TSTP Solution File: SET874+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET874+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 03:42:28 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (  19 unt;   0 def)
%            Number of atoms       :  114 (  78 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  134 (  52   ~;  54   |;  25   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-3 aty)
%            Number of variables   :   67 (   4 sgn  42   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/tmp/tmpDieGXG/sel_SET874+1.p_1',l23_zfmisc_1) ).

fof(4,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/tmp/tmpDieGXG/sel_SET874+1.p_1',commutativity_k2_xboole_0) ).

fof(6,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmpDieGXG/sel_SET874+1.p_1',commutativity_k2_tarski) ).

fof(10,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/tmp/tmpDieGXG/sel_SET874+1.p_1',d2_tarski) ).

fof(11,conjecture,
    ! [X1,X2] : set_union2(singleton(X1),unordered_pair(X1,X2)) = unordered_pair(X1,X2),
    file('/tmp/tmpDieGXG/sel_SET874+1.p_1',t14_zfmisc_1) ).

fof(12,negated_conjecture,
    ~ ! [X1,X2] : set_union2(singleton(X1),unordered_pair(X1,X2)) = unordered_pair(X1,X2),
    inference(assume_negation,[status(cth)],[11]) ).

fof(17,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | set_union2(singleton(X1),X2) = X2 ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(18,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | set_union2(singleton(X3),X4) = X4 ),
    inference(variable_rename,[status(thm)],[17]) ).

cnf(19,plain,
    ( set_union2(singleton(X1),X2) = X2
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(26,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(27,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[26]) ).

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]) ).

fof(41,plain,
    ! [X1,X2,X3] :
      ( ( X3 != unordered_pair(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | X4 = X1
              | X4 = X2 )
            & ( ( X4 != X1
                & X4 != X2 )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ( X4 != X1
                & X4 != X2 ) )
            & ( in(X4,X3)
              | X4 = X1
              | X4 = X2 ) )
        | X3 = unordered_pair(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(42,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ( X9 != X5
                & X9 != X6 ) )
            & ( in(X9,X7)
              | X9 = X5
              | X9 = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[41]) ).

fof(43,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
            | ( esk3_3(X5,X6,X7) != X5
              & esk3_3(X5,X6,X7) != X6 ) )
          & ( in(esk3_3(X5,X6,X7),X7)
            | esk3_3(X5,X6,X7) = X5
            | esk3_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(skolemize,[status(esa)],[42]) ).

fof(44,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | X8 = X5
            | X8 = X6 )
          & ( ( X8 != X5
              & X8 != X6 )
            | in(X8,X7) ) )
        | X7 != unordered_pair(X5,X6) )
      & ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
            | ( esk3_3(X5,X6,X7) != X5
              & esk3_3(X5,X6,X7) != X6 ) )
          & ( in(esk3_3(X5,X6,X7),X7)
            | esk3_3(X5,X6,X7) = X5
            | esk3_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[43]) ).

fof(45,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,X7)
        | X8 = X5
        | X8 = X6
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X5
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X6
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( esk3_3(X5,X6,X7) != X5
        | ~ in(esk3_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( esk3_3(X5,X6,X7) != X6
        | ~ in(esk3_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( in(esk3_3(X5,X6,X7),X7)
        | esk3_3(X5,X6,X7) = X5
        | esk3_3(X5,X6,X7) = X6
        | X7 = unordered_pair(X5,X6) ) ),
    inference(distribute,[status(thm)],[44]) ).

cnf(49,plain,
    ( in(X4,X1)
    | X1 != unordered_pair(X2,X3)
    | X4 != X3 ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(52,negated_conjecture,
    ? [X1,X2] : set_union2(singleton(X1),unordered_pair(X1,X2)) != unordered_pair(X1,X2),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(53,negated_conjecture,
    ? [X3,X4] : set_union2(singleton(X3),unordered_pair(X3,X4)) != unordered_pair(X3,X4),
    inference(variable_rename,[status(thm)],[52]) ).

fof(54,negated_conjecture,
    set_union2(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != unordered_pair(esk4_0,esk5_0),
    inference(skolemize,[status(esa)],[53]) ).

cnf(55,negated_conjecture,
    set_union2(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != unordered_pair(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[54]) ).

cnf(60,plain,
    ( X2 = set_union2(X2,singleton(X1))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[27,19,theory(equality)]) ).

cnf(62,plain,
    ( in(X1,X2)
    | unordered_pair(X3,X1) != X2 ),
    inference(er,[status(thm)],[49,theory(equality)]) ).

cnf(64,negated_conjecture,
    set_union2(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)) != unordered_pair(esk4_0,esk5_0),
    inference(rw,[status(thm)],[55,27,theory(equality)]) ).

cnf(81,negated_conjecture,
    ~ in(esk4_0,unordered_pair(esk4_0,esk5_0)),
    inference(spm,[status(thm)],[64,60,theory(equality)]) ).

cnf(85,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[62,theory(equality)]) ).

cnf(88,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(spm,[status(thm)],[85,32,theory(equality)]) ).

cnf(98,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[81,88,theory(equality)]) ).

cnf(99,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[98,theory(equality)]) ).

cnf(100,negated_conjecture,
    $false,
    99,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET874+1.p
% --creating new selector for []
% -running prover on /tmp/tmpDieGXG/sel_SET874+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET874+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET874+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET874+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
% 
%------------------------------------------------------------------------------