TSTP Solution File: SEU325+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU325+2 : TPTP v5.0.0. Released v3.3.0.
% 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 07:22:14 EST 2010

% Result   : Theorem 9.76s
% Output   : CNFRefutation 9.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   94 (  31 unt;   0 def)
%            Number of atoms       :  274 (  55 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  295 ( 115   ~; 105   |;  54   &)
%                                         (   6 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-2 aty)
%            Number of variables   :   93 (   4 sgn  65   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(10,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => ( empty_carrier(X1)
      <=> empty(the_carrier(X1)) ) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',d1_struct_0) ).

fof(52,axiom,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',t3_xboole_1) ).

fof(89,axiom,
    ( empty(empty_set)
    & relation(empty_set) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',fc4_relat_1) ).

fof(97,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => union_of_subsets(X1,X2) = union(X2) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',redefinition_k5_setfam_1) ).

fof(129,axiom,
    ! [X1] : singleton(X1) != empty_set,
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',l1_zfmisc_1) ).

fof(245,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( element(X2,powerset(powerset(the_carrier(X1))))
         => ~ ( is_a_cover_of_carrier(X1,X2)
              & X2 = empty_set ) ) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',t5_tops_2) ).

fof(250,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => ! [X2] :
          ( element(X2,powerset(powerset(the_carrier(X1))))
         => ( is_a_cover_of_carrier(X1,X2)
          <=> cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ) ) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',d8_pre_topc) ).

fof(279,axiom,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',l2_zfmisc_1) ).

fof(287,axiom,
    ! [X1] :
      ( being_limit_ordinal(X1)
    <=> X1 = union(X1) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',d6_ordinal1) ).

fof(315,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => cast_as_carrier_subset(X1) = the_carrier(X1) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',d3_pre_topc) ).

fof(360,axiom,
    ( relation(empty_set)
    & relation_empty_yielding(empty_set)
    & function(empty_set)
    & one_to_one(empty_set)
    & empty(empty_set)
    & epsilon_transitive(empty_set)
    & epsilon_connected(empty_set)
    & ordinal(empty_set) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',fc2_ordinal1) ).

fof(377,axiom,
    ! [X1] :
      ( ordinal(X1)
     => ( being_limit_ordinal(X1)
      <=> ! [X2] :
            ( ordinal(X2)
           => ( in(X2,X1)
             => in(succ(X2),X1) ) ) ) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',t41_ordinal1) ).

fof(466,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',t3_subset) ).

fof(479,axiom,
    ! [X1] : subset(empty_set,X1),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',t2_xboole_1) ).

fof(487,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/tmp/tmpTngZ5z/sel_SEU325+2.p_1',t69_enumset1) ).

fof(539,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( element(X2,powerset(powerset(the_carrier(X1))))
           => ~ ( is_a_cover_of_carrier(X1,X2)
                & X2 = empty_set ) ) ),
    inference(assume_negation,[status(cth)],[245]) ).

fof(576,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( element(X2,powerset(powerset(the_carrier(X1))))
           => ~ ( is_a_cover_of_carrier(X1,X2)
                & X2 = empty_set ) ) ),
    inference(fof_simplification,[status(thm)],[539,theory(equality)]) ).

fof(672,plain,
    ! [X1] :
      ( ~ one_sorted_str(X1)
      | ( ( ~ empty_carrier(X1)
          | empty(the_carrier(X1)) )
        & ( ~ empty(the_carrier(X1))
          | empty_carrier(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(673,plain,
    ! [X2] :
      ( ~ one_sorted_str(X2)
      | ( ( ~ empty_carrier(X2)
          | empty(the_carrier(X2)) )
        & ( ~ empty(the_carrier(X2))
          | empty_carrier(X2) ) ) ),
    inference(variable_rename,[status(thm)],[672]) ).

fof(674,plain,
    ! [X2] :
      ( ( ~ empty_carrier(X2)
        | empty(the_carrier(X2))
        | ~ one_sorted_str(X2) )
      & ( ~ empty(the_carrier(X2))
        | empty_carrier(X2)
        | ~ one_sorted_str(X2) ) ),
    inference(distribute,[status(thm)],[673]) ).

