TSTP Solution File: SET973+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET973+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 04:00:46 EST 2010

% Result   : Theorem 81.18s
% Output   : CNFRefutation 81.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   82 (  44 unt;   0 def)
%            Number of atoms       :  234 (  73 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  247 (  95   ~;  99   |;  46   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :  218 (  13 sgn  94   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2,X3,X4] : set_difference(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = set_union2(cartesian_product2(set_difference(X1,X3),X2),cartesian_product2(X1,set_difference(X2,X4))),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',t126_zfmisc_1) ).

fof(3,axiom,
    ! [X1,X2,X3] : set_difference(X1,set_intersection2(X2,X3)) = set_union2(set_difference(X1,X2),set_difference(X1,X3)),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',t54_xboole_1) ).

fof(6,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',commutativity_k2_xboole_0) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( cartesian_product2(set_difference(X1,X2),X3) = set_difference(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
      & cartesian_product2(X3,set_difference(X1,X2)) = set_difference(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',t125_zfmisc_1) ).

fof(12,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',d4_xboole_0) ).

fof(13,axiom,
    ! [X1,X2] : subset(set_intersection2(X1,X2),X1),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',t17_xboole_1) ).

fof(16,axiom,
    ! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',t123_zfmisc_1) ).

fof(18,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',commutativity_k3_xboole_0) ).

fof(21,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',d10_xboole_0) ).

fof(26,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/tmp/tmps_GMD8/sel_SET973+1.p_2',d3_tarski) ).

fof(27,negated_conjecture,
    ~ ! [X1,X2,X3,X4] : set_difference(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = set_union2(cartesian_product2(set_difference(X1,X3),X2),cartesian_product2(X1,set_difference(X2,X4))),
    inference(assume_negation,[status(cth)],[1]) ).

fof(32,plain,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(34,negated_conjecture,
    ? [X1,X2,X3,X4] : set_difference(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) != set_union2(cartesian_product2(set_difference(X1,X3),X2),cartesian_product2(X1,set_difference(X2,X4))),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(35,negated_conjecture,
    ? [X5,X6,X7,X8] : set_difference(cartesian_product2(X5,X6),cartesian_product2(X7,X8)) != set_union2(cartesian_product2(set_difference(X5,X7),X6),cartesian_product2(X5,set_difference(X6,X8))),
    inference(variable_rename,[status(thm)],[34]) ).

fof(36,negated_conjecture,
    set_difference(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) != set_union2(cartesian_product2(set_difference(esk1_0,esk3_0),esk2_0),cartesian_product2(esk1_0,set_difference(esk2_0,esk4_0))),
    inference(skolemize,[status(esa)],[35]) ).

cnf(37,negated_conjecture,
    set_difference(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) != set_union2(cartesian_product2(set_difference(esk1_0,esk3_0),esk2_0),cartesian_product2(esk1_0,set_difference(esk2_0,esk4_0))),
    inference(split_conjunct,[status(thm)],[36]) ).

fof(41,plain,
    ! [X4,X5,X6] : set_difference(X4,set_intersection2(X5,X6)) = set_union2(set_difference(X4,X5),set_difference(X4,X6)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(42,plain,
    set_difference(X1,set_intersection2(X2,X3)) = set_union2(set_difference(X1,X2),set_difference(X1,X3)),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(48,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(49,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(50,plain,
    ! [X4,X5,X6] :
      ( cartesian_product2(set_difference(X4,X5),X6) = set_difference(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
      & cartesian_product2(X6,set_difference(X4,X5)) = set_difference(cartesian_product2(X6,X4),cartesian_product2(X6,X5)) ),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(51,plain,
    cartesian_product2(X1,set_difference(X2,X3)) = set_difference(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(52,plain,
    cartesian_product2(set_difference(X1,X2),X3) = set_difference(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(63,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_difference(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ( in(X4,X1)
                & ~ in(X4,X2) ) )
            & ( ~ in(X4,X1)
              | in(X4,X2)
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,X1)
              | in(X4,X2) )
            & ( in(X4,X3)
              | ( in(X4,X1)
                & ~ in(X4,X2) ) ) )
        | X3 = set_difference(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(64,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & ~ in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ~ in(X9,X5)
              | in(X9,X6) )
            & ( in(X9,X7)
              | ( in(X9,X5)
                & ~ in(X9,X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[63]) ).

fof(65,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & ~ in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
            | ~ in(esk6_3(X5,X6,X7),X5)
            | in(esk6_3(X5,X6,X7),X6) )
          & ( in(esk6_3(X5,X6,X7),X7)
            | ( in(esk6_3(X5,X6,X7),X5)
              & ~ in(esk6_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(skolemize,[status(esa)],[64]) ).

