TSTP Solution File: SET945+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET945+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 03:49:54 EST 2010

% Result   : Theorem 3.08s
% Output   : CNFRefutation 3.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   51 (   3 unt;   0 def)
%            Number of atoms       :  267 (  40 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  357 ( 141   ~; 141   |;  66   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :  158 (   5 sgn  86   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
     => disjoint(X2,X1) ),
    file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',symmetry_r1_xboole_0) ).

fof(5,axiom,
    ! [X1,X2] :
      ( X2 = union(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X3,X4)
              & in(X4,X1) ) ) ),
    file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',d4_tarski) ).

fof(6,conjecture,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
         => disjoint(X3,X2) )
     => disjoint(union(X1),X2) ),
    file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',t98_zfmisc_1) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',d3_xboole_0) ).

fof(10,axiom,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',t4_xboole_0) ).

fof(11,negated_conjecture,
    ~ ! [X1,X2] :
        ( ! [X3] :
            ( in(X3,X1)
           => disjoint(X3,X2) )
       => disjoint(union(X1),X2) ),
    inference(assume_negation,[status(cth)],[6]) ).

fof(14,plain,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(19,plain,
    ! [X1,X2] :
      ( ~ disjoint(X1,X2)
      | disjoint(X2,X1) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(20,plain,
    ! [X3,X4] :
      ( ~ disjoint(X3,X4)
      | disjoint(X4,X3) ),
    inference(variable_rename,[status(thm)],[19]) ).

cnf(21,plain,
    ( disjoint(X1,X2)
    | ~ disjoint(X2,X1) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(25,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)],[5]) ).

fof(26,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)],[25]) ).

fof(27,plain,
    ! [X5,X6] :
      ( ( X6 != union(X5)
        | ! [X7] :
            ( ( ~ in(X7,X6)
              | ( in(X7,esk2_3(X5,X6,X7))
                & in(esk2_3(X5,X6,X7),X5) ) )
            & ( ! [X9] :
                  ( ~ in(X7,X9)
                  | ~ in(X9,X5) )
              | in(X7,X6) ) ) )
      & ( ( ( ~ in(esk3_2(X5,X6),X6)
            | ! [X11] :
                ( ~ in(esk3_2(X5,X6),X11)
                | ~ in(X11,X5) ) )
          & ( in(esk3_2(X5,X6),X6)
            | ( in(esk3_2(X5,X6),esk4_2(X5,X6))
              & in(esk4_2(X5,X6),X5) ) ) )
        | X6 = union(X5) ) ),
    inference(skolemize,[status(esa)],[26]) ).

fof(28,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ( ( ~ in(esk3_2(X5,X6),X11)
            | ~ in(X11,X5)
            | ~ in(esk3_2(X5,X6),X6) )
          & ( in(esk3_2(X5,X6),X6)
            | ( in(esk3_2(X5,X6),esk4_2(X5,X6))
              & in(esk4_2(X5,X6),X5) ) ) )
        | X6 = union(X5) )
      & ( ( ( ~ in(X7,X9)
            | ~ in(X9,X5)
            | in(X7,X6) )
          & ( ~ in(X7,X6)
            | ( in(X7,esk2_3(X5,X6,X7))
              & in(esk2_3(X5,X6,X7),X5) ) ) )
        | X6 != union(X5) ) ),
    inference(shift_quantors,[status(thm)],[27]) ).

fof(29,plain,
    ! [X5,X6,X7,X9,X11] :
      ( ( ~ in(esk3_2(X5,X6),X11)
        | ~ in(X11,X5)
        | ~ in(esk3_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk3_2(X5,X6),esk4_2(X5,X6))
        | in(esk3_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( in(esk4_2(X5,X6),X5)
        | in(esk3_2(X5,X6),X6)
        | X6 = union(X5) )
      & ( ~ in(X7,X9)
        | ~ in(X9,X5)
        | in(X7,X6)
        | X6 != union(X5) )
      & ( in(X7,esk2_3(X5,X6,X7))
        | ~ in(X7,X6)
        | X6 != union(X5) )
      & ( in(esk2_3(X5,X6,X7),X5)
        | ~ in(X7,X6)
        | X6 != union(X5) ) ),
    inference(distribute,[status(thm)],[28]) ).

cnf(30,plain,
    ( in(esk2_3(X2,X1,X3),X2)
    | X1 != union(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(31,plain,
    ( in(X3,esk2_3(X2,X1,X3))
    | X1 != union(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(36,negated_conjecture,
    ? [X1,X2] :
      ( ! [X3] :
          ( ~ in(X3,X1)
          | disjoint(X3,X2) )
      & ~ disjoint(union(X1),X2) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(37,negated_conjecture,
    ? [X4,X5] :
      ( ! [X6] :
          ( ~ in(X6,X4)
          | disjoint(X6,X5) )
      & ~ disjoint(union(X4),X5) ),
    inference(variable_rename,[status(thm)],[36]) ).

fof(38,negated_conjecture,
    ( ! [X6] :
        ( ~ in(X6,esk5_0)
        | disjoint(X6,esk6_0) )
    & ~ disjoint(union(esk5_0),esk6_0) ),
    inference(skolemize,[status(esa)],[37]) ).

