TSTP Solution File: SET941+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET941+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:49:19 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   35 (   4 unt;   0 def)
%            Number of atoms       :  166 (  17 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  205 (  74   ~;  83   |;  40   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   95 (   0 sgn  56   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( X2 = union(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X3,X4)
              & in(X4,X1) ) ) ),
    file('/tmp/tmpNE3Anv/sel_SET941+1.p_1',d4_tarski) ).

fof(3,conjecture,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
         => subset(X3,X2) )
     => subset(union(X1),X2) ),
    file('/tmp/tmpNE3Anv/sel_SET941+1.p_1',t94_zfmisc_1) ).

fof(6,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/tmp/tmpNE3Anv/sel_SET941+1.p_1',d3_tarski) ).

fof(8,negated_conjecture,
    ~ ! [X1,X2] :
        ( ! [X3] :
            ( in(X3,X1)
           => subset(X3,X2) )
       => subset(union(X1),X2) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(11,plain,
    ! [X1,X2] :
      ( ( X2 != union(X1)
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | ? [X4] :
                  ( in(X3,X4)
                  & in(X4,X1) ) )
            & ( ! [X4] :
                  ( ~ in(X3,X4)
                  | ~ in(X4,X1) )
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( ~ in(X3,X2)
              | ! [X4] :
                  ( ~ in(X3,X4)
                  | ~ in(X4,X1) ) )
            & ( in(X3,X2)
              | ? [X4] :
                  ( in(X3,X4)
                  & in(X4,X1) ) ) )
        | X2 = union(X1) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(12,plain,
    ! [X5,X6] :
      ( ( X6 != union(X5)
        | ! [X7] :
            ( ( ~ in(X7,X6)
              | ? [X8] :
                  ( in(X7,X8)
                  & in(X8,X5) ) )
            & ( ! [X9] :
                  ( ~ in(X7,X9)
                  | ~ in(X9,X5) )
              | in(X7,X6) ) ) )
      & ( ? [X10] :
            ( ( ~ in(X10,X6)
              | ! [X11] :
                  ( ~ in(X10,X11)
                  | ~ in(X11,X5) ) )
            & ( in(X10,X6)
              | ? [X12] :
                  ( in(X10,X12)
                  & in(X12,X5) ) ) )
        | X6 = union(X5) ) ),
    inference(variable_rename,[status(thm)],[11]) ).

fof(13,plain,
    ! [X5,X6] :
      ( ( X6 != union(X5)
        | ! [X7] :
            ( ( ~ in(X7,X6)
              | ( in(X7,esk1_3(X5,X6,X7))
                & in(esk1_3(X5,X6,X7),X5) ) )
            & ( ! [X9] :
                  ( ~ in(X7,X9)
                  | ~ in(X9,X5) )
              | in(X7,X6) ) ) )
      & ( ( ( ~ in(esk2_2(X5,X6),X6)
            | ! [X11] :
                ( ~ in(esk2_2(X5,X6),X11)
                | ~ in(X11,X5) ) )
          & ( in(esk2_2(X5,X6),X6)
            | ( in(esk2_2(X5,X6),esk3_2(X5,X6))
              & in(esk3_2(X5,X6),X5) ) ) )
        | X6 = union(X5) ) ),
    inference(skolemize,[status(esa)],[12]) ).

fof(14,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ~ in(esk2_2(X5,X6),X11)
            | ~ in(X11,X5)
            | ~ in(esk2_2(X5,X6),X6) )
          & ( in(esk2_2(X5,X6),X6)
            | ( in(esk2_2(X5,X6),esk3_2(X5,X6))
              & in(esk3_2(X5,X6),X5) ) ) )
        | X6 = union(X5) )
      & ( ( ( ~ in(X7,X9)
            | ~ in(X9,X5)
            | in(X7,X6) )
          & ( ~ in(X7,X6)
            | ( in(X7,esk1_3(X5,X6,X7))
              & in(esk1_3(X5,X6,X7),X5) ) ) )
        | X6 != union(X5) ) ),
    inference(shift_quantors,[status(thm)],[13]) ).

fof(15,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(esk2_2(X5,X6),X11)
        | ~ in(X11,X5)
        | ~ in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk2_2(X5,X6),esk3_2(X5,X6))
        | in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk3_2(X5,X6),X5)
        | in(esk2_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( ~ in(X7,X9)
        | ~ in(X9,X5)
        | in(X7,X6)
        | X6 != union(X5) )
      & ( in(X7,esk1_3(X5,X6,X7))
        | ~ in(X7,X6)
        | X6 != union(X5) )
      & ( in(esk1_3(X5,X6,X7),X5)
        | ~ in(X7,X6)
        | X6 != union(X5) ) ),
    inference(distribute,[status(thm)],[14]) ).