cnf(675,plain,
    ( empty_carrier(X1)
    | ~ one_sorted_str(X1)
    | ~ empty(the_carrier(X1)) ),
    inference(split_conjunct,[status(thm)],[674]) ).

fof(884,plain,
    ! [X1] :
      ( ~ subset(X1,empty_set)
      | X1 = empty_set ),
    inference(fof_nnf,[status(thm)],[52]) ).

fof(885,plain,
    ! [X2] :
      ( ~ subset(X2,empty_set)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[884]) ).

cnf(886,plain,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[885]) ).

cnf(1204,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[89]) ).

fof(1258,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(powerset(X1)))
      | union_of_subsets(X1,X2) = union(X2) ),
    inference(fof_nnf,[status(thm)],[97]) ).

fof(1259,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(X3)))
      | union_of_subsets(X3,X4) = union(X4) ),
    inference(variable_rename,[status(thm)],[1258]) ).

cnf(1260,plain,
    ( union_of_subsets(X1,X2) = union(X2)
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(split_conjunct,[status(thm)],[1259]) ).

fof(1620,plain,
    ! [X2] : singleton(X2) != empty_set,
    inference(variable_rename,[status(thm)],[129]) ).

cnf(1621,plain,
    singleton(X1) != empty_set,
    inference(split_conjunct,[status(thm)],[1620]) ).

fof(2195,negated_conjecture,
    ? [X1] :
      ( ~ empty_carrier(X1)
      & one_sorted_str(X1)
      & ? [X2] :
          ( element(X2,powerset(powerset(the_carrier(X1))))
          & is_a_cover_of_carrier(X1,X2)
          & X2 = empty_set ) ),
    inference(fof_nnf,[status(thm)],[576]) ).

fof(2196,negated_conjecture,
    ? [X3] :
      ( ~ empty_carrier(X3)
      & one_sorted_str(X3)
      & ? [X4] :
          ( element(X4,powerset(powerset(the_carrier(X3))))
          & is_a_cover_of_carrier(X3,X4)
          & X4 = empty_set ) ),
    inference(variable_rename,[status(thm)],[2195]) ).

fof(2197,negated_conjecture,
    ( ~ empty_carrier(esk157_0)
    & one_sorted_str(esk157_0)
    & element(esk158_0,powerset(powerset(the_carrier(esk157_0))))
    & is_a_cover_of_carrier(esk157_0,esk158_0)
    & esk158_0 = empty_set ),
    inference(skolemize,[status(esa)],[2196]) ).

cnf(2198,negated_conjecture,
    esk158_0 = empty_set,
    inference(split_conjunct,[status(thm)],[2197]) ).

cnf(2199,negated_conjecture,
    is_a_cover_of_carrier(esk157_0,esk158_0),
    inference(split_conjunct,[status(thm)],[2197]) ).

cnf(2200,negated_conjecture,
    element(esk158_0,powerset(powerset(the_carrier(esk157_0)))),
    inference(split_conjunct,[status(thm)],[2197]) ).

cnf(2201,negated_conjecture,
    one_sorted_str(esk157_0),
    inference(split_conjunct,[status(thm)],[2197]) ).

cnf(2202,negated_conjecture,
    ~ empty_carrier(esk157_0),
    inference(split_conjunct,[status(thm)],[2197]) ).

fof(2229,plain,
    ! [X1] :
      ( ~ one_sorted_str(X1)
      | ! [X2] :
          ( ~ element(X2,powerset(powerset(the_carrier(X1))))
          | ( ( ~ is_a_cover_of_carrier(X1,X2)
              | cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) )
            & ( cast_as_carrier_subset(X1) != union_of_subsets(the_carrier(X1),X2)
              | is_a_cover_of_carrier(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[250]) ).

fof(2230,plain,
    ! [X3] :
      ( ~ one_sorted_str(X3)
      | ! [X4] :
          ( ~ element(X4,powerset(powerset(the_carrier(X3))))
          | ( ( ~ is_a_cover_of_carrier(X3,X4)
              | cast_as_carrier_subset(X3) = union_of_subsets(the_carrier(X3),X4) )
            & ( cast_as_carrier_subset(X3) != union_of_subsets(the_carrier(X3),X4)
              | is_a_cover_of_carrier(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[2229]) ).

