%------------------------------------------------------------------------------
% File     : SEV375^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory (GvNB)
% Problem  : TPS problem from GVB-MB-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0751 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.67 v9.0.0, 0.75 v8.1.0, 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v5.4.0, 1.00 v5.0.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unt;   4 typ;   0 def)
%            Number of atoms       :    3 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :    9 (   0   ~;   0   |;   1   &;   7   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    2 (   0   ^;   1   !;   1   ?;   2   :)
% 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/
%------------------------------------------------------------------------------
thf(f,type,
    f: $i ).

thf(cGVB_M,type,
    cGVB_M: $i > $o ).

thf(cGVB_COMPOSE,type,
    cGVB_COMPOSE: $i > $i > $i ).

thf(cGVB_IN,type,
    cGVB_IN: $i > $i > $o ).

thf(cTHM15B_EXISTS,conjecture,
    ? [P: $i] :
    ! [Xg: $i] :
      ( ( cGVB_IN @ Xg @ P )
    <=> ( ( ( cGVB_COMPOSE @ f @ Xg )
          = ( cGVB_COMPOSE @ Xg @ f ) )
        & ( cGVB_M @ Xg ) ) ) ).

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