set_difference(X1,X2)
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[376]) ).

fof(394,plain,
    ! [X1] :
      ( ~ empty(X1)
      | X1 = empty_set ),
    inference(fof_nnf,[status(thm)],[78]) ).

fof(395,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[394]) ).

cnf(396,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[395]) ).

fof(408,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | element(subset_complement(X1,X2),powerset(X1)) ),
    inference(fof_nnf,[status(thm)],[80]) ).

fof(409,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | element(subset_complement(X3,X4),powerset(X3)) ),
    inference(variable_rename,[status(thm)],[408]) ).

cnf(410,plain,
    ( element(subset_complement(X1,X2),powerset(X1))
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[409]) ).

fof(430,negated_conjecture,
    ? [X1] :
      ( X1 != empty_set
      & ? [X2] :
          ( element(X2,powerset(X1))
          & ? [X3] :
              ( element(X3,X1)
              & ~ in(X3,X2)
              & ~ in(X3,subset_complement(X1,X2)) ) ) ),
    inference(fof_nnf,[status(thm)],[130]) ).

fof(431,negated_conjecture,
    ? [X4] :
      ( X4 != empty_set
      & ? [X5] :
          ( element(X5,powerset(X4))
          & ? [X6] :
              ( element(X6,X4)
              & ~ in(X6,X5)
              & ~ in(X6,subset_complement(X4,X5)) ) ) ),
    inference(variable_rename,[status(thm)],[430]) ).

fof(432,negated_conjecture,
    ( esk18_0 != empty_set
    & element(esk19_0,powerset(esk18_0))
    & element(esk20_0,esk18_0)
    & ~ in(esk20_0,esk19_0)
    & ~ in(esk20_0,subset_complement(esk18_0,esk19_0)) ),
    inference(skolemize,[status(esa)],[431]) ).

cnf(433,negated_conjecture,
    ~ in(esk20_0,subset_complement(esk18_0,esk19_0)),
    inference(split_conjunct,[status(thm)],[432]) ).

cnf(434,negated_conjecture,
    ~ in(esk20_0,esk19_0),
    inference(split_conjunct,[status(thm)],[432]) ).

cnf(435,negated_conjecture,
    element(esk20_0,esk18_0),
    inference(split_conjunct,[status(thm)],[432]) ).

cnf(436,negated_conjecture,
    element(esk19_0,powerset(esk18_0)),
    inference(split_conjunct,[status(thm)],[432]) ).

cnf(437,negated_conjecture,
    esk18_0 != empty_set,
    inference(split_conjunct,[status(thm)],[432]) ).

fof(503,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | ! [X3] :
          ( ~ element(X3,powerset(X1))
          | ( ( ~ disjoint(X2,X3)
              | subset(X2,subset_complement(X1,X3)) )
            & ( ~ subset(X2,subset_complement(X1,X3))
              | disjoint(X2,X3) ) ) ) ),
    inference(fof_nnf,[status(thm)],[100]) ).

fof(504,plain,
    ! [X4,X5] :
      ( ~ element(X5,powerset(X4))
      | ! [X6] :
          ( ~ element(X6,powerset(X4))
          | ( ( ~ disjoint(X5,X6)
              | subset(X5,subset_complement(X4,X6)) )
            & ( ~ subset(X5,subset_complement(X4,X6))
              | disjoint(X5,X6) ) ) ) ),
    inference(variable_rename,[status(thm)],[503]) ).

fof(505,plain,
    ! [X4,X5,X6] :
      ( ~ element(X6,powerset(X4))
      | ( ( ~ disjoint(X5,X6)
          | subset(X5,subset_complement(X4,X6)) )
        & ( ~ subset(X5,subset_complement(X4,X6))
          | disjoint(X5,X6) ) )
      | ~ element(X5,powerset(X4)) ),
    inference(shift_quantors,[status(thm)],[504]) ).

fof(506,plain,
    ! [X4,X5,X6] :
      ( ( ~ disjoint(X5,X6)
        | subset(X5,subset_complement(X4,X6))
        | ~ element(X6,powerset(X4))
        | ~ element(X5,powerset(X4)) )
      & ( ~ subset(X5,subset_complement(X4,X6))
        | disjoint(X5,X6)
        | ~ element(X6,powerset(X4))
        | ~ element(X5,powerset(X4)) ) ),
    inference(distribute,[status(thm)],[505]) ).

cnf(508,plain,
    ( subset(X1,subset_complement(X2,X3))
    | ~ element(X1,powerset(X2))
    | ~ element(X3,powerset(X2))
    | ~ disjoint(X1,X3) ),
    inference(split_conjunct,[status(thm)],[506]) ).

cnf(560,plain,
    ( in(X1,X2)
    | disjoint(unordered_pair(X1,X1),X2) ),
    inference(rw,[status(thm)],[368,324,theory(equality)]),
    [unfolding] ).