fof(2231,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(the_carrier(X3))))
      | ( ( ~ is_a_cover_of_carrier(X3,X4)
          | cast_as_carrier_subset(X3) = union_of_subsets(the_carrier(X3),X4) )
        & ( cast_as_carrier_subset(X3) != union_of_subsets(the_carrier(X3),X4)
          | is_a_cover_of_carrier(X3,X4) ) )
      | ~ one_sorted_str(X3) ),
    inference(shift_quantors,[status(thm)],[2230]) ).

fof(2232,plain,
    ! [X3,X4] :
      ( ( ~ is_a_cover_of_carrier(X3,X4)
        | cast_as_carrier_subset(X3) = union_of_subsets(the_carrier(X3),X4)
        | ~ element(X4,powerset(powerset(the_carrier(X3))))
        | ~ one_sorted_str(X3) )
      & ( cast_as_carrier_subset(X3) != union_of_subsets(the_carrier(X3),X4)
        | is_a_cover_of_carrier(X3,X4)
        | ~ element(X4,powerset(powerset(the_carrier(X3))))
        | ~ one_sorted_str(X3) ) ),
    inference(distribute,[status(thm)],[2231]) ).

cnf(2234,plain,
    ( cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2)
    | ~ one_sorted_str(X1)
    | ~ element(X2,powerset(powerset(the_carrier(X1))))
    | ~ is_a_cover_of_carrier(X1,X2) ),
    inference(split_conjunct,[status(thm)],[2232]) ).

fof(2424,plain,
    ! [X1,X2] :
      ( ( ~ subset(singleton(X1),X2)
        | in(X1,X2) )
      & ( ~ in(X1,X2)
        | subset(singleton(X1),X2) ) ),
    inference(fof_nnf,[status(thm)],[279]) ).

fof(2425,plain,
    ! [X3,X4] :
      ( ( ~ subset(singleton(X3),X4)
        | in(X3,X4) )
      & ( ~ in(X3,X4)
        | subset(singleton(X3),X4) ) ),
    inference(variable_rename,[status(thm)],[2424]) ).

cnf(2426,plain,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[2425]) ).

fof(2472,plain,
    ! [X1] :
      ( ( ~ being_limit_ordinal(X1)
        | X1 = union(X1) )
      & ( X1 != union(X1)
        | being_limit_ordinal(X1) ) ),
    inference(fof_nnf,[status(thm)],[287]) ).

fof(2473,plain,
    ! [X2] :
      ( ( ~ being_limit_ordinal(X2)
        | X2 = union(X2) )
      & ( X2 != union(X2)
        | being_limit_ordinal(X2) ) ),
    inference(variable_rename,[status(thm)],[2472]) ).

cnf(2475,plain,
    ( X1 = union(X1)
    | ~ being_limit_ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[2473]) ).

fof(2633,plain,
    ! [X1] :
      ( ~ one_sorted_str(X1)
      | cast_as_carrier_subset(X1) = the_carrier(X1) ),
    inference(fof_nnf,[status(thm)],[315]) ).

fof(2634,plain,
    ! [X2] :
      ( ~ one_sorted_str(X2)
      | cast_as_carrier_subset(X2) = the_carrier(X2) ),
    inference(variable_rename,[status(thm)],[2633]) ).

cnf(2635,plain,
    ( cast_as_carrier_subset(X1) = the_carrier(X1)
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[2634]) ).

cnf(2927,plain,
    ordinal(empty_set),
    inference(split_conjunct,[status(thm)],[360]) ).

fof(3031,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | ( ( ~ being_limit_ordinal(X1)
          | ! [X2] :
              ( ~ ordinal(X2)
              | ~ in(X2,X1)
              | in(succ(X2),X1) ) )
        & ( ? [X2] :
              ( ordinal(X2)
              & in(X2,X1)
              & ~ in(succ(X2),X1) )
          | being_limit_ordinal(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[377]) ).

fof(3032,plain,
    ! [X3] :
      ( ~ ordinal(X3)
      | ( ( ~ being_limit_ordinal(X3)
          | ! [X4] :
              ( ~ ordinal(X4)
              | ~ in(X4,X3)
              | in(succ(X4),X3) ) )
        & ( ? [X5] :
              ( ordinal(X5)
              & in(X5,X3)
              & ~ in(succ(X5),X3) )
          | being_limit_ordinal(X3) ) ) ),
    inference(variable_rename,[status(thm)],[3031]) ).

