TSTP Solution File: SEU154+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU154+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 04:54:11 EST 2010

% Result   : Theorem 79.87s
% Output   : CNFRefutation 79.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   49 (  26 unt;   0 def)
%            Number of atoms       :   96 (  41 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   83 (  36   ~;  28   |;  13   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   72 (   1 sgn  42   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(10,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t69_enumset1) ).

fof(11,axiom,
    ! [X1,X2] : subset(set_difference(X1,X2),X1),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t36_xboole_1) ).

fof(12,axiom,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',l4_zfmisc_1) ).

fof(21,axiom,
    ! [X1] : set_difference(X1,empty_set) = X1,
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t3_boole) ).

fof(47,axiom,
    ! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t48_xboole_1) ).

fof(51,conjecture,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',l28_zfmisc_1) ).

fof(55,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',commutativity_k3_xboole_0) ).

fof(69,axiom,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',l2_zfmisc_1) ).

fof(76,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_difference(X1,X2) = X1 ),
    file('/tmp/tmpWqZsKp/sel_SEU154+2.p_2',t83_xboole_1) ).

fof(78,negated_conjecture,
    ~ ! [X1,X2] :
        ( ~ in(X1,X2)
       => disjoint(singleton(X1),X2) ),
    inference(assume_negation,[status(cth)],[51]) ).

fof(86,negated_conjecture,
    ~ ! [X1,X2] :
        ( ~ in(X1,X2)
       => disjoint(singleton(X1),X2) ),
    inference(fof_simplification,[status(thm)],[78,theory(equality)]) ).

fof(120,plain,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(121,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[120]) ).

fof(122,plain,
    ! [X3,X4] : subset(set_difference(X3,X4),X3),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(123,plain,
    subset(set_difference(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[122]) ).

fof(124,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,singleton(X2))
        | X1 = empty_set
        | X1 = singleton(X2) )
      & ( ( X1 != empty_set
          & X1 != singleton(X2) )
        | subset(X1,singleton(X2)) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(125,plain,
    ! [X3,X4] :
      ( ( ~ subset(X3,singleton(X4))
        | X3 = empty_set
        | X3 = singleton(X4) )
      & ( ( X3 != empty_set
          & X3 != singleton(X4) )
        | subset(X3,singleton(X4)) ) ),
    inference(variable_rename,[status(thm)],[124]) ).

fof(126,plain,
    ! [X3,X4] :
      ( ( ~ subset(X3,singleton(X4))
        | X3 = empty_set
        | X3 = singleton(X4) )
      & ( X3 != empty_set
        | subset(X3,singleton(X4)) )
      & ( X3 != singleton(X4)
        | subset(X3,singleton(X4)) ) ),
    inference(distribute,[status(thm)],[125]) ).

cnf(129,plain,
    ( X1 = singleton(X2)
    | X1 = empty_set
    | ~ subset(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[126]) ).

fof(151,plain,
    ! [X2] : set_difference(X2,empty_set) = X2,
    inference(variable_rename,[status(thm)],[21]) ).

cnf(152,plain,
    set_difference(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[151]) ).

fof(244,plain,
    ! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
    inference(variable_rename,[status(thm)],[47]) ).

cnf(245,plain,
    set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
    inference(split_conjunct,[status(thm)],[244]) ).

fof(254,negated_conjecture,
    ? [X1,X2] :
      ( ~ in(X1,X2)
      & ~ disjoint(singleton(X1),X2) ),
    inference(fof_nnf,[status(thm)],[86]) ).

fof(255,negated_conjecture,
    ? [X3,X4] :
      ( ~ in(X3,X4)
      & ~ disjoint(singleton(X3),X4) ),
    inference(variable_rename,[status(thm)],[254]) ).

fof(256,negated_conjecture,
    ( ~ in(esk8_0,esk9_0)
    & ~ disjoint(singleton(esk8_0),esk9_0) ),
    inference(skolemize,[status(esa)],[255]) ).

cnf(257,negated_conjecture,
    ~ disjoint(singleton(esk8_0),esk9_0),
    inference(split_conjunct,[status(thm)],[256]) ).

