TSTP Solution File: SEU327+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU327+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 07:23:01 EST 2010

% Result   : Theorem 0.56s
% Output   : CNFRefutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   45 (  16 unt;   0 def)
%            Number of atoms       :   99 (  48 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   97 (  43   ~;  38   |;   7   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   61 (   0 sgn  35   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2,X3] :
      ( ( element(X2,powerset(X1))
        & element(X3,powerset(X1)) )
     => subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
    file('/tmp/tmpIu7kZY/sel_SEU327+1.p_1',redefinition_k6_subset_1) ).

fof(13,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => element(union_of_subsets(X1,X2),powerset(X1)) ),
    file('/tmp/tmpIu7kZY/sel_SEU327+1.p_1',dt_k5_setfam_1) ).

fof(15,axiom,
    ! [X1] : element(cast_to_subset(X1),powerset(X1)),
    file('/tmp/tmpIu7kZY/sel_SEU327+1.p_1',dt_k2_subset_1) ).

fof(21,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
    file('/tmp/tmpIu7kZY/sel_SEU327+1.p_1',t47_setfam_1) ).

fof(36,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,X2) = set_difference(X1,X2) ),
    file('/tmp/tmpIu7kZY/sel_SEU327+1.p_1',d5_subset_1) ).

fof(40,conjecture,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
    file('/tmp/tmpIu7kZY/sel_SEU327+1.p_1',t11_tops_2) ).

fof(58,axiom,
    ! [X1] : cast_to_subset(X1) = X1,
    file('/tmp/tmpIu7kZY/sel_SEU327+1.p_1',d4_subset_1) ).

fof(60,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,powerset(powerset(X1)))
       => ( X2 != empty_set
         => meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
    inference(assume_negation,[status(cth)],[40]) ).

fof(70,plain,
    ! [X1,X2,X3] :
      ( ~ element(X2,powerset(X1))
      | ~ element(X3,powerset(X1))
      | subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(71,plain,
    ! [X4,X5,X6] :
      ( ~ element(X5,powerset(X4))
      | ~ element(X6,powerset(X4))
      | subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
    inference(variable_rename,[status(thm)],[70]) ).

cnf(72,plain,
    ( subset_difference(X1,X2,X3) = set_difference(X2,X3)
    | ~ element(X3,powerset(X1))
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[71]) ).

fof(105,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(powerset(X1)))
      | element(union_of_subsets(X1,X2),powerset(X1)) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(106,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(X3)))
      | element(union_of_subsets(X3,X4),powerset(X3)) ),
    inference(variable_rename,[status(thm)],[105]) ).

cnf(107,plain,
    ( element(union_of_subsets(X1,X2),powerset(X1))
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(split_conjunct,[status(thm)],[106]) ).

fof(111,plain,
    ! [X2] : element(cast_to_subset(X2),powerset(X2)),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(112,plain,
    element(cast_to_subset(X1),powerset(X1)),
    inference(split_conjunct,[status(thm)],[111]) ).

fof(135,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(powerset(X1)))
      | X2 = empty_set
      | subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(136,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(X3)))
      | X4 = empty_set
      | subset_difference(X3,cast_to_subset(X3),union_of_subsets(X3,X4)) = meet_of_subsets(X3,complements_of_subsets(X3,X4)) ),
    inference(variable_rename,[status(thm)],[135]) ).

cnf(137,plain,
    ( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
    | X2 = empty_set
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(split_conjunct,[status(thm)],[136]) ).

fof(204,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | subset_complement(X1,X2) = set_difference(X1,X2) ),
    inference(fof_nnf,[status(thm)],[36]) ).

fof(205,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | subset_complement(X3,X4) = set_difference(X3,X4) ),
    inference(variable_rename,[status(thm)],[204]) ).

cnf(206,plain,
    ( subset_complement(X1,X2) = set_difference(X1,X2)
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[205]) ).

fof(218,negated_conjecture,
    ? [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
      & X2 != empty_set
      & meet_of_subsets(X1,complements_of_subsets(X1,X2)) != subset_complement(X1,union_of_subsets(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[60]) ).

fof(219,negated_conjecture,
    ? [X3,X4] :
      ( element(X4,powerset(powerset(X3)))
      & X4 != empty_set
      & meet_of_subsets(X3,complements_of_subsets(X3,X4)) != subset_complement(X3,union_of_subsets(X3,X4)) ),
    inference(variable_rename,[status(thm)],[218]) ).

