TSTP Solution File: SEU125+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU125+1 : 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 04:43:34 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   48 (  11 unt;   0 def)
%            Number of atoms       :  186 (  20 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  214 (  76   ~;  89   |;  43   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :  107 (   8 sgn  52   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X3,X2) )
     => subset(set_union2(X1,X3),X2) ),
    file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',t8_xboole_1) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',d2_xboole_0) ).

fof(13,axiom,
    ! [X1,X2] : set_union2(X1,X1) = X1,
    file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',idempotence_k2_xboole_0) ).

fof(16,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',d3_tarski) ).

fof(19,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & subset(X3,X2) )
       => subset(set_union2(X1,X3),X2) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(26,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(X1,X2)
      & subset(X3,X2)
      & ~ subset(set_union2(X1,X3),X2) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(27,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(X4,X5)
      & subset(X6,X5)
      & ~ subset(set_union2(X4,X6),X5) ),
    inference(variable_rename,[status(thm)],[26]) ).

fof(28,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & subset(esk3_0,esk2_0)
    & ~ subset(set_union2(esk1_0,esk3_0),esk2_0) ),
    inference(skolemize,[status(esa)],[27]) ).

cnf(29,negated_conjecture,
    ~ subset(set_union2(esk1_0,esk3_0),esk2_0),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(30,negated_conjecture,
    subset(esk3_0,esk2_0),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(31,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(43,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_union2(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | in(X4,X1)
              | in(X4,X2) )
            & ( ( ~ in(X4,X1)
                & ~ in(X4,X2) )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) )
            & ( in(X4,X3)
              | in(X4,X1)
              | in(X4,X2) ) )
        | X3 = set_union2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(44,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_union2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | in(X8,X5)
              | in(X8,X6) )
            & ( ( ~ in(X8,X5)
                & ~ in(X8,X6) )
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ( ~ in(X9,X5)
                & ~ in(X9,X6) ) )
            & ( in(X9,X7)
              | in(X9,X5)
              | in(X9,X6) ) )
        | X7 = set_union2(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[43]) ).

fof(45,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_union2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | in(X8,X5)
              | in(X8,X6) )
            & ( ( ~ in(X8,X5)
                & ~ in(X8,X6) )
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
            | ( ~ in(esk5_3(X5,X6,X7),X5)
              & ~ in(esk5_3(X5,X6,X7),X6) ) )
          & ( in(esk5_3(X5,X6,X7),X7)
            | in(esk5_3(X5,X6,X7),X5)
            | in(esk5_3(X5,X6,X7),X6) ) )
        | X7 = set_union2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[44]) ).

fof(46,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | in(X8,X5)
            | in(X8,X6) )
          & ( ( ~ in(X8,X5)
              & ~ in(X8,X6) )
            | in(X8,X7) ) )
        | X7 != set_union2(X5,X6) )
      & ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
            | ( ~ in(esk5_3(X5,X6,X7),X5)
              & ~ in(esk5_3(X5,X6,X7),X6) ) )
          & ( in(esk5_3(X5,X6,X7),X7)
            | in(esk5_3(X5,X6,X7),X5)
            | in(esk5_3(X5,X6,X7),X6) ) )
        | X7 = set_union2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[45]) ).

fof(47,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,X7)
        | in(X8,X5)
        | in(X8,X6)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_union2(X5,X6) )
      & ( ~ in(esk5_3(X5,X6,X7),X5)
        | ~ in(esk5_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( ~ in(esk5_3(X5,X6,X7),X6)
        | ~ in(esk5_3(X5,X6,X7),X7)
        | X7 = set_union2(X5,X6) )
      & ( in(esk5_3(X5,X6,X7),X7)
        | in(esk5_3(X5,X6,X7),X5)
        | in(esk5_3(X5,X6,X7),X6)
        | X7 = set_union2(X5,X6) ) ),
    inference(distribute,[status(thm)],[46]) ).

cnf(51,plain,
    ( in(X4,X1)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[47]) ).

cnf(53,plain,
    ( in(X4,X3)
    | in(X4,X2)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(65,plain,
    ! [X3,X4] : set_union2(X3,X3) = X3,
    inference(variable_rename,[status(thm)],[13]) ).

cnf(66,plain,
    set_union2(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[65]) ).

fof(73,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X2) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(74,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ? [X7] :
            ( in(X7,X4)
            & ~ in(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[73]) ).