cnf(573,plain,
    ( subset(unordered_pair(X1,X1),X2)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[342,324,theory(equality)]),
    [unfolding] ).

cnf(749,negated_conjecture,
    ( empty(esk18_0)
    | in(esk20_0,esk18_0) ),
    inference(spm,[status(thm)],[356,435,theory(equality)]) ).

cnf(828,negated_conjecture,
    subset_complement(esk18_0,esk19_0) = set_difference(esk18_0,esk19_0),
    inference(spm,[status(thm)],[377,436,theory(equality)]) ).

cnf(888,negated_conjecture,
    element(subset_complement(esk18_0,esk19_0),powerset(esk18_0)),
    inference(spm,[status(thm)],[410,436,theory(equality)]) ).

cnf(971,negated_conjecture,
    subset_complement(esk18_0,subset_complement(esk18_0,esk19_0)) = esk19_0,
    inference(spm,[status(thm)],[218,436,theory(equality)]) ).

cnf(1300,plain,
    ( in(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(er,[status(thm)],[253,theory(equality)]) ).

cnf(2503,negated_conjecture,
    ( empty_set = esk18_0
    | in(esk20_0,esk18_0) ),
    inference(spm,[status(thm)],[396,749,theory(equality)]) ).

cnf(2507,negated_conjecture,
    in(esk20_0,esk18_0),
    inference(sr,[status(thm)],[2503,437,theory(equality)]) ).

cnf(2514,negated_conjecture,
    subset(unordered_pair(esk20_0,esk20_0),esk18_0),
    inference(spm,[status(thm)],[573,2507,theory(equality)]) ).

cnf(2712,negated_conjecture,
    ~ in(esk20_0,set_difference(esk18_0,esk19_0)),
    inference(rw,[status(thm)],[433,828,theory(equality)]) ).

cnf(2714,negated_conjecture,
    element(set_difference(esk18_0,esk19_0),powerset(esk18_0)),
    inference(rw,[status(thm)],[888,828,theory(equality)]) ).

cnf(2725,negated_conjecture,
    ( subset(X1,subset_complement(esk18_0,set_difference(esk18_0,esk19_0)))
    | ~ element(X1,powerset(esk18_0))
    | ~ disjoint(X1,set_difference(esk18_0,esk19_0)) ),
    inference(spm,[status(thm)],[508,2714,theory(equality)]) ).

cnf(2735,negated_conjecture,
    subset_complement(esk18_0,set_difference(esk18_0,esk19_0)) = esk19_0,
    inference(rw,[status(thm)],[971,828,theory(equality)]) ).

cnf(48490,negated_conjecture,
    in(unordered_pair(esk20_0,esk20_0),powerset(esk18_0)),
    inference(spm,[status(thm)],[1300,2514,theory(equality)]) ).

cnf(48775,negated_conjecture,
    ( element(unordered_pair(esk20_0,esk20_0),powerset(esk18_0))
    | empty(powerset(esk18_0)) ),
    inference(spm,[status(thm)],[355,48490,theory(equality)]) ).

cnf(48801,negated_conjecture,
    element(unordered_pair(esk20_0,esk20_0),powerset(esk18_0)),
    inference(sr,[status(thm)],[48775,339,theory(equality)]) ).

cnf(737458,negated_conjecture,
    ( subset(X1,esk19_0)
    | ~ element(X1,powerset(esk18_0))
    | ~ disjoint(X1,set_difference(esk18_0,esk19_0)) ),
    inference(rw,[status(thm)],[2725,2735,theory(equality)]) ).

cnf(737468,negated_conjecture,
    ( subset(unordered_pair(esk20_0,esk20_0),esk19_0)
    | ~ disjoint(unordered_pair(esk20_0,esk20_0),set_difference(esk18_0,esk19_0)) ),
    inference(spm,[status(thm)],[737458,48801,theory(equality)]) ).

cnf(737655,plain,
    ( subset(unordered_pair(esk20_0,esk20_0),esk19_0)
    | in(esk20_0,set_difference(esk18_0,esk19_0)) ),
    inference(spm,[status(thm)],[737468,560,theory(equality)]) ).

cnf(737676,plain,
    subset(unordered_pair(esk20_0,esk20_0),esk19_0),
    inference(sr,[status(thm)],[737655,2712,theory(equality)]) ).

cnf(737684,plain,
    in(esk20_0,esk19_0),
    inference(spm,[status(thm)],[336,737676,theory(equality)]) ).

cnf(737821,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[434,737684,theory(equality)]) ).

cnf(737822,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[737821,theory(equality)]) ).

cnf(737823,negated_conjecture,
    $false,
    737822,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU171+2.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpeA0GWR/sel_SEU171+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpeA0GWR/sel_SEU171+2.p_2 with time limit 80
% -prover status Theorem
% Problem SEU171+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU171+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU171+2.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
% 
%------------------------------------------------------------------------------