TSTP Solution File: SET954+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET954+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:54:04 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   33 (  17 unt;   0 def)
%            Number of atoms       :   65 (   6 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   58 (  26   ~;  19   |;  10   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   70 (   7 sgn  32   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
     => in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
    file('/tmp/tmppYR2kK/sel_SET954+1.p_1',t107_zfmisc_1) ).

fof(2,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/tmp/tmppYR2kK/sel_SET954+1.p_1',l55_zfmisc_1) ).

fof(3,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/tmp/tmppYR2kK/sel_SET954+1.p_1',d5_tarski) ).

fof(6,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmppYR2kK/sel_SET954+1.p_1',commutativity_k2_tarski) ).

fof(9,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
       => in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(13,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
      & ~ in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(14,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
      & ~ in(ordered_pair(X6,X5),cartesian_product2(X8,X7)) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    ( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
    & ~ in(ordered_pair(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0)) ),
    inference(skolemize,[status(esa)],[14]) ).

cnf(16,negated_conjecture,
    ~ in(ordered_pair(esk2_0,esk1_0),cartesian_product2(esk4_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,negated_conjecture,
    in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(18,plain,
    ! [X1,X2,X3,X4] :
      ( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
        | ( in(X1,X3)
          & in(X2,X4) ) )
      & ( ~ in(X1,X3)
        | ~ in(X2,X4)
        | in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(19,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
        | ( in(X5,X7)
          & in(X6,X8) ) )
      & ( ~ in(X5,X7)
        | ~ in(X6,X8)
        | in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X5,X7)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( in(X6,X8)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( ~ in(X5,X7)
        | ~ in(X6,X8)
        | in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
    inference(distribute,[status(thm)],[19]) ).

cnf(21,plain,
    ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    | ~ in(X2,X4)
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,plain,
    ( in(X2,X4)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(23,plain,
    ( in(X1,X3)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(24,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(25,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(31,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(32,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(39,negated_conjecture,
    in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,esk4_0)),
    inference(rw,[status(thm)],[17,25,theory(equality)]),
    [unfolding] ).

cnf(40,plain,
    ( in(X2,X4)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
    inference(rw,[status(thm)],[22,25,theory(equality)]),
    [unfolding] ).

cnf(41,plain,
    ( in(X1,X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
    inference(rw,[status(thm)],[23,25,theory(equality)]),
    [unfolding] ).

cnf(42,plain,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
    | ~ in(X2,X4)
    | ~ in(X1,X3) ),
    inference(rw,[status(thm)],[21,25,theory(equality)]),
    [unfolding] ).

cnf(44,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(esk2_0,esk1_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
    inference(rw,[status(thm)],[16,25,theory(equality)]),
    [unfolding] ).

cnf(49,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
    inference(rw,[status(thm)],[44,32,theory(equality)]) ).

cnf(52,negated_conjecture,
    in(esk2_0,esk4_0),
    inference(spm,[status(thm)],[40,39,theory(equality)]) ).

cnf(57,negated_conjecture,
    in(esk1_0,esk3_0),
    inference(spm,[status(thm)],[41,39,theory(equality)]) ).

cnf(65,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,esk1_0),singleton(X1)),cartesian_product2(X2,esk3_0))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[42,57,theory(equality)]) ).

cnf(132,negated_conjecture,
    in(unordered_pair(unordered_pair(esk2_0,esk1_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
    inference(spm,[status(thm)],[65,52,theory(equality)]) ).

cnf(136,negated_conjecture,
    in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)),cartesian_product2(esk4_0,esk3_0)),
    inference(rw,[status(thm)],[132,32,theory(equality)]) ).

cnf(137,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[136,49,theory(equality)]) ).

cnf(138,negated_conjecture,
    $false,
    137,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET954+1.p
% --creating new selector for []
% -running prover on /tmp/tmppYR2kK/sel_SET954+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET954+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET954+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET954+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
% 
%------------------------------------------------------------------------------