%------------------------------------------------------------------------------
% File     : SYO234^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-EQ-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0703 [Bro09]

% Status   : Theorem
% Rating   : 0.10 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    5 (   1 unt;   4 typ;   0 def)
%            Number of atoms       :    3 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   3 avg)
%            Number of connectives :    5 (   0   ~;   1   |;   0   &;   4   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   2 usr;   0 con; 2-2 aty)
%            Number of variables   :    3 (   2   ^;   0   !;   1   ?;   3   :)
% SPC      : TH0_THM_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(d_type,type,
    d: $tType ).

thf(c_type,type,
    c: $tType ).

thf(cB,type,
    cB: d > c > $o ).

thf(cA,type,
    cA: c > d > $o ).

thf(cSV4,conjecture,
    ? [Xu: c > d > $o] :
      ( Xu
      = ( ^ [Xx: c,Xy: d] :
            ( ( cA @ Xx @ Xy )
            | ( cB @ Xy @ Xx ) ) ) ) ).

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