TSTP Solution File: SEU140+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU140+2 : TPTP v5.0.0. Released v3.3.0.
% 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 04:50:51 EST 2010

% Result   : Theorem 2.98s
% Output   : CNFRefutation 2.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   62 (  26 unt;   0 def)
%            Number of atoms       :  122 (  32 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  104 (  44   ~;  39   |;  14   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  104 (   6 sgn  55   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : subset(set_difference(X1,X2),X1),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t36_xboole_1) ).

fof(5,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t1_xboole_1) ).

fof(7,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & disjoint(X2,X3) )
     => disjoint(X1,X3) ),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t63_xboole_1) ).

fof(12,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',reflexivity_r1_tarski) ).

fof(15,axiom,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t3_xboole_1) ).

fof(23,axiom,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t37_xboole_1) ).

fof(31,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_intersection2(X1,X2) = empty_set ),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',d7_xboole_0) ).

fof(34,axiom,
    ! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t48_xboole_1) ).

fof(41,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',commutativity_k3_xboole_0) ).

fof(50,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X1,X3) )
     => subset(X1,set_intersection2(X2,X3)) ),
    file('/tmp/tmpMGnc_S/sel_SEU140+2.p_1',t19_xboole_1) ).

fof(57,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & disjoint(X2,X3) )
       => disjoint(X1,X3) ),
    inference(assume_negation,[status(cth)],[7]) ).

fof(68,plain,
    ! [X3,X4] : subset(set_difference(X3,X4),X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(69,plain,
    subset(set_difference(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[68]) ).

fof(77,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | ~ subset(X2,X3)
      | subset(X1,X3) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(78,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X5,X6)
      | subset(X4,X6) ),
    inference(variable_rename,[status(thm)],[77]) ).

cnf(79,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[78]) ).

fof(83,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(X1,X2)
      & disjoint(X2,X3)
      & ~ disjoint(X1,X3) ),
    inference(fof_nnf,[status(thm)],[57]) ).

fof(84,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(X4,X5)
      & disjoint(X5,X6)
      & ~ disjoint(X4,X6) ),
    inference(variable_rename,[status(thm)],[83]) ).

fof(85,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    & disjoint(esk3_0,esk4_0)
    & ~ disjoint(esk2_0,esk4_0) ),
    inference(skolemize,[status(esa)],[84]) ).

cnf(86,negated_conjecture,
    ~ disjoint(esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(87,negated_conjecture,
    disjoint(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(88,negated_conjecture,
    subset(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[85]) ).

fof(100,plain,
    ! [X3,X4] : subset(X3,X3),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(101,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[100]) ).

fof(106,plain,
    ! [X1] :
      ( ~ subset(X1,empty_set)
      | X1 = empty_set ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(107,plain,
    ! [X2] :
      ( ~ subset(X2,empty_set)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[106]) ).

cnf(108,plain,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[107]) ).

fof(134,plain,
    ! [X1,X2] :
      ( ( set_difference(X1,X2) != empty_set
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | set_difference(X1,X2) = empty_set ) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(135,plain,
    ! [X3,X4] :
      ( ( set_difference(X3,X4) != empty_set
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | set_difference(X3,X4) = empty_set ) ),
    inference(variable_rename,[status(thm)],[134]) ).

cnf(136,plain,
    ( set_difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(137,plain,
    ( subset(X1,X2)
    | set_difference(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[135]) ).

fof(165,plain,
    ! [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | set_intersection2(X1,X2) = empty_set )
      & ( set_intersection2(X1,X2) != empty_set
        | disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(166,plain,
    ! [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | set_intersection2(X3,X4) = empty_set )
      & ( set_intersection2(X3,X4) != empty_set
        | disjoint(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[165]) ).

cnf(167,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[166]) ).

cnf(168,plain,
    ( set_intersection2(X1,X2) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[166]) ).

fof(183,plain,
    ! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
    inference(variable_rename,[status(thm)],[34]) ).

cnf(184,plain,
    set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
    inference(split_conjunct,[status(thm)],[183]) ).

fof(208,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[41]) ).

cnf(209,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[208]) ).

fof(229,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | ~ subset(X1,X3)
      | subset(X1,set_intersection2(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[50]) ).