fof(66,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | ( in(X8,X5)
              & ~ in(X8,X6) ) )
          & ( ~ in(X8,X5)
            | in(X8,X6)
            | in(X8,X7) ) )
        | X7 != set_difference(X5,X6) )
      & ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
            | ~ in(esk6_3(X5,X6,X7),X5)
            | in(esk6_3(X5,X6,X7),X6) )
          & ( in(esk6_3(X5,X6,X7),X7)
            | ( in(esk6_3(X5,X6,X7),X5)
              & ~ in(esk6_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[65]) ).

fof(67,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X6)
        | in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(esk6_3(X5,X6,X7),X7)
        | ~ in(esk6_3(X5,X6,X7),X5)
        | in(esk6_3(X5,X6,X7),X6)
        | X7 = set_difference(X5,X6) )
      & ( in(esk6_3(X5,X6,X7),X5)
        | in(esk6_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) )
      & ( ~ in(esk6_3(X5,X6,X7),X6)
        | in(esk6_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) ) ),
    inference(distribute,[status(thm)],[66]) ).

cnf(69,plain,
    ( X1 = set_difference(X2,X3)
    | in(esk6_3(X2,X3,X1),X1)
    | in(esk6_3(X2,X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(70,plain,
    ( X1 = set_difference(X2,X3)
    | in(esk6_3(X2,X3,X1),X3)
    | ~ in(esk6_3(X2,X3,X1),X2)
    | ~ in(esk6_3(X2,X3,X1),X1) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(72,plain,
    ( X1 != set_difference(X2,X3)
    | ~ in(X4,X1)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(73,plain,
    ( in(X4,X2)
    | X1 != set_difference(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[67]) ).

fof(74,plain,
    ! [X3,X4] : subset(set_intersection2(X3,X4),X3),
    inference(variable_rename,[status(thm)],[13]) ).

cnf(75,plain,
    subset(set_intersection2(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(90,plain,
    ! [X5,X6,X7,X8] : cartesian_product2(set_intersection2(X5,X6),set_intersection2(X7,X8)) = set_intersection2(cartesian_product2(X5,X7),cartesian_product2(X6,X8)),
    inference(variable_rename,[status(thm)],[16]) ).

cnf(91,plain,
    cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    inference(split_conjunct,[status(thm)],[90]) ).

fof(94,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(95,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[94]) ).

fof(104,plain,
    ! [X1,X2] :
      ( ( X1 != X2
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(105,plain,
    ! [X3,X4] :
      ( ( X3 != X4
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(variable_rename,[status(thm)],[104]) ).

fof(106,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[105]) ).

cnf(107,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[106]) ).

fof(131,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X2) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(132,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ? [X7] :
            ( in(X7,X4)
            & ~ in(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[131]) ).

fof(133,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ( in(esk14_2(X4,X5),X4)
          & ~ in(esk14_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[132]) ).

fof(134,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( in(esk14_2(X4,X5),X4)
          & ~ in(esk14_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[133]) ).

fof(135,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( in(esk14_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk14_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[134]) ).

cnf(136,plain,
    ( subset(X1,X2)
    | ~ in(esk14_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(137,plain,
    ( subset(X1,X2)
    | in(esk14_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(138,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(168,plain,
    set_union2(cartesian_product2(X1,set_difference(X2,X3)),set_difference(cartesian_product2(X1,X2),X4)) = set_difference(cartesian_product2(X1,X2),set_intersection2(cartesian_product2(X1,X3),X4)),
    inference(spm,[status(thm)],[42,51,theory(equality)]) ).

cnf(182,plain,
    ( X1 = set_intersection2(X1,X2)
    | ~ subset(X1,set_intersection2(X1,X2)) ),
    inference(spm,[status(thm)],[107,75,theory(equality)]) ).

cnf(190,plain,
    ( in(X1,X2)
    | ~ in(X1,set_difference(X2,X3)) ),
    inference(er,[status(thm)],[73,theory(equality)]) ).

cnf(213,plain,
    ( ~ in(X1,X2)
    | ~ in(X1,set_difference(X3,X2)) ),
    inference(er,[status(thm)],[72,theory(equality)]) ).

cnf(223,plain,
    cartesian_product2(set_intersection2(X1,X2),set_intersection2(X4,X3)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    inference(spm,[status(thm)],[91,95,theory(equality)]) ).

cnf(227,plain,
    set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    inference(rw,[status(thm)],[223,91,theory(equality)]) ).

cnf(230,negated_conjecture,
    set_union2(cartesian_product2(esk1_0,set_difference(esk2_0,esk4_0)),cartesian_product2(set_difference(esk1_0,esk3_0),esk2_0)) != set_difference(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),
    inference(rw,[status(thm)],[37,49,theory(equality)]) ).

