TSTP Solution File: SEU126+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU126+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 04:43:55 EST 2010

% Result   : Theorem 0.25s
% Output   : CNFRefutation 0.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   34 (  16 unt;   0 def)
%            Number of atoms       :   73 (  23 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   69 (  30   ~;  24   |;  11   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   55 (   3 sgn  33   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(5,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X3,X2) )
     => subset(set_union2(X1,X3),X2) ),
    file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',t8_xboole_1) ).

fof(7,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',reflexivity_r1_tarski) ).

fof(12,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',commutativity_k2_xboole_0) ).

fof(14,axiom,
    ! [X1,X2] : subset(X1,set_union2(X1,X2)),
    file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',t7_xboole_1) ).

fof(24,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',d10_xboole_0) ).

fof(29,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',t12_xboole_1) ).

fof(34,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => set_union2(X1,X2) = X2 ),
    inference(assume_negation,[status(cth)],[29]) ).

fof(53,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | ~ subset(X3,X2)
      | subset(set_union2(X1,X3),X2) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(54,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X6,X5)
      | subset(set_union2(X4,X6),X5) ),
    inference(variable_rename,[status(thm)],[53]) ).

cnf(55,plain,
    ( subset(set_union2(X1,X2),X3)
    | ~ subset(X2,X3)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[54]) ).

fof(67,plain,
    ! [X3,X4] : subset(X3,X3),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(68,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[67]) ).

fof(84,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(85,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[84]) ).

fof(89,plain,
    ! [X3,X4] : subset(X3,set_union2(X3,X4)),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(90,plain,
    subset(X1,set_union2(X1,X2)),
    inference(split_conjunct,[status(thm)],[89]) ).

fof(125,plain,
    ! [X1,X2] :
      ( ( X1 != X2
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

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

fof(127,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[126]) ).

cnf(128,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[127]) ).

fof(139,negated_conjecture,
    ? [X1,X2] :
      ( subset(X1,X2)
      & set_union2(X1,X2) != X2 ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(140,negated_conjecture,
    ? [X3,X4] :
      ( subset(X3,X4)
      & set_union2(X3,X4) != X4 ),
    inference(variable_rename,[status(thm)],[139]) ).

fof(141,negated_conjecture,
    ( subset(esk6_0,esk7_0)
    & set_union2(esk6_0,esk7_0) != esk7_0 ),
    inference(skolemize,[status(esa)],[140]) ).

cnf(142,negated_conjecture,
    set_union2(esk6_0,esk7_0) != esk7_0,
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(143,negated_conjecture,
    subset(esk6_0,esk7_0),
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(178,negated_conjecture,
    set_union2(esk7_0,esk6_0) != esk7_0,
    inference(rw,[status(thm)],[142,85,theory(equality)]) ).

cnf(185,plain,
    ( set_union2(X1,X2) = X1
    | ~ subset(set_union2(X1,X2),X1) ),
    inference(spm,[status(thm)],[128,90,theory(equality)]) ).

cnf(402,plain,
    ( set_union2(X1,X2) = X1
    | ~ subset(X2,X1)
    | ~ subset(X1,X1) ),
    inference(spm,[status(thm)],[185,55,theory(equality)]) ).

cnf(404,plain,
    ( set_union2(X1,X2) = X1
    | ~ subset(X2,X1)
    | $false ),
    inference(rw,[status(thm)],[402,68,theory(equality)]) ).

cnf(405,plain,
    ( set_union2(X1,X2) = X1
    | ~ subset(X2,X1) ),
    inference(cn,[status(thm)],[404,theory(equality)]) ).

cnf(417,plain,
    ~ subset(esk6_0,esk7_0),
    inference(spm,[status(thm)],[178,405,theory(equality)]) ).

cnf(425,plain,
    $false,
    inference(rw,[status(thm)],[417,143,theory(equality)]) ).

cnf(426,plain,
    $false,
    inference(cn,[status(thm)],[425,theory(equality)]) ).

cnf(427,plain,
    $false,
    426,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU126+2.p
% --creating new selector for []
% -running prover on /tmp/tmpgeI2X_/sel_SEU126+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU126+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU126+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU126+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
% 
%------------------------------------------------------------------------------