fof(230,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X4,X6)
      | subset(X4,set_intersection2(X5,X6)) ),
    inference(variable_rename,[status(thm)],[229]) ).

cnf(231,plain,
    ( subset(X1,set_intersection2(X2,X3))
    | ~ subset(X1,X3)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[230]) ).

cnf(266,plain,
    set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[209,184,theory(equality)]),184,theory(equality)]),
    [unfolding] ).

cnf(272,plain,
    ( set_difference(X1,set_difference(X1,X2)) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(rw,[status(thm)],[168,184,theory(equality)]),
    [unfolding] ).

cnf(273,plain,
    ( disjoint(X1,X2)
    | set_difference(X1,set_difference(X1,X2)) != empty_set ),
    inference(rw,[status(thm)],[167,184,theory(equality)]),
    [unfolding] ).

cnf(277,plain,
    ( subset(X1,set_difference(X2,set_difference(X2,X3)))
    | ~ subset(X1,X3)
    | ~ subset(X1,X2) ),
    inference(rw,[status(thm)],[231,184,theory(equality)]),
    [unfolding] ).

cnf(302,negated_conjecture,
    ( subset(X1,esk3_0)
    | ~ subset(X1,esk2_0) ),
    inference(spm,[status(thm)],[79,88,theory(equality)]) ).

cnf(329,plain,
    ( subset(X1,X2)
    | ~ subset(X1,X3)
    | set_difference(X3,X2) != empty_set ),
    inference(spm,[status(thm)],[79,137,theory(equality)]) ).

cnf(395,negated_conjecture,
    set_difference(esk3_0,set_difference(esk3_0,esk4_0)) = empty_set,
    inference(spm,[status(thm)],[272,87,theory(equality)]) ).

cnf(971,negated_conjecture,
    ( set_difference(X1,esk3_0) = empty_set
    | ~ subset(X1,esk2_0) ),
    inference(spm,[status(thm)],[136,302,theory(equality)]) ).

cnf(1435,negated_conjecture,
    ( subset(X1,empty_set)
    | ~ subset(X1,esk4_0)
    | ~ subset(X1,esk3_0) ),
    inference(spm,[status(thm)],[277,395,theory(equality)]) ).

cnf(1481,plain,
    ( subset(set_difference(esk4_0,X1),empty_set)
    | ~ subset(set_difference(esk4_0,X1),esk3_0) ),
    inference(spm,[status(thm)],[1435,69,theory(equality)]) ).

cnf(1826,plain,
    set_difference(set_difference(esk2_0,X1),esk3_0) = empty_set,
    inference(spm,[status(thm)],[971,69,theory(equality)]) ).

cnf(1889,plain,
    ( subset(X1,esk3_0)
    | ~ subset(X1,set_difference(esk2_0,X2)) ),
    inference(spm,[status(thm)],[329,1826,theory(equality)]) ).

cnf(3388,plain,
    subset(set_difference(esk2_0,X1),esk3_0),
    inference(spm,[status(thm)],[1889,101,theory(equality)]) ).

cnf(3421,plain,
    subset(set_difference(X1,set_difference(X1,esk2_0)),esk3_0),
    inference(spm,[status(thm)],[3388,266,theory(equality)]) ).

cnf(58287,plain,
    subset(set_difference(esk4_0,set_difference(esk4_0,esk2_0)),empty_set),
    inference(spm,[status(thm)],[1481,3421,theory(equality)]) ).

cnf(58336,plain,
    subset(set_difference(esk2_0,set_difference(esk2_0,esk4_0)),empty_set),
    inference(rw,[status(thm)],[58287,266,theory(equality)]) ).

cnf(58532,plain,
    empty_set = set_difference(esk2_0,set_difference(esk2_0,esk4_0)),
    inference(spm,[status(thm)],[108,58336,theory(equality)]) ).

cnf(58767,plain,
    disjoint(esk2_0,esk4_0),
    inference(spm,[status(thm)],[273,58532,theory(equality)]) ).

cnf(59105,plain,
    $false,
    inference(sr,[status(thm)],[58767,86,theory(equality)]) ).

cnf(59106,plain,
    $false,
    59105,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU140+2.p
% --creating new selector for []
% -running prover on /tmp/tmpMGnc_S/sel_SEU140+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU140+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU140+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU140+2.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
% 
%------------------------------------------------------------------------------