TSTP Solution File: SET812+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET812+4 : 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 03:41:21 EST 2010

% Result   : Theorem 84.87s
% Output   : CNFRefutation 84.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   54 (   7 unt;   0 def)
%            Number of atoms       :  214 (   0 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  259 (  99   ~; 100   |;  51   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  106 (   2 sgn  58   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',subset) ).

fof(2,axiom,
    ! [X1] :
      ( member(X1,on)
    <=> ( set(X1)
        & strict_well_order(member_predicate,X1)
        & ! [X3] :
            ( member(X3,X1)
           => subset(X3,X1) ) ) ),
    file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',ordinal_number) ).

fof(5,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',equal_set) ).

fof(7,axiom,
    ! [X3,X1,X2] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',intersection) ).

fof(10,axiom,
    ! [X3,X1] :
      ( member(X3,power_set(X1))
    <=> subset(X3,X1) ),
    file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',power_set) ).

fof(11,conjecture,
    ! [X1] :
      ( member(X1,on)
     => equal_set(X1,intersection(X1,power_set(X1))) ),
    file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',thV10) ).

fof(12,negated_conjecture,
    ~ ! [X1] :
        ( member(X1,on)
       => equal_set(X1,intersection(X1,power_set(X1))) ),
    inference(assume_negation,[status(cth)],[11]) ).

fof(13,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)],[1]) ).

fof(14,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)],[13]) ).

fof(15,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[14]) ).

fof(16,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[15]) ).

fof(17,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[16]) ).

cnf(18,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(19,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(20,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(21,plain,
    ! [X1] :
      ( ( ~ member(X1,on)
        | ( set(X1)
          & strict_well_order(member_predicate,X1)
          & ! [X3] :
              ( ~ member(X3,X1)
              | subset(X3,X1) ) ) )
      & ( ~ set(X1)
        | ~ strict_well_order(member_predicate,X1)
        | ? [X3] :
            ( member(X3,X1)
            & ~ subset(X3,X1) )
        | member(X1,on) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(22,plain,
    ! [X4] :
      ( ( ~ member(X4,on)
        | ( set(X4)
          & strict_well_order(member_predicate,X4)
          & ! [X5] :
              ( ~ member(X5,X4)
              | subset(X5,X4) ) ) )
      & ( ~ set(X4)
        | ~ strict_well_order(member_predicate,X4)
        | ? [X6] :
            ( member(X6,X4)
            & ~ subset(X6,X4) )
        | member(X4,on) ) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,plain,
    ! [X4] :
      ( ( ~ member(X4,on)
        | ( set(X4)
          & strict_well_order(member_predicate,X4)
          & ! [X5] :
              ( ~ member(X5,X4)
              | subset(X5,X4) ) ) )
      & ( ~ set(X4)
        | ~ strict_well_order(member_predicate,X4)
        | ( member(esk2_1(X4),X4)
          & ~ subset(esk2_1(X4),X4) )
        | member(X4,on) ) ),
    inference(skolemize,[status(esa)],[22]) ).

fof(24,plain,
    ! [X4,X5] :
      ( ( ( ( ~ member(X5,X4)
            | subset(X5,X4) )
          & set(X4)
          & strict_well_order(member_predicate,X4) )
        | ~ member(X4,on) )
      & ( ~ set(X4)
        | ~ strict_well_order(member_predicate,X4)
        | ( member(esk2_1(X4),X4)
          & ~ subset(esk2_1(X4),X4) )
        | member(X4,on) ) ),
    inference(shift_quantors,[status(thm)],[23]) ).

fof(25,plain,
    ! [X4,X5] :
      ( ( ~ member(X5,X4)
        | subset(X5,X4)
        | ~ member(X4,on) )
      & ( set(X4)
        | ~ member(X4,on) )
      & ( strict_well_order(member_predicate,X4)
        | ~ member(X4,on) )
      & ( member(esk2_1(X4),X4)
        | ~ set(X4)
        | ~ strict_well_order(member_predicate,X4)
        | member(X4,on) )
      & ( ~ subset(esk2_1(X4),X4)
        | ~ set(X4)
        | ~ strict_well_order(member_predicate,X4)
        | member(X4,on) ) ),
    inference(distribute,[status(thm)],[24]) ).

cnf(30,plain,
    ( subset(X2,X1)
    | ~ member(X1,on)
    | ~ member(X2,X1) ),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(45,plain,
    ! [X1,X2] :
      ( ( ~ equal_set(X1,X2)
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | equal_set(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(46,plain,
    ! [X3,X4] :
      ( ( ~ equal_set(X3,X4)
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[45]) ).

fof(47,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | ~ equal_set(X3,X4) )
      & ( subset(X4,X3)
        | ~ equal_set(X3,X4) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(distribute,[status(thm)],[46]) ).

cnf(48,plain,
    ( equal_set(X1,X2)
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(61,plain,
    ! [X3,X1,X2] :
      ( ( ~ member(X3,intersection(X1,X2))
        | ( member(X3,X1)
          & member(X3,X2) ) )
      & ( ~ member(X3,X1)
        | ~ member(X3,X2)
        | member(X3,intersection(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(62,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X4,intersection(X5,X6))
        | ( member(X4,X5)
          & member(X4,X6) ) )
      & ( ~ member(X4,X5)
        | ~ member(X4,X6)
        | member(X4,intersection(X5,X6)) ) ),
    inference(variable_rename,[status(thm)],[61]) ).