fof(3033,plain,
    ! [X3] :
      ( ~ ordinal(X3)
      | ( ( ~ being_limit_ordinal(X3)
          | ! [X4] :
              ( ~ ordinal(X4)
              | ~ in(X4,X3)
              | in(succ(X4),X3) ) )
        & ( ( ordinal(esk242_1(X3))
            & in(esk242_1(X3),X3)
            & ~ in(succ(esk242_1(X3)),X3) )
          | being_limit_ordinal(X3) ) ) ),
    inference(skolemize,[status(esa)],[3032]) ).

fof(3034,plain,
    ! [X3,X4] :
      ( ( ( ~ ordinal(X4)
          | ~ in(X4,X3)
          | in(succ(X4),X3)
          | ~ being_limit_ordinal(X3) )
        & ( ( ordinal(esk242_1(X3))
            & in(esk242_1(X3),X3)
            & ~ in(succ(esk242_1(X3)),X3) )
          | being_limit_ordinal(X3) ) )
      | ~ ordinal(X3) ),
    inference(shift_quantors,[status(thm)],[3033]) ).

fof(3035,plain,
    ! [X3,X4] :
      ( ( ~ ordinal(X4)
        | ~ in(X4,X3)
        | in(succ(X4),X3)
        | ~ being_limit_ordinal(X3)
        | ~ ordinal(X3) )
      & ( ordinal(esk242_1(X3))
        | being_limit_ordinal(X3)
        | ~ ordinal(X3) )
      & ( in(esk242_1(X3),X3)
        | being_limit_ordinal(X3)
        | ~ ordinal(X3) )
      & ( ~ in(succ(esk242_1(X3)),X3)
        | being_limit_ordinal(X3)
        | ~ ordinal(X3) ) ),
    inference(distribute,[status(thm)],[3034]) ).

cnf(3037,plain,
    ( being_limit_ordinal(X1)
    | in(esk242_1(X1),X1)
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[3035]) ).

fof(3733,plain,
    ! [X1,X2] :
      ( ( ~ element(X1,powerset(X2))
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | element(X1,powerset(X2)) ) ),
    inference(fof_nnf,[status(thm)],[466]) ).

fof(3734,plain,
    ! [X3,X4] :
      ( ( ~ element(X3,powerset(X4))
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | element(X3,powerset(X4)) ) ),
    inference(variable_rename,[status(thm)],[3733]) ).

cnf(3735,plain,
    ( element(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[3734]) ).

fof(3812,plain,
    ! [X2] : subset(empty_set,X2),
    inference(variable_rename,[status(thm)],[479]) ).

cnf(3813,plain,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[3812]) ).

fof(3849,plain,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[487]) ).

cnf(3850,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[3849]) ).

cnf(4212,plain,
    ( subset(unordered_pair(X1,X1),X2)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[2426,3850,theory(equality)]),
    [unfolding] ).

cnf(4315,plain,
    unordered_pair(X1,X1) != empty_set,
    inference(rw,[status(thm)],[1621,3850,theory(equality)]),
    [unfolding] ).

cnf(4947,negated_conjecture,
    is_a_cover_of_carrier(esk157_0,empty_set),
    inference(rw,[status(thm)],[2199,2198,theory(equality)]) ).

cnf(4955,negated_conjecture,
    element(empty_set,powerset(powerset(the_carrier(esk157_0)))),
    inference(rw,[status(thm)],[2200,2198,theory(equality)]) ).

cnf(4983,negated_conjecture,
    cast_as_carrier_subset(esk157_0) = the_carrier(esk157_0),
    inference(spm,[status(thm)],[2635,2201,theory(equality)]) ).

cnf(4987,negated_conjecture,
    ( ~ one_sorted_str(esk157_0)
    | ~ empty(the_carrier(esk157_0)) ),
    inference(spm,[status(thm)],[2202,675,theory(equality)]) ).

cnf(4990,negated_conjecture,
    ( $false
    | ~ empty(the_carrier(esk157_0)) ),
    inference(rw,[status(thm)],[4987,2201,theory(equality)]) ).

