TSTP Solution File: SET624+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET624+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 03:04:47 EST 2010

% Result   : Theorem 0.19s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   58 (  10 unt;   0 def)
%            Number of atoms       :  173 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  186 (  71   ~;  85   |;  25   &)
%                                         (   4 <=>;   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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   96 (   6 sgn  45   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',commutativity_of_union) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',union_defn) ).

fof(3,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',intersect_defn) ).

fof(4,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
     => intersect(X2,X1) ),
    file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',symmetry_of_intersect) ).

fof(6,conjecture,
    ! [X1,X2,X3] :
      ( intersect(X1,union(X2,X3))
    <=> ( intersect(X1,X2)
        | intersect(X1,X3) ) ),
    file('/tmp/tmpA1EXSk/sel_SET624+3.p_1',prove_intersect_with_union) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( intersect(X1,union(X2,X3))
      <=> ( intersect(X1,X2)
          | intersect(X1,X3) ) ),
    inference(assume_negation,[status(cth)],[6]) ).

fof(8,plain,
    ! [X3,X4] : union(X3,X4) = union(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(9,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[8]) ).

fof(10,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)],[2]) ).

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

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

cnf(13,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(15,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(16,plain,
    ! [X1,X2] :
      ( ( ~ intersect(X1,X2)
        | ? [X3] :
            ( member(X3,X1)
            & member(X3,X2) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | ~ member(X3,X2) )
        | intersect(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(17,plain,
    ! [X4,X5] :
      ( ( ~ intersect(X4,X5)
        | ? [X6] :
            ( member(X6,X4)
            & member(X6,X5) ) )
      & ( ! [X7] :
            ( ~ member(X7,X4)
            | ~ member(X7,X5) )
        | intersect(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[16]) ).

fof(18,plain,
    ! [X4,X5] :
      ( ( ~ intersect(X4,X5)
        | ( member(esk1_2(X4,X5),X4)
          & member(esk1_2(X4,X5),X5) ) )
      & ( ! [X7] :
            ( ~ member(X7,X4)
            | ~ member(X7,X5) )
        | intersect(X4,X5) ) ),
    inference(skolemize,[status(esa)],[17]) ).

fof(19,plain,
    ! [X4,X5,X7] :
      ( ( ~ member(X7,X4)
        | ~ member(X7,X5)
        | intersect(X4,X5) )
      & ( ~ intersect(X4,X5)
        | ( member(esk1_2(X4,X5),X4)
          & member(esk1_2(X4,X5),X5) ) ) ),
    inference(shift_quantors,[status(thm)],[18]) ).

fof(20,plain,
    ! [X4,X5,X7] :
      ( ( ~ member(X7,X4)
        | ~ member(X7,X5)
        | intersect(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | ~ intersect(X4,X5) )
      & ( member(esk1_2(X4,X5),X5)
        | ~ intersect(X4,X5) ) ),
    inference(distribute,[status(thm)],[19]) ).

cnf(21,plain,
    ( member(esk1_2(X1,X2),X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,plain,
    ( member(esk1_2(X1,X2),X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(23,plain,
    ( intersect(X1,X2)
    | ~ member(X3,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(24,plain,
    ! [X1,X2] :
      ( ~ intersect(X1,X2)
      | intersect(X2,X1) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(25,plain,
    ! [X3,X4] :
      ( ~ intersect(X3,X4)
      | intersect(X4,X3) ),
    inference(variable_rename,[status(thm)],[24]) ).

cnf(26,plain,
    ( intersect(X1,X2)
    | ~ intersect(X2,X1) ),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(36,negated_conjecture,
    ? [X1,X2,X3] :
      ( ( ~ intersect(X1,union(X2,X3))
        | ( ~ intersect(X1,X2)
          & ~ intersect(X1,X3) ) )
      & ( intersect(X1,union(X2,X3))
        | intersect(X1,X2)
        | intersect(X1,X3) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(37,negated_conjecture,
    ? [X4,X5,X6] :
      ( ( ~ intersect(X4,union(X5,X6))
        | ( ~ intersect(X4,X5)
          & ~ intersect(X4,X6) ) )
      & ( intersect(X4,union(X5,X6))
        | intersect(X4,X5)
        | intersect(X4,X6) ) ),
    inference(variable_rename,[status(thm)],[36]) ).

fof(38,negated_conjecture,
    ( ( ~ intersect(esk3_0,union(esk4_0,esk5_0))
      | ( ~ intersect(esk3_0,esk4_0)
        & ~ intersect(esk3_0,esk5_0) ) )
    & ( intersect(esk3_0,union(esk4_0,esk5_0))
      | intersect(esk3_0,esk4_0)
      | intersect(esk3_0,esk5_0) ) ),
    inference(skolemize,[status(esa)],[37]) ).

fof(39,negated_conjecture,
    ( ( ~ intersect(esk3_0,esk4_0)
      | ~ intersect(esk3_0,union(esk4_0,esk5_0)) )
    & ( ~ intersect(esk3_0,esk5_0)
      | ~ intersect(esk3_0,union(esk4_0,esk5_0)) )
    & ( intersect(esk3_0,union(esk4_0,esk5_0))
      | intersect(esk3_0,esk4_0)
      | intersect(esk3_0,esk5_0) ) ),
    inference(distribute,[status(thm)],[38]) ).