fof(75,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ( in(esk7_2(X4,X5),X4)
          & ~ in(esk7_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[74]) ).

fof(76,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( in(esk7_2(X4,X5),X4)
          & ~ in(esk7_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[75]) ).

fof(77,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( in(esk7_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk7_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[76]) ).

cnf(78,plain,
    ( subset(X1,X2)
    | ~ in(esk7_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[77]) ).

cnf(79,plain,
    ( subset(X1,X2)
    | in(esk7_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[77]) ).

cnf(80,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[77]) ).

cnf(104,negated_conjecture,
    ( in(X1,esk2_0)
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[80,31,theory(equality)]) ).

cnf(105,negated_conjecture,
    ( in(X1,esk2_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[80,30,theory(equality)]) ).

cnf(109,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[51,theory(equality)]) ).

cnf(123,plain,
    ( in(X1,X2)
    | in(X1,X3)
    | ~ in(X1,set_union2(X2,X3)) ),
    inference(er,[status(thm)],[53,theory(equality)]) ).

cnf(165,negated_conjecture,
    ( in(esk7_2(esk1_0,X1),esk2_0)
    | subset(esk1_0,X1) ),
    inference(spm,[status(thm)],[104,79,theory(equality)]) ).

cnf(198,negated_conjecture,
    ( in(esk7_2(esk3_0,X1),esk2_0)
    | subset(esk3_0,X1) ),
    inference(spm,[status(thm)],[105,79,theory(equality)]) ).

cnf(217,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ in(esk7_2(X1,set_union2(X2,X3)),X3) ),
    inference(spm,[status(thm)],[78,109,theory(equality)]) ).

cnf(316,plain,
    ( in(esk7_2(set_union2(X1,X2),X3),X2)
    | in(esk7_2(set_union2(X1,X2),X3),X1)
    | subset(set_union2(X1,X2),X3) ),
    inference(spm,[status(thm)],[123,79,theory(equality)]) ).

cnf(430,negated_conjecture,
    subset(esk1_0,set_union2(X1,esk2_0)),
    inference(spm,[status(thm)],[217,165,theory(equality)]) ).

cnf(431,negated_conjecture,
    subset(esk3_0,set_union2(X1,esk2_0)),
    inference(spm,[status(thm)],[217,198,theory(equality)]) ).

cnf(438,negated_conjecture,
    ( in(X1,set_union2(X2,esk2_0))
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[80,430,theory(equality)]) ).

cnf(461,negated_conjecture,
    ( in(X1,set_union2(X2,esk2_0))
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[80,431,theory(equality)]) ).

cnf(554,negated_conjecture,
    ( subset(X1,set_union2(X2,esk2_0))
    | ~ in(esk7_2(X1,set_union2(X2,esk2_0)),esk1_0) ),
    inference(spm,[status(thm)],[78,438,theory(equality)]) ).

cnf(631,negated_conjecture,
    ( subset(X1,set_union2(X2,esk2_0))
    | ~ in(esk7_2(X1,set_union2(X2,esk2_0)),esk3_0) ),
    inference(spm,[status(thm)],[78,461,theory(equality)]) ).

cnf(889,negated_conjecture,
    ( subset(X1,esk2_0)
    | ~ in(esk7_2(X1,esk2_0),esk1_0) ),
    inference(spm,[status(thm)],[554,66,theory(equality)]) ).

cnf(898,negated_conjecture,
    ( subset(X1,esk2_0)
    | ~ in(esk7_2(X1,esk2_0),esk3_0) ),
    inference(spm,[status(thm)],[631,66,theory(equality)]) ).

cnf(1700,negated_conjecture,
    ( subset(set_union2(esk1_0,X1),esk2_0)
    | in(esk7_2(set_union2(esk1_0,X1),esk2_0),X1) ),
    inference(spm,[status(thm)],[889,316,theory(equality)]) ).

cnf(1748,negated_conjecture,
    subset(set_union2(esk1_0,esk3_0),esk2_0),
    inference(spm,[status(thm)],[898,1700,theory(equality)]) ).

cnf(1761,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1748,29,theory(equality)]) ).

cnf(1762,negated_conjecture,
    $false,
    1761,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU125+1.p
% --creating new selector for []
% -running prover on /tmp/tmpeR65Xk/sel_SEU125+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU125+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU125+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU125+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
% 
%------------------------------------------------------------------------------