TSTP Solution File: SEU152+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU152+2 : TPTP v5.0.0. Released v3.3.0.
% 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 04:53:49 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (  16 unt;   0 def)
%            Number of atoms       :   48 (  20 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   34 (  16   ~;   9   |;   5   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   35 (   0 sgn  22   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(9,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/tmp/tmp609jCY/sel_SEU152+2.p_1',t69_enumset1) ).

fof(30,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/tmp/tmp609jCY/sel_SEU152+2.p_1',commutativity_k2_xboole_0) ).

fof(36,conjecture,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/tmp/tmp609jCY/sel_SEU152+2.p_1',l23_zfmisc_1) ).

fof(38,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/tmp/tmp609jCY/sel_SEU152+2.p_1',t12_xboole_1) ).

fof(68,axiom,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/tmp/tmp609jCY/sel_SEU152+2.p_1',l2_zfmisc_1) ).

fof(76,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X1,X2)
       => set_union2(singleton(X1),X2) = X2 ),
    inference(assume_negation,[status(cth)],[36]) ).

fof(109,plain,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[9]) ).

cnf(110,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[109]) ).

fof(181,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[30]) ).

cnf(182,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[181]) ).

fof(199,negated_conjecture,
    ? [X1,X2] :
      ( in(X1,X2)
      & set_union2(singleton(X1),X2) != X2 ),
    inference(fof_nnf,[status(thm)],[76]) ).

fof(200,negated_conjecture,
    ? [X3,X4] :
      ( in(X3,X4)
      & set_union2(singleton(X3),X4) != X4 ),
    inference(variable_rename,[status(thm)],[199]) ).

fof(201,negated_conjecture,
    ( in(esk5_0,esk6_0)
    & set_union2(singleton(esk5_0),esk6_0) != esk6_0 ),
    inference(skolemize,[status(esa)],[200]) ).

cnf(202,negated_conjecture,
    set_union2(singleton(esk5_0),esk6_0) != esk6_0,
    inference(split_conjunct,[status(thm)],[201]) ).

cnf(203,negated_conjecture,
    in(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[201]) ).

fof(205,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | set_union2(X1,X2) = X2 ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(206,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | set_union2(X3,X4) = X4 ),
    inference(variable_rename,[status(thm)],[205]) ).

cnf(207,plain,
    ( set_union2(X1,X2) = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[206]) ).

fof(304,plain,
    ! [X1,X2] :
      ( ( ~ subset(singleton(X1),X2)
        | in(X1,X2) )
      & ( ~ in(X1,X2)
        | subset(singleton(X1),X2) ) ),
    inference(fof_nnf,[status(thm)],[68]) ).

fof(305,plain,
    ! [X3,X4] :
      ( ( ~ subset(singleton(X3),X4)
        | in(X3,X4) )
      & ( ~ in(X3,X4)
        | subset(singleton(X3),X4) ) ),
    inference(variable_rename,[status(thm)],[304]) ).

cnf(306,plain,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[305]) ).

cnf(361,plain,
    ( subset(unordered_pair(X1,X1),X2)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[306,110,theory(equality)]),
    [unfolding] ).

cnf(368,negated_conjecture,
    set_union2(unordered_pair(esk5_0,esk5_0),esk6_0) != esk6_0,
    inference(rw,[status(thm)],[202,110,theory(equality)]),
    [unfolding] ).

cnf(508,negated_conjecture,
    subset(unordered_pair(esk5_0,esk5_0),esk6_0),
    inference(spm,[status(thm)],[361,203,theory(equality)]) ).

cnf(545,negated_conjecture,
    set_union2(esk6_0,unordered_pair(esk5_0,esk5_0)) != esk6_0,
    inference(rw,[status(thm)],[368,182,theory(equality)]) ).

cnf(1339,negated_conjecture,
    set_union2(unordered_pair(esk5_0,esk5_0),esk6_0) = esk6_0,
    inference(spm,[status(thm)],[207,508,theory(equality)]) ).

cnf(1354,negated_conjecture,
    set_union2(esk6_0,unordered_pair(esk5_0,esk5_0)) = esk6_0,
    inference(rw,[status(thm)],[1339,182,theory(equality)]) ).

cnf(1435,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[545,1354,theory(equality)]) ).

cnf(1436,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[1435,theory(equality)]) ).

cnf(1437,negated_conjecture,
    $false,
    1436,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU152+2.p
% --creating new selector for []
% -running prover on /tmp/tmp609jCY/sel_SEU152+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU152+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU152+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU152+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
% 
%------------------------------------------------------------------------------