cnf(265,plain,
    ( set_difference(X4,X5) = X4
    | in(esk6_3(X4,X5,X4),X4) ),
    inference(ef,[status(thm)],[69,theory(equality)]) ).

cnf(342,plain,
    ( subset(set_difference(X1,X2),X3)
    | ~ in(esk14_2(set_difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[213,137,theory(equality)]) ).

cnf(377,plain,
    set_union2(cartesian_product2(X1,set_difference(X2,X3)),cartesian_product2(set_difference(X1,X4),X2)) = set_difference(cartesian_product2(X1,X2),set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X4,X2))),
    inference(spm,[status(thm)],[168,52,theory(equality)]) ).

cnf(392,plain,
    ( in(esk14_2(set_difference(X1,X2),X3),X1)
    | subset(set_difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[190,137,theory(equality)]) ).

cnf(1081,plain,
    subset(set_difference(X1,X2),X1),
    inference(spm,[status(thm)],[136,392,theory(equality)]) ).

cnf(1091,plain,
    ( X1 = set_difference(X1,X2)
    | ~ subset(X1,set_difference(X1,X2)) ),
    inference(spm,[status(thm)],[107,1081,theory(equality)]) ).

cnf(1272,plain,
    subset(set_difference(X1,X1),X2),
    inference(spm,[status(thm)],[342,392,theory(equality)]) ).

cnf(1276,plain,
    ( in(X1,X2)
    | ~ in(X1,set_difference(X3,X3)) ),
    inference(spm,[status(thm)],[138,1272,theory(equality)]) ).

cnf(1277,plain,
    set_intersection2(set_difference(X1,X1),X2) = set_difference(X1,X1),
    inference(spm,[status(thm)],[182,1272,theory(equality)]) ).

cnf(1278,plain,
    set_difference(set_difference(X1,X1),X2) = set_difference(X1,X1),
    inference(spm,[status(thm)],[1091,1272,theory(equality)]) ).

cnf(1307,plain,
    ( ~ in(X1,set_difference(X2,X2))
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[213,1278,theory(equality)]) ).

cnf(1350,plain,
    set_difference(X1,X1) = set_intersection2(X2,set_difference(X1,X1)),
    inference(spm,[status(thm)],[95,1277,theory(equality)]) ).

cnf(1369,plain,
    set_difference(X2,X2) = set_difference(X1,X1),
    inference(spm,[status(thm)],[1277,1350,theory(equality)]) ).

cnf(1387,plain,
    set_union2(set_difference(X3,X3),set_difference(X1,X2)) = set_difference(X1,set_intersection2(X1,X2)),
    inference(spm,[status(thm)],[42,1369,theory(equality)]) ).

cnf(3527,plain,
    ~ in(X1,set_difference(X2,X2)),
    inference(csr,[status(thm)],[1307,1276]) ).

cnf(7387,plain,
    ( set_difference(X1,X2) = X1
    | in(esk6_3(X1,X2,X1),X2)
    | ~ in(esk6_3(X1,X2,X1),X1) ),
    inference(spm,[status(thm)],[70,265,theory(equality)]) ).

cnf(19062,negated_conjecture,
    set_difference(cartesian_product2(esk1_0,esk2_0),set_intersection2(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))) != set_difference(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[230,377,theory(equality)]),227,theory(equality)]) ).

cnf(1498614,plain,
    ( set_difference(X1,X2) = X1
    | in(esk6_3(X1,X2,X1),X2) ),
    inference(csr,[status(thm)],[7387,265]) ).

cnf(1498615,plain,
    set_difference(X1,set_difference(X2,X2)) = X1,
    inference(spm,[status(thm)],[3527,1498614,theory(equality)]) ).

cnf(1499161,plain,
    set_union2(set_difference(X1,X1),X2) = set_difference(X2,set_intersection2(X2,set_difference(X3,X3))),
    inference(spm,[status(thm)],[1387,1498615,theory(equality)]) ).

cnf(1500489,plain,
    set_union2(set_difference(X1,X1),X2) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1499161,1350,theory(equality)]),1498615,theory(equality)]) ).

cnf(1509047,plain,
    set_difference(X2,X3) = set_difference(X2,set_intersection2(X2,X3)),
    inference(rw,[status(thm)],[1387,1500489,theory(equality)]) ).

cnf(1514230,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[19062,1509047,theory(equality)]) ).

cnf(1514231,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[1514230,theory(equality)]) ).

cnf(1514232,negated_conjecture,
    $false,
    1514231,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET973+1.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmps_GMD8/sel_SET973+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmps_GMD8/sel_SET973+1.p_2 with time limit 81
% -prover status Theorem
% Problem SET973+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET973+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET973+1.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
% 
%------------------------------------------------------------------------------