cnf(16,plain,
    ( in(esk1_3(X2,X1,X3),X2)
    | X1 != union(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,plain,
    ( in(X3,esk1_3(X2,X1,X3))
    | X1 != union(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(25,negated_conjecture,
    ? [X1,X2] :
      ( ! [X3] :
          ( ~ in(X3,X1)
          | subset(X3,X2) )
      & ~ subset(union(X1),X2) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(26,negated_conjecture,
    ? [X4,X5] :
      ( ! [X6] :
          ( ~ in(X6,X4)
          | subset(X6,X5) )
      & ~ subset(union(X4),X5) ),
    inference(variable_rename,[status(thm)],[25]) ).

fof(27,negated_conjecture,
    ( ! [X6] :
        ( ~ in(X6,esk5_0)
        | subset(X6,esk6_0) )
    & ~ subset(union(esk5_0),esk6_0) ),
    inference(skolemize,[status(esa)],[26]) ).

fof(28,negated_conjecture,
    ! [X6] :
      ( ( ~ in(X6,esk5_0)
        | subset(X6,esk6_0) )
      & ~ subset(union(esk5_0),esk6_0) ),
    inference(shift_quantors,[status(thm)],[27]) ).

cnf(29,negated_conjecture,
    ~ subset(union(esk5_0),esk6_0),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(30,negated_conjecture,
    ( subset(X1,esk6_0)
    | ~ in(X1,esk5_0) ),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(37,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X2) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(38,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ? [X7] :
            ( in(X7,X4)
            & ~ in(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[37]) ).

fof(39,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ( in(esk8_2(X4,X5),X4)
          & ~ in(esk8_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[38]) ).

fof(40,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( in(esk8_2(X4,X5),X4)
          & ~ in(esk8_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[39]) ).

fof(41,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( in(esk8_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk8_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[40]) ).

cnf(42,plain,
    ( subset(X1,X2)
    | ~ in(esk8_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(43,plain,
    ( subset(X1,X2)
    | in(esk8_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(44,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(53,plain,
    ( in(X1,esk1_3(X2,union(X2),X1))
    | ~ in(X1,union(X2)) ),
    inference(er,[status(thm)],[17,theory(equality)]) ).

cnf(54,plain,
    ( in(esk1_3(X1,union(X1),X2),X1)
    | ~ in(X2,union(X1)) ),
    inference(er,[status(thm)],[16,theory(equality)]) ).

cnf(72,plain,
    ( in(esk8_2(union(X1),X2),esk1_3(X1,union(X1),esk8_2(union(X1),X2)))
    | subset(union(X1),X2) ),
    inference(spm,[status(thm)],[53,43,theory(equality)]) ).

cnf(75,plain,
    ( in(esk1_3(X1,union(X1),esk8_2(union(X1),X2)),X1)
    | subset(union(X1),X2) ),
    inference(spm,[status(thm)],[54,43,theory(equality)]) ).

cnf(92,negated_conjecture,
    ( subset(esk1_3(esk5_0,union(esk5_0),esk8_2(union(esk5_0),X1)),esk6_0)
    | subset(union(esk5_0),X1) ),
    inference(spm,[status(thm)],[30,75,theory(equality)]) ).

cnf(100,negated_conjecture,
    ( in(X1,esk6_0)
    | subset(union(esk5_0),X2)
    | ~ in(X1,esk1_3(esk5_0,union(esk5_0),esk8_2(union(esk5_0),X2))) ),
    inference(spm,[status(thm)],[44,92,theory(equality)]) ).

cnf(172,negated_conjecture,
    ( subset(union(esk5_0),X1)
    | in(esk8_2(union(esk5_0),X1),esk6_0) ),
    inference(spm,[status(thm)],[100,72,theory(equality)]) ).

cnf(175,negated_conjecture,
    subset(union(esk5_0),esk6_0),
    inference(spm,[status(thm)],[42,172,theory(equality)]) ).

cnf(178,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[175,29,theory(equality)]) ).

cnf(179,negated_conjecture,
    $false,
    178,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET941+1.p
% --creating new selector for []
% -running prover on /tmp/tmpNE3Anv/sel_SET941+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET941+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET941+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET941+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
% 
%------------------------------------------------------------------------------