TSTP Solution File: SET751+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET751+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:34:31 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   34 (   6 unt;   0 def)
%            Number of atoms       :  125 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  141 (  50   ~;  47   |;  39   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   96 (   0 sgn  51   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmp2nlmEJ/sel_SET751+4.p_1',subset) ).

fof(3,axiom,
    ! [X4,X1,X5] :
      ( member(X5,image2(X4,X1))
    <=> ? [X3] :
          ( member(X3,X1)
          & apply(X4,X3,X5) ) ),
    file('/tmp/tmp2nlmEJ/sel_SET751+4.p_1',image2) ).

fof(4,conjecture,
    ! [X4,X1,X2,X3,X5] :
      ( ( maps(X4,X1,X2)
        & subset(X3,X1)
        & subset(X5,X1)
        & subset(X3,X5) )
     => subset(image2(X4,X3),image2(X4,X5)) ),
    file('/tmp/tmp2nlmEJ/sel_SET751+4.p_1',thIIa01) ).

fof(5,negated_conjecture,
    ~ ! [X4,X1,X2,X3,X5] :
        ( ( maps(X4,X1,X2)
          & subset(X3,X1)
          & subset(X5,X1)
          & subset(X3,X5) )
       => subset(image2(X4,X3),image2(X4,X5)) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(6,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(7,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ? [X7] :
            ( member(X7,X4)
            & ~ member(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[6]) ).

fof(8,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[7]) ).

fof(9,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[8]) ).

fof(10,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[9]) ).

cnf(11,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(12,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(13,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[10]) ).

fof(34,plain,
    ! [X4,X1,X5] :
      ( ( ~ member(X5,image2(X4,X1))
        | ? [X3] :
            ( member(X3,X1)
            & apply(X4,X3,X5) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | ~ apply(X4,X3,X5) )
        | member(X5,image2(X4,X1)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(35,plain,
    ! [X6,X7,X8] :
      ( ( ~ member(X8,image2(X6,X7))
        | ? [X9] :
            ( member(X9,X7)
            & apply(X6,X9,X8) ) )
      & ( ! [X10] :
            ( ~ member(X10,X7)
            | ~ apply(X6,X10,X8) )
        | member(X8,image2(X6,X7)) ) ),
    inference(variable_rename,[status(thm)],[34]) ).

fof(36,plain,
    ! [X6,X7,X8] :
      ( ( ~ member(X8,image2(X6,X7))
        | ( member(esk7_3(X6,X7,X8),X7)
          & apply(X6,esk7_3(X6,X7,X8),X8) ) )
      & ( ! [X10] :
            ( ~ member(X10,X7)
            | ~ apply(X6,X10,X8) )
        | member(X8,image2(X6,X7)) ) ),
    inference(skolemize,[status(esa)],[35]) ).

fof(37,plain,
    ! [X6,X7,X8,X10] :
      ( ( ~ member(X10,X7)
        | ~ apply(X6,X10,X8)
        | member(X8,image2(X6,X7)) )
      & ( ~ member(X8,image2(X6,X7))
        | ( member(esk7_3(X6,X7,X8),X7)
          & apply(X6,esk7_3(X6,X7,X8),X8) ) ) ),
    inference(shift_quantors,[status(thm)],[36]) ).

fof(38,plain,
    ! [X6,X7,X8,X10] :
      ( ( ~ member(X10,X7)
        | ~ apply(X6,X10,X8)
        | member(X8,image2(X6,X7)) )
      & ( member(esk7_3(X6,X7,X8),X7)
        | ~ member(X8,image2(X6,X7)) )
      & ( apply(X6,esk7_3(X6,X7,X8),X8)
        | ~ member(X8,image2(X6,X7)) ) ),
    inference(distribute,[status(thm)],[37]) ).

cnf(39,plain,
    ( apply(X2,esk7_3(X2,X3,X1),X1)
    | ~ member(X1,image2(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[38]) ).

cnf(40,plain,
    ( member(esk7_3(X2,X3,X1),X3)
    | ~ member(X1,image2(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[38]) ).

cnf(41,plain,
    ( member(X1,image2(X2,X3))
    | ~ apply(X2,X4,X1)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[38]) ).

fof(42,negated_conjecture,
    ? [X4,X1,X2,X3,X5] :
      ( maps(X4,X1,X2)
      & subset(X3,X1)
      & subset(X5,X1)
      & subset(X3,X5)
      & ~ subset(image2(X4,X3),image2(X4,X5)) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(43,negated_conjecture,
    ? [X6,X7,X8,X9,X10] :
      ( maps(X6,X7,X8)
      & subset(X9,X7)
      & subset(X10,X7)
      & subset(X9,X10)
      & ~ subset(image2(X6,X9),image2(X6,X10)) ),
    inference(variable_rename,[status(thm)],[42]) ).

fof(44,negated_conjecture,
    ( maps(esk8_0,esk9_0,esk10_0)
    & subset(esk11_0,esk9_0)
    & subset(esk12_0,esk9_0)
    & subset(esk11_0,esk12_0)
    & ~ subset(image2(esk8_0,esk11_0),image2(esk8_0,esk12_0)) ),
    inference(skolemize,[status(esa)],[43]) ).

cnf(45,negated_conjecture,
    ~ subset(image2(esk8_0,esk11_0),image2(esk8_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(46,negated_conjecture,
    subset(esk11_0,esk12_0),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(52,negated_conjecture,
    ( member(X1,esk12_0)
    | ~ member(X1,esk11_0) ),
    inference(spm,[status(thm)],[13,46,theory(equality)]) ).

cnf(54,plain,
    ( member(X1,image2(X2,X3))
    | ~ member(esk7_3(X2,X4,X1),X3)
    | ~ member(X1,image2(X2,X4)) ),
    inference(spm,[status(thm)],[41,39,theory(equality)]) ).

cnf(90,negated_conjecture,
    ( member(X1,image2(X2,esk12_0))
    | ~ member(X1,image2(X2,X3))
    | ~ member(esk7_3(X2,X3,X1),esk11_0) ),
    inference(spm,[status(thm)],[54,52,theory(equality)]) ).

cnf(124,negated_conjecture,
    ( member(X1,image2(X2,esk12_0))
    | ~ member(X1,image2(X2,esk11_0)) ),
    inference(spm,[status(thm)],[90,40,theory(equality)]) ).

cnf(125,negated_conjecture,
    ( subset(X1,image2(X2,esk12_0))
    | ~ member(esk1_2(X1,image2(X2,esk12_0)),image2(X2,esk11_0)) ),
    inference(spm,[status(thm)],[11,124,theory(equality)]) ).

cnf(128,negated_conjecture,
    subset(image2(X1,esk11_0),image2(X1,esk12_0)),
    inference(spm,[status(thm)],[125,12,theory(equality)]) ).

cnf(130,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[45,128,theory(equality)]) ).

cnf(131,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[130,theory(equality)]) ).

cnf(132,negated_conjecture,
    $false,
    131,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET751+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmp2nlmEJ/sel_SET751+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET751+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET751+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET751+4.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
% 
%------------------------------------------------------------------------------