cnf(4991,negated_conjecture,
    ~ empty(the_carrier(esk157_0)),
    inference(cn,[status(thm)],[4990,theory(equality)]) ).

cnf(5048,plain,
    element(empty_set,powerset(X1)),
    inference(spm,[status(thm)],[3735,3813,theory(equality)]) ).

cnf(6558,plain,
    ( empty_set = unordered_pair(X1,X1)
    | ~ in(X1,empty_set) ),
    inference(spm,[status(thm)],[886,4212,theory(equality)]) ).

cnf(6563,plain,
    ~ in(X1,empty_set),
    inference(sr,[status(thm)],[6558,4315,theory(equality)]) ).

cnf(8967,negated_conjecture,
    ( union_of_subsets(the_carrier(esk157_0),empty_set) = cast_as_carrier_subset(esk157_0)
    | ~ one_sorted_str(esk157_0)
    | ~ element(empty_set,powerset(powerset(the_carrier(esk157_0)))) ),
    inference(spm,[status(thm)],[2234,4947,theory(equality)]) ).

cnf(8968,negated_conjecture,
    ( union_of_subsets(the_carrier(esk157_0),empty_set) = cast_as_carrier_subset(esk157_0)
    | $false
    | ~ element(empty_set,powerset(powerset(the_carrier(esk157_0)))) ),
    inference(rw,[status(thm)],[8967,2201,theory(equality)]) ).

cnf(8969,negated_conjecture,
    ( union_of_subsets(the_carrier(esk157_0),empty_set) = cast_as_carrier_subset(esk157_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[8968,4955,theory(equality)]) ).

cnf(8970,negated_conjecture,
    union_of_subsets(the_carrier(esk157_0),empty_set) = cast_as_carrier_subset(esk157_0),
    inference(cn,[status(thm)],[8969,theory(equality)]) ).

cnf(99808,plain,
    ( being_limit_ordinal(empty_set)
    | ~ ordinal(empty_set) ),
    inference(spm,[status(thm)],[6563,3037,theory(equality)]) ).

cnf(99959,plain,
    ( being_limit_ordinal(empty_set)
    | $false ),
    inference(rw,[status(thm)],[99808,2927,theory(equality)]) ).

cnf(99960,plain,
    being_limit_ordinal(empty_set),
    inference(cn,[status(thm)],[99959,theory(equality)]) ).

cnf(100836,negated_conjecture,
    union_of_subsets(the_carrier(esk157_0),empty_set) = the_carrier(esk157_0),
    inference(rw,[status(thm)],[8970,4983,theory(equality)]) ).

cnf(100838,negated_conjecture,
    ( the_carrier(esk157_0) = union(empty_set)
    | ~ element(empty_set,powerset(powerset(the_carrier(esk157_0)))) ),
    inference(spm,[status(thm)],[1260,100836,theory(equality)]) ).

cnf(100844,negated_conjecture,
    ( the_carrier(esk157_0) = union(empty_set)
    | $false ),
    inference(rw,[status(thm)],[100838,5048,theory(equality)]) ).

cnf(100845,negated_conjecture,
    the_carrier(esk157_0) = union(empty_set),
    inference(cn,[status(thm)],[100844,theory(equality)]) ).

cnf(100850,negated_conjecture,
    ( the_carrier(esk157_0) = empty_set
    | ~ being_limit_ordinal(empty_set) ),
    inference(spm,[status(thm)],[2475,100845,theory(equality)]) ).

cnf(100857,negated_conjecture,
    ( the_carrier(esk157_0) = empty_set
    | $false ),
    inference(rw,[status(thm)],[100850,99960,theory(equality)]) ).

cnf(100858,negated_conjecture,
    the_carrier(esk157_0) = empty_set,
    inference(cn,[status(thm)],[100857,theory(equality)]) ).

cnf(100987,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[4991,100858,theory(equality)]),1204,theory(equality)]) ).

cnf(100988,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[100987,theory(equality)]) ).

cnf(100989,negated_conjecture,
    $false,
    100988,
    [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/SEU/SEU325+2.p
% --creating new selector for []
% -running prover on /tmp/tmpTngZ5z/sel_SEU325+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU325+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU325+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU325+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
% 
%------------------------------------------------------------------------------