cnf(258,negated_conjecture,
    ~ in(esk8_0,esk9_0),
    inference(split_conjunct,[status(thm)],[256]) ).

fof(274,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[55]) ).

cnf(275,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[274]) ).

fof(309,plain,
    ! [X1,X2] :
      ( ( ~ subset(singleton(X1),X2)
        | in(X1,X2) )
      & ( ~ in(X1,X2)
        | subset(singleton(X1),X2) ) ),
    inference(fof_nnf,[status(thm)],[69]) ).

fof(310,plain,
    ! [X3,X4] :
      ( ( ~ subset(singleton(X3),X4)
        | in(X3,X4) )
      & ( ~ in(X3,X4)
        | subset(singleton(X3),X4) ) ),
    inference(variable_rename,[status(thm)],[309]) ).

cnf(312,plain,
    ( in(X1,X2)
    | ~ subset(singleton(X1),X2) ),
    inference(split_conjunct,[status(thm)],[310]) ).

fof(356,plain,
    ! [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | set_difference(X1,X2) = X1 )
      & ( set_difference(X1,X2) != X1
        | disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[76]) ).

fof(357,plain,
    ! [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | set_difference(X3,X4) = X3 )
      & ( set_difference(X3,X4) != X3
        | disjoint(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[356]) ).

cnf(358,plain,
    ( disjoint(X1,X2)
    | set_difference(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[357]) ).

cnf(370,plain,
    ( in(X1,X2)
    | ~ subset(unordered_pair(X1,X1),X2) ),
    inference(rw,[status(thm)],[312,121,theory(equality)]),
    [unfolding] ).

cnf(372,plain,
    ( empty_set = X1
    | unordered_pair(X2,X2) = X1
    | ~ subset(X1,unordered_pair(X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[129,121,theory(equality)]),121,theory(equality)]),
    [unfolding] ).

cnf(378,negated_conjecture,
    ~ disjoint(unordered_pair(esk8_0,esk8_0),esk9_0),
    inference(rw,[status(thm)],[257,121,theory(equality)]),
    [unfolding] ).

cnf(382,plain,
    set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[275,245,theory(equality)]),245,theory(equality)]),
    [unfolding] ).

cnf(591,plain,
    ( unordered_pair(X1,X1) = set_difference(unordered_pair(X1,X1),X2)
    | empty_set = set_difference(unordered_pair(X1,X1),X2) ),
    inference(spm,[status(thm)],[372,123,theory(equality)]) ).

cnf(876,plain,
    subset(set_difference(X2,set_difference(X2,X1)),X1),
    inference(spm,[status(thm)],[123,382,theory(equality)]) ).

cnf(5878,plain,
    ( disjoint(unordered_pair(X1,X1),X2)
    | set_difference(unordered_pair(X1,X1),X2) = empty_set ),
    inference(spm,[status(thm)],[358,591,theory(equality)]) ).

cnf(548236,plain,
    set_difference(unordered_pair(esk8_0,esk8_0),esk9_0) = empty_set,
    inference(spm,[status(thm)],[378,5878,theory(equality)]) ).

cnf(548381,plain,
    subset(set_difference(unordered_pair(esk8_0,esk8_0),empty_set),esk9_0),
    inference(spm,[status(thm)],[876,548236,theory(equality)]) ).

cnf(548688,plain,
    subset(unordered_pair(esk8_0,esk8_0),esk9_0),
    inference(rw,[status(thm)],[548381,152,theory(equality)]) ).

cnf(549053,plain,
    in(esk8_0,esk9_0),
    inference(spm,[status(thm)],[370,548688,theory(equality)]) ).

cnf(549095,plain,
    $false,
    inference(sr,[status(thm)],[549053,258,theory(equality)]) ).

cnf(549096,plain,
    $false,
    549095,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU154+2.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpWqZsKp/sel_SEU154+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpWqZsKp/sel_SEU154+2.p_2 with time limit 80
% -prover status Theorem
% Problem SEU154+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU154+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU154+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
% 
%------------------------------------------------------------------------------