TSTP Solution File: SET146+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET146+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 02:50:25 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   33 (  19 unt;   0 def)
%            Number of atoms       :  105 (  28 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  119 (  47   ~;  47   |;  22   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   56 (   4 sgn  39   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1] : intersection(X1,empty_set) = empty_set,
    file('/tmp/tmphh7ZZ4/sel_SET146+3.p_1',prove_th61) ).

fof(2,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmphh7ZZ4/sel_SET146+3.p_1',commutativity_of_intersection) ).

fof(6,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ! [X3] :
          ( member(X3,X1)
        <=> member(X3,X2) ) ),
    file('/tmp/tmphh7ZZ4/sel_SET146+3.p_1',equal_member_defn) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/tmp/tmphh7ZZ4/sel_SET146+3.p_1',intersection_defn) ).

fof(9,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/tmp/tmphh7ZZ4/sel_SET146+3.p_1',empty_set_defn) ).

fof(10,negated_conjecture,
    ~ ! [X1] : intersection(X1,empty_set) = empty_set,
    inference(assume_negation,[status(cth)],[1]) ).

fof(12,plain,
    ! [X1] : ~ member(X1,empty_set),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

fof(13,negated_conjecture,
    ? [X1] : intersection(X1,empty_set) != empty_set,
    inference(fof_nnf,[status(thm)],[10]) ).

fof(14,negated_conjecture,
    ? [X2] : intersection(X2,empty_set) != empty_set,
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    intersection(esk1_0,empty_set) != empty_set,
    inference(skolemize,[status(esa)],[14]) ).

cnf(16,negated_conjecture,
    intersection(esk1_0,empty_set) != empty_set,
    inference(split_conjunct,[status(thm)],[15]) ).

fof(17,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[2]) ).

cnf(18,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(39,plain,
    ! [X1,X2] :
      ( ( X1 != X2
        | ! [X3] :
            ( ( ~ member(X3,X1)
              | member(X3,X2) )
            & ( ~ member(X3,X2)
              | member(X3,X1) ) ) )
      & ( ? [X3] :
            ( ( ~ member(X3,X1)
              | ~ member(X3,X2) )
            & ( member(X3,X1)
              | member(X3,X2) ) )
        | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(40,plain,
    ! [X4,X5] :
      ( ( X4 != X5
        | ! [X6] :
            ( ( ~ member(X6,X4)
              | member(X6,X5) )
            & ( ~ member(X6,X5)
              | member(X6,X4) ) ) )
      & ( ? [X7] :
            ( ( ~ member(X7,X4)
              | ~ member(X7,X5) )
            & ( member(X7,X4)
              | member(X7,X5) ) )
        | X4 = X5 ) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,plain,
    ! [X4,X5] :
      ( ( X4 != X5
        | ! [X6] :
            ( ( ~ member(X6,X4)
              | member(X6,X5) )
            & ( ~ member(X6,X5)
              | member(X6,X4) ) ) )
      & ( ( ( ~ member(esk4_2(X4,X5),X4)
            | ~ member(esk4_2(X4,X5),X5) )
          & ( member(esk4_2(X4,X5),X4)
            | member(esk4_2(X4,X5),X5) ) )
        | X4 = X5 ) ),
    inference(skolemize,[status(esa)],[40]) ).

fof(42,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ member(X6,X4)
            | member(X6,X5) )
          & ( ~ member(X6,X5)
            | member(X6,X4) ) )
        | X4 != X5 )
      & ( ( ( ~ member(esk4_2(X4,X5),X4)
            | ~ member(esk4_2(X4,X5),X5) )
          & ( member(esk4_2(X4,X5),X4)
            | member(esk4_2(X4,X5),X5) ) )
        | X4 = X5 ) ),
    inference(shift_quantors,[status(thm)],[41]) ).

fof(43,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | X4 != X5 )
      & ( ~ member(X6,X5)
        | member(X6,X4)
        | X4 != X5 )
      & ( ~ member(esk4_2(X4,X5),X4)
        | ~ member(esk4_2(X4,X5),X5)
        | X4 = X5 )
      & ( member(esk4_2(X4,X5),X4)
        | member(esk4_2(X4,X5),X5)
        | X4 = X5 ) ),
    inference(distribute,[status(thm)],[42]) ).

cnf(44,plain,
    ( X1 = X2
    | member(esk4_2(X1,X2),X2)
    | member(esk4_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(48,plain,
    ! [X1,X2,X3] :
      ( ( ~ member(X3,intersection(X1,X2))
        | ( member(X3,X1)
          & member(X3,X2) ) )
      & ( ~ member(X3,X1)
        | ~ member(X3,X2)
        | member(X3,intersection(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(49,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,intersection(X4,X5))
        | ( member(X6,X4)
          & member(X6,X5) ) )
      & ( ~ member(X6,X4)
        | ~ member(X6,X5)
        | member(X6,intersection(X4,X5)) ) ),
    inference(variable_rename,[status(thm)],[48]) ).

fof(50,plain,
    ! [X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,intersection(X4,X5)) )
      & ( member(X6,X5)
        | ~ member(X6,intersection(X4,X5)) )
      & ( ~ member(X6,X4)
        | ~ member(X6,X5)
        | member(X6,intersection(X4,X5)) ) ),
    inference(distribute,[status(thm)],[49]) ).

cnf(52,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(56,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(57,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[56]) ).

cnf(58,negated_conjecture,
    intersection(empty_set,esk1_0) != empty_set,
    inference(rw,[status(thm)],[16,18,theory(equality)]) ).

cnf(86,plain,
    ( empty_set = X1
    | member(esk4_2(empty_set,X1),X1) ),
    inference(spm,[status(thm)],[57,44,theory(equality)]) ).

cnf(102,plain,
    ( member(esk4_2(empty_set,intersection(X1,X2)),X2)
    | empty_set = intersection(X1,X2) ),
    inference(spm,[status(thm)],[52,86,theory(equality)]) ).

cnf(107,plain,
    intersection(X1,empty_set) = empty_set,
    inference(spm,[status(thm)],[57,102,theory(equality)]) ).

cnf(111,plain,
    empty_set = intersection(empty_set,X1),
    inference(spm,[status(thm)],[18,107,theory(equality)]) ).

cnf(121,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[58,111,theory(equality)]) ).

cnf(122,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[121,theory(equality)]) ).

cnf(123,negated_conjecture,
    $false,
    122,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET146+3.p
% --creating new selector for []
% -running prover on /tmp/tmphh7ZZ4/sel_SET146+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET146+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET146+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET146+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
% 
%------------------------------------------------------------------------------