TSTP Solution File: SET600+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET600+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 03:00:15 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   64 (  14 unt;   0 def)
%            Number of atoms       :  235 (  88 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  272 ( 101   ~; 115   |;  48   &)
%                                         (   7 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  105 (   8 sgn  67   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',commutativity_of_union) ).

fof(3,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',equal_defn) ).

fof(4,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',union_defn) ).

fof(5,conjecture,
    ! [X1,X2] :
      ( union(X1,X2) = empty_set
    <=> ( X1 = empty_set
        & X2 = empty_set ) ),
    file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',prove_th59) ).

fof(6,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',subset_defn) ).

fof(7,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ! [X3] :
          ( member(X3,X1)
        <=> member(X3,X2) ) ),
    file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',equal_member_defn) ).

fof(9,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',empty_set_defn) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( union(X1,X2) = empty_set
      <=> ( X1 = empty_set
          & X2 = empty_set ) ),
    inference(assume_negation,[status(cth)],[5]) ).

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

fof(13,plain,
    ! [X3,X4] : union(X3,X4) = union(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(14,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(21,plain,
    ! [X1,X2] :
      ( ( X1 != X2
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(22,plain,
    ! [X3,X4] :
      ( ( X3 != X4
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[22]) ).

cnf(24,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(27,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)],[4]) ).

fof(28,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)],[27]) ).

fof(29,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)],[28]) ).

cnf(30,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(31,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(32,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(33,negated_conjecture,
    ? [X1,X2] :
      ( ( union(X1,X2) != empty_set
        | X1 != empty_set
        | X2 != empty_set )
      & ( union(X1,X2) = empty_set
        | ( X1 = empty_set
          & X2 = empty_set ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(34,negated_conjecture,
    ? [X3,X4] :
      ( ( union(X3,X4) != empty_set
        | X3 != empty_set
        | X4 != empty_set )
      & ( union(X3,X4) = empty_set
        | ( X3 = empty_set
          & X4 = empty_set ) ) ),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,negated_conjecture,
    ( ( union(esk2_0,esk3_0) != empty_set
      | esk2_0 != empty_set
      | esk3_0 != empty_set )
    & ( union(esk2_0,esk3_0) = empty_set
      | ( esk2_0 = empty_set
        & esk3_0 = empty_set ) ) ),
    inference(skolemize,[status(esa)],[34]) ).

fof(36,negated_conjecture,
    ( ( union(esk2_0,esk3_0) != empty_set
      | esk2_0 != empty_set
      | esk3_0 != empty_set )
    & ( esk2_0 = empty_set
      | union(esk2_0,esk3_0) = empty_set )
    & ( esk3_0 = empty_set
      | union(esk2_0,esk3_0) = empty_set ) ),
    inference(distribute,[status(thm)],[35]) ).

cnf(37,negated_conjecture,
    ( union(esk2_0,esk3_0) = empty_set
    | esk3_0 = empty_set ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(38,negated_conjecture,
    ( union(esk2_0,esk3_0) = empty_set
    | esk2_0 = empty_set ),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(39,negated_conjecture,
    ( esk3_0 != empty_set
    | esk2_0 != empty_set
    | union(esk2_0,esk3_0) != empty_set ),
    inference(split_conjunct,[status(thm)],[36]) ).

fof(40,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)],[6]) ).

fof(41,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)],[40]) ).

fof(42,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk4_2(X4,X5),X4)
          & ~ member(esk4_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[41]) ).

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

fof(44,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk4_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk4_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[43]) ).

cnf(46,plain,
    ( subset(X1,X2)
    | member(esk4_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(48,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)],[7]) ).

fof(49,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)],[48]) ).

fof(50,plain,
    ! [X4,X5] :
      ( ( X4 != X5
        | ! [X6] :
            ( ( ~ member(X6,X4)
              | member(X6,X5) )
            & ( ~ member(X6,X5)
              | member(X6,X4) ) ) )
      & ( ( ( ~ member(esk5_2(X4,X5),X4)
            | ~ member(esk5_2(X4,X5),X5) )
          & ( member(esk5_2(X4,X5),X4)
            | member(esk5_2(X4,X5),X5) ) )
        | X4 = X5 ) ),
    inference(skolemize,[status(esa)],[49]) ).

fof(51,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ member(X6,X4)
            | member(X6,X5) )
          & ( ~ member(X6,X5)
            | member(X6,X4) ) )
        | X4 != X5 )
      & ( ( ( ~ member(esk5_2(X4,X5),X4)
            | ~ member(esk5_2(X4,X5),X5) )
          & ( member(esk5_2(X4,X5),X4)
            | member(esk5_2(X4,X5),X5) ) )
        | X4 = X5 ) ),
    inference(shift_quantors,[status(thm)],[50]) ).