fof(39,negated_conjecture,
    ! [X6] :
      ( ( ~ in(X6,esk5_0)
        | disjoint(X6,esk6_0) )
      & ~ disjoint(union(esk5_0),esk6_0) ),
    inference(shift_quantors,[status(thm)],[38]) ).

cnf(40,negated_conjecture,
    ~ disjoint(union(esk5_0),esk6_0),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(41,negated_conjecture,
    ( disjoint(X1,esk6_0)
    | ~ in(X1,esk5_0) ),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(45,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)],[8]) ).

fof(46,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)],[45]) ).

fof(47,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(esk8_3(X5,X6,X7),X7)
            | ~ in(esk8_3(X5,X6,X7),X5)
            | ~ in(esk8_3(X5,X6,X7),X6) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | ( in(esk8_3(X5,X6,X7),X5)
              & in(esk8_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[46]) ).

fof(48,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(esk8_3(X5,X6,X7),X7)
            | ~ in(esk8_3(X5,X6,X7),X5)
            | ~ in(esk8_3(X5,X6,X7),X6) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | ( in(esk8_3(X5,X6,X7),X5)
              & in(esk8_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[47]) ).

fof(49,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(esk8_3(X5,X6,X7),X7)
        | ~ in(esk8_3(X5,X6,X7),X5)
        | ~ in(esk8_3(X5,X6,X7),X6)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk8_3(X5,X6,X7),X5)
        | in(esk8_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk8_3(X5,X6,X7),X6)
        | in(esk8_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) ) ),
    inference(distribute,[status(thm)],[48]) ).

cnf(53,plain,
    ( in(X4,X1)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(54,plain,
    ( in(X4,X3)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(55,plain,
    ( in(X4,X2)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[49]) ).

fof(59,plain,
    ! [X1,X2] :
      ( ( disjoint(X1,X2)
        | ? [X3] : in(X3,set_intersection2(X1,X2)) )
      & ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
        | ~ disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(60,plain,
    ! [X4,X5] :
      ( ( disjoint(X4,X5)
        | ? [X6] : in(X6,set_intersection2(X4,X5)) )
      & ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[59]) ).

fof(61,plain,
    ! [X4,X5] :
      ( ( disjoint(X4,X5)
        | in(esk9_2(X4,X5),set_intersection2(X4,X5)) )
      & ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) ) ),
    inference(skolemize,[status(esa)],[60]) ).

fof(62,plain,
    ! [X4,X5,X7] :
      ( ( ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) )
      & ( disjoint(X4,X5)
        | in(esk9_2(X4,X5),set_intersection2(X4,X5)) ) ),
    inference(shift_quantors,[status(thm)],[61]) ).

cnf(63,plain,
    ( in(esk9_2(X1,X2),set_intersection2(X1,X2))
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[62]) ).

cnf(64,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[62]) ).

cnf(66,negated_conjecture,
    ( disjoint(esk6_0,X1)
    | ~ in(X1,esk5_0) ),
    inference(spm,[status(thm)],[21,41,theory(equality)]) ).

cnf(71,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[54,theory(equality)]) ).

cnf(79,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X2,X3)) ),
    inference(er,[status(thm)],[55,theory(equality)]) ).

cnf(95,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[53,theory(equality)]) ).

cnf(135,plain,
    ( in(esk9_2(X1,X2),X2)
    | disjoint(X1,X2) ),
    inference(spm,[status(thm)],[71,63,theory(equality)]) ).

cnf(178,plain,
    ( in(esk9_2(X1,X2),X1)
    | disjoint(X1,X2) ),
    inference(spm,[status(thm)],[79,63,theory(equality)]) ).

cnf(274,plain,
    ( ~ disjoint(X2,X3)
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[64,95,theory(equality)]) ).

cnf(284,plain,
    ( ~ in(X1,X4)
    | ~ disjoint(X4,esk2_3(X2,X3,X1))
    | union(X2) != X3
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[274,31,theory(equality)]) ).

cnf(4185,negated_conjecture,
    ( union(X1) != X2
    | ~ in(X3,esk6_0)
    | ~ in(X3,X2)
    | ~ in(esk2_3(X1,X2,X3),esk5_0) ),
    inference(spm,[status(thm)],[284,66,theory(equality)]) ).

cnf(53348,negated_conjecture,
    ( union(esk5_0) != X1
    | ~ in(X2,esk6_0)
    | ~ in(X2,X1) ),
    inference(spm,[status(thm)],[4185,30,theory(equality)]) ).

cnf(53363,negated_conjecture,
    ( disjoint(X2,esk6_0)
    | union(esk5_0) != X1
    | ~ in(esk9_2(X2,esk6_0),X1) ),
    inference(spm,[status(thm)],[53348,135,theory(equality)]) ).

cnf(53494,negated_conjecture,
    ( disjoint(X1,esk6_0)
    | union(esk5_0) != X1 ),
    inference(spm,[status(thm)],[53363,178,theory(equality)]) ).

cnf(53930,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[40,53494,theory(equality)]) ).

cnf(54140,negated_conjecture,
    $false,
    53930,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET945+1.p
% --creating new selector for []
% -running prover on /tmp/tmpb-6oXC/sel_SET945+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET945+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET945+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET945+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
% 
%------------------------------------------------------------------------------