TPTP Problem File: SEV182^5.p

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%------------------------------------------------------------------------------
% File     : SEV182^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from CANTOR-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0949 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   26 (   3 equality;  23 variable)
%            Maximal formula depth :   16 (  16 average)
%            Number of connectives :   20 (   1   ~;   0   |;   3   &;  11   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   12 (   0 sgn;   6   !;   3   ?;   3   ^)
%                                         (  12   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%------------------------------------------------------------------------------
thf(cTHM110_pme,conjecture,(
    ! [S: $i > $o] :
      ~ ( ? [Z: $i > $o] :
            ( ! [Xx: $i] :
                ( ( Z @ Xx )
               => ( S @ Xx ) )
            & ? [Xs: ( $i > $o ) > $i] :
                ( ! [Xx: $i > $o] :
                    ( ! [Xx0: $i] :
                        ( ( Xx @ Xx0 )
                       => ( S @ Xx0 ) )
                   => ( Z @ ( Xs @ Xx ) ) )
                & ! [Xy: $i] :
                    ( ( Z @ Xy )
                   => ? [Xy0: $i > $o] :
                        ( ( ^ [Xx: $i > $o] :
                              ( ! [Xx0: $i] :
                                  ( ( Xx @ Xx0 )
                                 => ( S @ Xx0 ) )
                              & ( Xy
                                = ( Xs @ Xx ) ) ) )
                        = ( ^ [Xx: $i > $o,Xy: $i > $o] : ( Xx = Xy )
                          @ Xy0 ) ) ) ) ) ) )).

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