TSTP Solution File: SET920+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET920+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 03:47:27 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   32 (  10 unt;   0 def)
%            Number of atoms       :  192 (  86 equ)
%            Maximal formula atoms :   20 (   6 avg)
%            Number of connectives :  248 (  88   ~; 100   |;  54   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   87 (   5 sgn  58   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',commutativity_k3_xboole_0) ).

fof(6,conjecture,
    ! [X1,X2,X3] :
      ( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
     => in(X1,X3) ),
    file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',t63_zfmisc_1) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',d3_xboole_0) ).

fof(9,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',d2_tarski) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
       => in(X1,X3) ),
    inference(assume_negation,[status(cth)],[6]) ).

fof(13,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(14,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(25,negated_conjecture,
    ? [X1,X2,X3] :
      ( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
      & ~ in(X1,X3) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(26,negated_conjecture,
    ? [X4,X5,X6] :
      ( set_intersection2(unordered_pair(X4,X5),X6) = unordered_pair(X4,X5)
      & ~ in(X4,X6) ),
    inference(variable_rename,[status(thm)],[25]) ).

fof(27,negated_conjecture,
    ( set_intersection2(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0)
    & ~ in(esk3_0,esk5_0) ),
    inference(skolemize,[status(esa)],[26]) ).

cnf(28,negated_conjecture,
    ~ in(esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(29,negated_conjecture,
    set_intersection2(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(30,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_intersection2(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) )
            & ( ~ in(X4,X1)
              | ~ in(X4,X2)
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) ) )
        | X3 = set_intersection2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(31,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ~ in(X9,X5)
              | ~ in(X9,X6) )
            & ( in(X9,X7)
              | ( in(X9,X5)
                & in(X9,X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[30]) ).

fof(32,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
            | ~ in(esk6_3(X5,X6,X7),X5)
            | ~ in(esk6_3(X5,X6,X7),X6) )
          & ( in(esk6_3(X5,X6,X7),X7)
            | ( in(esk6_3(X5,X6,X7),X5)
              & in(esk6_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[31]) ).

fof(33,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | ( in(X8,X5)
              & in(X8,X6) ) )
          & ( ~ in(X8,X5)
            | ~ in(X8,X6)
            | in(X8,X7) ) )
        | X7 != set_intersection2(X5,X6) )
      & ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
            | ~ in(esk6_3(X5,X6,X7),X5)
            | ~ in(esk6_3(X5,X6,X7),X6) )
          & ( in(esk6_3(X5,X6,X7),X7)
            | ( in(esk6_3(X5,X6,X7),X5)
              & in(esk6_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[32]) ).

fof(34,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(X8,X5)
        | ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(esk6_3(X5,X6,X7),X7)
        | ~ in(esk6_3(X5,X6,X7),X5)
        | ~ in(esk6_3(X5,X6,X7),X6)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk6_3(X5,X6,X7),X5)
        | in(esk6_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk6_3(X5,X6,X7),X6)
        | in(esk6_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) ) ),
    inference(distribute,[status(thm)],[33]) ).

cnf(40,plain,
    ( in(X4,X2)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(44,plain,
    ! [X1,X2,X3] :
      ( ( X3 != unordered_pair(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | X4 = X1
              | X4 = X2 )
            & ( ( X4 != X1
                & X4 != X2 )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ( X4 != X1
                & X4 != X2 ) )
            & ( in(X4,X3)
              | X4 = X1
              | X4 = X2 ) )
        | X3 = unordered_pair(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(45,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ( X9 != X5
                & X9 != X6 ) )
            & ( in(X9,X7)
              | X9 = X5
              | X9 = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[44]) ).

fof(46,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
            | ( esk7_3(X5,X6,X7) != X5
              & esk7_3(X5,X6,X7) != X6 ) )
          & ( in(esk7_3(X5,X6,X7),X7)
            | esk7_3(X5,X6,X7) = X5
            | esk7_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(skolemize,[status(esa)],[45]) ).

fof(47,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | X8 = X5
            | X8 = X6 )
          & ( ( X8 != X5
              & X8 != X6 )
            | in(X8,X7) ) )
        | X7 != unordered_pair(X5,X6) )
      & ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
            | ( esk7_3(X5,X6,X7) != X5
              & esk7_3(X5,X6,X7) != X6 ) )
          & ( in(esk7_3(X5,X6,X7),X7)
            | esk7_3(X5,X6,X7) = X5
            | esk7_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[46]) ).

fof(48,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,X7)
        | X8 = X5
        | X8 = X6
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X5
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X6
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( esk7_3(X5,X6,X7) != X5
        | ~ in(esk7_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( esk7_3(X5,X6,X7) != X6
        | ~ in(esk7_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( in(esk7_3(X5,X6,X7),X7)
        | esk7_3(X5,X6,X7) = X5
        | esk7_3(X5,X6,X7) = X6
        | X7 = unordered_pair(X5,X6) ) ),
    inference(distribute,[status(thm)],[47]) ).

cnf(53,plain,
    ( in(X4,X1)
    | X1 != unordered_pair(X2,X3)
    | X4 != X2 ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(57,negated_conjecture,
    set_intersection2(esk5_0,unordered_pair(esk3_0,esk4_0)) = unordered_pair(esk3_0,esk4_0),
    inference(rw,[status(thm)],[29,14,theory(equality)]) ).

cnf(61,plain,
    ( in(X1,X2)
    | unordered_pair(X1,X3) != X2 ),
    inference(er,[status(thm)],[53,theory(equality)]) ).

cnf(67,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X2,X3)) ),
    inference(er,[status(thm)],[40,theory(equality)]) ).

cnf(108,negated_conjecture,
    ( in(X1,esk5_0)
    | ~ in(X1,unordered_pair(esk3_0,esk4_0)) ),
    inference(spm,[status(thm)],[67,57,theory(equality)]) ).

cnf(119,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(er,[status(thm)],[61,theory(equality)]) ).

cnf(137,negated_conjecture,
    in(esk3_0,esk5_0),
    inference(spm,[status(thm)],[108,119,theory(equality)]) ).

cnf(143,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[137,28,theory(equality)]) ).

cnf(144,negated_conjecture,
    $false,
    143,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET920+1.p
% --creating new selector for []
% -running prover on /tmp/tmp7s5L5w/sel_SET920+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET920+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET920+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET920+1.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
% 
%------------------------------------------------------------------------------