fof(220,negated_conjecture,
    ( element(esk4_0,powerset(powerset(esk3_0)))
    & esk4_0 != empty_set
    & meet_of_subsets(esk3_0,complements_of_subsets(esk3_0,esk4_0)) != subset_complement(esk3_0,union_of_subsets(esk3_0,esk4_0)) ),
    inference(skolemize,[status(esa)],[219]) ).

cnf(221,negated_conjecture,
    meet_of_subsets(esk3_0,complements_of_subsets(esk3_0,esk4_0)) != subset_complement(esk3_0,union_of_subsets(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(222,negated_conjecture,
    esk4_0 != empty_set,
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(223,negated_conjecture,
    element(esk4_0,powerset(powerset(esk3_0))),
    inference(split_conjunct,[status(thm)],[220]) ).

fof(287,plain,
    ! [X2] : cast_to_subset(X2) = X2,
    inference(variable_rename,[status(thm)],[58]) ).

cnf(288,plain,
    cast_to_subset(X1) = X1,
    inference(split_conjunct,[status(thm)],[287]) ).

cnf(297,plain,
    element(X1,powerset(X1)),
    inference(rw,[status(thm)],[112,288,theory(equality)]),
    [unfolding] ).

cnf(298,plain,
    ( empty_set = X2
    | subset_difference(X1,X1,union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(rw,[status(thm)],[137,288,theory(equality)]),
    [unfolding] ).

cnf(727,plain,
    ( meet_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,union_of_subsets(X1,X2))
    | empty_set = X2
    | ~ element(union_of_subsets(X1,X2),powerset(X1))
    | ~ element(X1,powerset(X1))
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(spm,[status(thm)],[72,298,theory(equality)]) ).

cnf(730,plain,
    ( meet_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,union_of_subsets(X1,X2))
    | empty_set = X2
    | ~ element(union_of_subsets(X1,X2),powerset(X1))
    | $false
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(rw,[status(thm)],[727,297,theory(equality)]) ).

cnf(731,plain,
    ( meet_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,union_of_subsets(X1,X2))
    | empty_set = X2
    | ~ element(union_of_subsets(X1,X2),powerset(X1))
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(cn,[status(thm)],[730,theory(equality)]) ).

cnf(6305,plain,
    ( meet_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,union_of_subsets(X1,X2))
    | empty_set = X2
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(csr,[status(thm)],[731,107]) ).

cnf(6306,negated_conjecture,
    ( empty_set = esk4_0
    | set_difference(esk3_0,union_of_subsets(esk3_0,esk4_0)) != subset_complement(esk3_0,union_of_subsets(esk3_0,esk4_0))
    | ~ element(esk4_0,powerset(powerset(esk3_0))) ),
    inference(spm,[status(thm)],[221,6305,theory(equality)]) ).

cnf(6352,negated_conjecture,
    ( empty_set = esk4_0
    | set_difference(esk3_0,union_of_subsets(esk3_0,esk4_0)) != subset_complement(esk3_0,union_of_subsets(esk3_0,esk4_0))
    | $false ),
    inference(rw,[status(thm)],[6306,223,theory(equality)]) ).

cnf(6353,negated_conjecture,
    ( empty_set = esk4_0
    | set_difference(esk3_0,union_of_subsets(esk3_0,esk4_0)) != subset_complement(esk3_0,union_of_subsets(esk3_0,esk4_0)) ),
    inference(cn,[status(thm)],[6352,theory(equality)]) ).

cnf(6354,negated_conjecture,
    subset_complement(esk3_0,union_of_subsets(esk3_0,esk4_0)) != set_difference(esk3_0,union_of_subsets(esk3_0,esk4_0)),
    inference(sr,[status(thm)],[6353,222,theory(equality)]) ).

cnf(6361,negated_conjecture,
    ~ element(union_of_subsets(esk3_0,esk4_0),powerset(esk3_0)),
    inference(spm,[status(thm)],[6354,206,theory(equality)]) ).

cnf(6388,negated_conjecture,
    ~ element(esk4_0,powerset(powerset(esk3_0))),
    inference(spm,[status(thm)],[6361,107,theory(equality)]) ).

cnf(6397,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[6388,223,theory(equality)]) ).

cnf(6398,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[6397,theory(equality)]) ).

cnf(6399,negated_conjecture,
    $false,
    6398,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU327+1.p
% --creating new selector for []
% -running prover on /tmp/tmpIu7kZY/sel_SEU327+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU327+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU327+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU327+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
% 
%------------------------------------------------------------------------------