fof(52,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | X4 != X5 )
      & ( ~ member(X6,X5)
        | member(X6,X4)
        | X4 != X5 )
      & ( ~ member(esk5_2(X4,X5),X4)
        | ~ member(esk5_2(X4,X5),X5)
        | X4 = X5 )
      & ( member(esk5_2(X4,X5),X4)
        | member(esk5_2(X4,X5),X5)
        | X4 = X5 ) ),
    inference(distribute,[status(thm)],[51]) ).

cnf(53,plain,
    ( X1 = X2
    | member(esk5_2(X1,X2),X2)
    | member(esk5_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(59,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(60,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[59]) ).

cnf(72,negated_conjecture,
    ( member(X1,empty_set)
    | esk3_0 = empty_set
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[30,37,theory(equality)]) ).

cnf(75,negated_conjecture,
    ( esk3_0 = empty_set
    | ~ member(X1,esk3_0) ),
    inference(sr,[status(thm)],[72,60,theory(equality)]) ).

cnf(78,negated_conjecture,
    ( member(X1,empty_set)
    | esk2_0 = empty_set
    | ~ member(X1,esk2_0) ),
    inference(spm,[status(thm)],[31,38,theory(equality)]) ).

cnf(81,negated_conjecture,
    ( esk2_0 = empty_set
    | ~ member(X1,esk2_0) ),
    inference(sr,[status(thm)],[78,60,theory(equality)]) ).

cnf(83,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[60,46,theory(equality)]) ).

cnf(100,plain,
    ( empty_set = X1
    | member(esk5_2(empty_set,X1),X1) ),
    inference(spm,[status(thm)],[60,53,theory(equality)]) ).

cnf(109,plain,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(spm,[status(thm)],[24,83,theory(equality)]) ).

cnf(118,negated_conjecture,
    ( esk3_0 = empty_set
    | subset(esk3_0,X1) ),
    inference(spm,[status(thm)],[75,46,theory(equality)]) ).

cnf(128,negated_conjecture,
    ( esk2_0 = empty_set
    | subset(esk2_0,X1) ),
    inference(spm,[status(thm)],[81,46,theory(equality)]) ).

cnf(142,negated_conjecture,
    esk3_0 = empty_set,
    inference(spm,[status(thm)],[109,118,theory(equality)]) ).

cnf(143,negated_conjecture,
    esk2_0 = empty_set,
    inference(spm,[status(thm)],[109,128,theory(equality)]) ).

cnf(161,negated_conjecture,
    ( union(empty_set,esk2_0) != empty_set
    | esk2_0 != empty_set
    | esk3_0 != empty_set ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[39,142,theory(equality)]),14,theory(equality)]) ).

cnf(162,negated_conjecture,
    ( union(empty_set,esk2_0) != empty_set
    | esk2_0 != empty_set
    | $false ),
    inference(rw,[status(thm)],[161,142,theory(equality)]) ).

cnf(163,negated_conjecture,
    ( union(empty_set,esk2_0) != empty_set
    | esk2_0 != empty_set ),
    inference(cn,[status(thm)],[162,theory(equality)]) ).

cnf(178,negated_conjecture,
    ( union(empty_set,empty_set) != empty_set
    | esk2_0 != empty_set ),
    inference(rw,[status(thm)],[163,143,theory(equality)]) ).

cnf(179,negated_conjecture,
    ( union(empty_set,empty_set) != empty_set
    | $false ),
    inference(rw,[status(thm)],[178,143,theory(equality)]) ).

cnf(180,negated_conjecture,
    union(empty_set,empty_set) != empty_set,
    inference(cn,[status(thm)],[179,theory(equality)]) ).

cnf(187,plain,
    ( member(esk5_2(empty_set,union(X1,X2)),X2)
    | member(esk5_2(empty_set,union(X1,X2)),X1)
    | empty_set = union(X1,X2) ),
    inference(spm,[status(thm)],[32,100,theory(equality)]) ).

cnf(231,plain,
    ( union(X3,X3) = empty_set
    | member(esk5_2(empty_set,union(X3,X3)),X3) ),
    inference(ef,[status(thm)],[187,theory(equality)]) ).

cnf(243,plain,
    union(empty_set,empty_set) = empty_set,
    inference(spm,[status(thm)],[60,231,theory(equality)]) ).

cnf(246,plain,
    $false,
    inference(sr,[status(thm)],[243,180,theory(equality)]) ).

cnf(247,plain,
    $false,
    246,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET600+3.p
% --creating new selector for []
% -running prover on /tmp/tmpuQ0N-6/sel_SET600+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET600+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET600+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET600+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
% 
%------------------------------------------------------------------------------