cnf(40,negated_conjecture,
    ( intersect(esk3_0,esk5_0)
    | intersect(esk3_0,esk4_0)
    | intersect(esk3_0,union(esk4_0,esk5_0)) ),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(41,negated_conjecture,
    ( ~ intersect(esk3_0,union(esk4_0,esk5_0))
    | ~ intersect(esk3_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(42,negated_conjecture,
    ( ~ intersect(esk3_0,union(esk4_0,esk5_0))
    | ~ intersect(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(48,plain,
    ( intersect(X1,X2)
    | ~ member(esk1_2(X3,X2),X1)
    | ~ intersect(X3,X2) ),
    inference(spm,[status(thm)],[23,21,theory(equality)]) ).

cnf(49,plain,
    ( intersect(X1,X2)
    | ~ member(esk1_2(X2,X3),X1)
    | ~ intersect(X2,X3) ),
    inference(spm,[status(thm)],[23,22,theory(equality)]) ).

cnf(56,plain,
    ( member(esk1_2(X1,union(X2,X3)),X3)
    | member(esk1_2(X1,union(X2,X3)),X2)
    | ~ intersect(X1,union(X2,X3)) ),
    inference(spm,[status(thm)],[15,21,theory(equality)]) ).

cnf(72,plain,
    ( intersect(union(X1,X2),X3)
    | ~ intersect(X4,X3)
    | ~ member(esk1_2(X4,X3),X2) ),
    inference(spm,[status(thm)],[48,13,theory(equality)]) ).

cnf(112,plain,
    ( intersect(union(X1,X2),X3)
    | ~ intersect(X2,X3) ),
    inference(spm,[status(thm)],[72,22,theory(equality)]) ).

cnf(115,plain,
    ( intersect(union(X2,X1),X3)
    | ~ intersect(X2,X3) ),
    inference(spm,[status(thm)],[112,9,theory(equality)]) ).

cnf(117,plain,
    ( intersect(X1,union(X2,X3))
    | ~ intersect(X3,X1) ),
    inference(spm,[status(thm)],[26,112,theory(equality)]) ).

cnf(122,plain,
    ( intersect(X1,union(X2,X3))
    | ~ intersect(X2,X1) ),
    inference(spm,[status(thm)],[26,115,theory(equality)]) ).

cnf(129,negated_conjecture,
    ( ~ intersect(esk3_0,esk5_0)
    | ~ intersect(esk5_0,esk3_0) ),
    inference(spm,[status(thm)],[41,117,theory(equality)]) ).

cnf(139,negated_conjecture,
    ~ intersect(esk3_0,esk5_0),
    inference(csr,[status(thm)],[129,26]) ).

cnf(140,negated_conjecture,
    ( intersect(esk3_0,union(esk4_0,esk5_0))
    | intersect(esk3_0,esk4_0) ),
    inference(sr,[status(thm)],[40,139,theory(equality)]) ).

cnf(148,negated_conjecture,
    ( member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
    | member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk5_0)
    | intersect(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[56,140,theory(equality)]) ).

cnf(429,negated_conjecture,
    ( ~ intersect(esk3_0,esk4_0)
    | ~ intersect(esk4_0,esk3_0) ),
    inference(spm,[status(thm)],[42,122,theory(equality)]) ).

cnf(442,negated_conjecture,
    ~ intersect(esk3_0,esk4_0),
    inference(csr,[status(thm)],[429,26]) ).

cnf(443,negated_conjecture,
    intersect(esk3_0,union(esk4_0,esk5_0)),
    inference(sr,[status(thm)],[140,442,theory(equality)]) ).

cnf(446,negated_conjecture,
    ( member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk5_0)
    | member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0) ),
    inference(sr,[status(thm)],[148,442,theory(equality)]) ).

cnf(518,negated_conjecture,
    ( intersect(esk5_0,esk3_0)
    | member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
    | ~ intersect(esk3_0,union(esk4_0,esk5_0)) ),
    inference(spm,[status(thm)],[49,446,theory(equality)]) ).

cnf(524,negated_conjecture,
    ( intersect(esk5_0,esk3_0)
    | member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
    | $false ),
    inference(rw,[status(thm)],[518,443,theory(equality)]) ).

cnf(525,negated_conjecture,
    ( intersect(esk5_0,esk3_0)
    | member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0) ),
    inference(cn,[status(thm)],[524,theory(equality)]) ).

cnf(530,negated_conjecture,
    ( intersect(esk4_0,esk3_0)
    | intersect(esk5_0,esk3_0)
    | ~ intersect(esk3_0,union(esk4_0,esk5_0)) ),
    inference(spm,[status(thm)],[49,525,theory(equality)]) ).

cnf(536,negated_conjecture,
    ( intersect(esk4_0,esk3_0)
    | intersect(esk5_0,esk3_0)
    | $false ),
    inference(rw,[status(thm)],[530,443,theory(equality)]) ).

cnf(537,negated_conjecture,
    ( intersect(esk4_0,esk3_0)
    | intersect(esk5_0,esk3_0) ),
    inference(cn,[status(thm)],[536,theory(equality)]) ).

cnf(540,negated_conjecture,
    ( intersect(esk3_0,esk5_0)
    | intersect(esk4_0,esk3_0) ),
    inference(spm,[status(thm)],[26,537,theory(equality)]) ).

cnf(545,negated_conjecture,
    intersect(esk4_0,esk3_0),
    inference(sr,[status(thm)],[540,139,theory(equality)]) ).

cnf(548,negated_conjecture,
    intersect(esk3_0,esk4_0),
    inference(spm,[status(thm)],[26,545,theory(equality)]) ).

cnf(553,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[548,442,theory(equality)]) ).

cnf(554,negated_conjecture,
    $false,
    553,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET624+3.p
% --creating new selector for []
% -running prover on /tmp/tmpA1EXSk/sel_SET624+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET624+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET624+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET624+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
% 
%------------------------------------------------------------------------------