fof(63,plain,
    ! [X4,X5,X6] :
      ( ( member(X4,X5)
        | ~ member(X4,intersection(X5,X6)) )
      & ( member(X4,X6)
        | ~ member(X4,intersection(X5,X6)) )
      & ( ~ member(X4,X5)
        | ~ member(X4,X6)
        | member(X4,intersection(X5,X6)) ) ),
    inference(distribute,[status(thm)],[62]) ).

cnf(64,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[63]) ).

cnf(66,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[63]) ).

fof(102,plain,
    ! [X3,X1] :
      ( ( ~ member(X3,power_set(X1))
        | subset(X3,X1) )
      & ( ~ subset(X3,X1)
        | member(X3,power_set(X1)) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(103,plain,
    ! [X4,X5] :
      ( ( ~ member(X4,power_set(X5))
        | subset(X4,X5) )
      & ( ~ subset(X4,X5)
        | member(X4,power_set(X5)) ) ),
    inference(variable_rename,[status(thm)],[102]) ).

cnf(104,plain,
    ( member(X1,power_set(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[103]) ).

fof(106,negated_conjecture,
    ? [X1] :
      ( member(X1,on)
      & ~ equal_set(X1,intersection(X1,power_set(X1))) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(107,negated_conjecture,
    ? [X2] :
      ( member(X2,on)
      & ~ equal_set(X2,intersection(X2,power_set(X2))) ),
    inference(variable_rename,[status(thm)],[106]) ).

fof(108,negated_conjecture,
    ( member(esk12_0,on)
    & ~ equal_set(esk12_0,intersection(esk12_0,power_set(esk12_0))) ),
    inference(skolemize,[status(esa)],[107]) ).

cnf(109,negated_conjecture,
    ~ equal_set(esk12_0,intersection(esk12_0,power_set(esk12_0))),
    inference(split_conjunct,[status(thm)],[108]) ).

cnf(110,negated_conjecture,
    member(esk12_0,on),
    inference(split_conjunct,[status(thm)],[108]) ).

cnf(116,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ member(X2,on)
    | ~ member(X3,X2) ),
    inference(spm,[status(thm)],[20,30,theory(equality)]) ).

cnf(121,plain,
    ( member(esk1_2(intersection(X1,X2),X3),X1)
    | subset(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[66,19,theory(equality)]) ).

cnf(125,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ member(esk1_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[18,64,theory(equality)]) ).

cnf(127,negated_conjecture,
    ( ~ subset(intersection(esk12_0,power_set(esk12_0)),esk12_0)
    | ~ subset(esk12_0,intersection(esk12_0,power_set(esk12_0))) ),
    inference(spm,[status(thm)],[109,48,theory(equality)]) ).

cnf(244,plain,
    subset(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[18,121,theory(equality)]) ).

cnf(247,negated_conjecture,
    ( $false
    | ~ subset(esk12_0,intersection(esk12_0,power_set(esk12_0))) ),
    inference(rw,[status(thm)],[127,244,theory(equality)]) ).

cnf(248,negated_conjecture,
    ~ subset(esk12_0,intersection(esk12_0,power_set(esk12_0))),
    inference(cn,[status(thm)],[247,theory(equality)]) ).

cnf(251,negated_conjecture,
    ( member(X1,esk12_0)
    | ~ member(X1,X2)
    | ~ member(X2,esk12_0) ),
    inference(spm,[status(thm)],[116,110,theory(equality)]) ).

cnf(263,negated_conjecture,
    ( member(X1,esk12_0)
    | subset(esk12_0,X2)
    | ~ member(X1,esk1_2(esk12_0,X2)) ),
    inference(spm,[status(thm)],[251,19,theory(equality)]) ).

cnf(275,negated_conjecture,
    ( member(esk1_2(esk1_2(esk12_0,X1),X2),esk12_0)
    | subset(esk12_0,X1)
    | subset(esk1_2(esk12_0,X1),X2) ),
    inference(spm,[status(thm)],[263,19,theory(equality)]) ).

cnf(347,plain,
    ( subset(X1,intersection(X2,power_set(X3)))
    | ~ member(esk1_2(X1,intersection(X2,power_set(X3))),X2)
    | ~ subset(esk1_2(X1,intersection(X2,power_set(X3))),X3) ),
    inference(spm,[status(thm)],[125,104,theory(equality)]) ).

cnf(4325,negated_conjecture,
    ( subset(esk1_2(esk12_0,X1),esk12_0)
    | subset(esk12_0,X1) ),
    inference(spm,[status(thm)],[18,275,theory(equality)]) ).

cnf(11933,plain,
    ( subset(X1,intersection(X1,power_set(X2)))
    | ~ subset(esk1_2(X1,intersection(X1,power_set(X2))),X2) ),
    inference(spm,[status(thm)],[347,19,theory(equality)]) ).

cnf(805838,negated_conjecture,
    subset(esk12_0,intersection(esk12_0,power_set(esk12_0))),
    inference(spm,[status(thm)],[11933,4325,theory(equality)]) ).

cnf(805892,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[805838,248,theory(equality)]) ).

cnf(805893,negated_conjecture,
    $false,
    805892,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET812+4.p
% --creating new selector for [SET006+0.ax, SET006+4.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpOf_kV2/sel_SET812+4.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpOf_kV2/sel_SET812+4.p_2 with time limit 81
% -prover status Theorem
% Problem SET812+4.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET812+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET812+4.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
% 
%------------------------------------------------------------------------------