TSTP Solution File: SET194+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET194+3 : TPTP v5.0.0. Released v2.2.0.
% 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 02:54:17 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   28 (  14 unt;   0 def)
%            Number of atoms       :   78 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   82 (  32   ~;  31   |;  16   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   60 (   3 sgn  38   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmp_KQz1N/sel_SET194+3.p_1',subset_defn) ).

fof(2,conjecture,
    ! [X1,X2] : subset(X1,union(X1,X2)),
    file('/tmp/tmp_KQz1N/sel_SET194+3.p_1',prove_subset_of_union) ).

fof(3,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/tmp/tmp_KQz1N/sel_SET194+3.p_1',union_defn) ).

fof(4,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/tmp/tmp_KQz1N/sel_SET194+3.p_1',commutativity_of_union) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2] : subset(X1,union(X1,X2)),
    inference(assume_negation,[status(cth)],[2]) ).

fof(8,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(9,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)],[8]) ).

fof(10,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)],[9]) ).

fof(11,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)],[10]) ).

fof(12,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)],[11]) ).

cnf(13,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(14,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(16,negated_conjecture,
    ? [X1,X2] : ~ subset(X1,union(X1,X2)),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(17,negated_conjecture,
    ? [X3,X4] : ~ subset(X3,union(X3,X4)),
    inference(variable_rename,[status(thm)],[16]) ).

fof(18,negated_conjecture,
    ~ subset(esk2_0,union(esk2_0,esk3_0)),
    inference(skolemize,[status(esa)],[17]) ).

cnf(19,negated_conjecture,
    ~ subset(esk2_0,union(esk2_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(20,plain,
    ! [X1,X2,X3] :
      ( ( ~ member(X3,union(X1,X2))
        | member(X3,X1)
        | member(X3,X2) )
      & ( ( ~ member(X3,X1)
          & ~ member(X3,X2) )
        | member(X3,union(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(21,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ( ~ member(X6,X4)
          & ~ member(X6,X5) )
        | member(X6,union(X4,X5)) ) ),
    inference(variable_rename,[status(thm)],[20]) ).

fof(22,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ~ member(X6,X4)
        | member(X6,union(X4,X5)) )
      & ( ~ member(X6,X5)
        | member(X6,union(X4,X5)) ) ),
    inference(distribute,[status(thm)],[21]) ).

cnf(23,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[22]) ).

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

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

cnf(44,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[13,23,theory(equality)]) ).

cnf(62,plain,
    subset(X1,union(X2,X1)),
    inference(spm,[status(thm)],[44,14,theory(equality)]) ).

cnf(65,plain,
    subset(X1,union(X1,X2)),
    inference(spm,[status(thm)],[62,27,theory(equality)]) ).

cnf(71,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[19,65,theory(equality)]) ).

cnf(72,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[71,theory(equality)]) ).

cnf(73,negated_conjecture,
    $false,
    72,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET194+3.p
% --creating new selector for []
% -running prover on /tmp/tmp_KQz1N/sel_SET194+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET194+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET194+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET194+3.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
% 
%------------------------------------------------------------------------------