TPTP Problem File: SEV173^5.p

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%------------------------------------------------------------------------------
% File     : SEV173^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SETPAIRS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0929 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   26 (   2 equality;  16 variable)
%            Maximal formula depth :   11 (   4 average)
%            Number of connectives :   21 (   0   ~;   4   |;   4   &;  12   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   1   !;   4   ?;   2   ^)
%                                         (   7   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_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/
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thf(b_type,type,(
    b: $tType )).

thf(cZ,type,(
    cZ: b > $o )).

thf(cR,type,(
    cR: b > $o )).

thf(cS,type,(
    cS: b > $o )).

thf(cTHM32_pme,conjecture,(
    ! [Xx: ( b > b > b ) > b] :
      ( ? [X: b,Y: b] :
          ( ( ( cR @ X )
            | ( cS @ X ) )
          & ( ( cR @ Y )
            | ( cS @ Y ) )
          & ( Xx
            = ( ^ [G: b > b > b] :
                  ( G @ X @ Y ) ) ) )
    <=> ? [X: b,Y: b] :
          ( ( ( cR @ X )
            | ( cZ @ X ) )
          & ( ( cR @ Y )
            | ( cZ @ Y ) )
          & ( Xx
            = ( ^ [G: b > b > b] :
                  ( G @ X @ Y ) ) ) ) ) )).

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