%------------------------------------------------------------------------------
% File     : SEV123^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from SETS-OF-RELNS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1077 [Bro09]

% Status   : Theorem
% Rating   : 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   1 unt;   1 typ;   0 def)
%            Number of atoms       :    1 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   36 (   0   ~;   0   |;   6   &;  23   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (  17 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :   18 (   2   ^;  13   !;   3   ?;  18   :)
% 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(a_type,type,
    a: $tType ).

thf(cTHM254_B_pme,conjecture,
    ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
      ( ! [Xp: a > a > $o] :
          ( ( ! [Xx0: a,Xy0: a] :
                ( ? [R: a > a > $o] :
                    ( ? [Q: a > a > $o] :
                        ( ( S @ Q )
                        & ( R
                          = ( ^ [Xx1: a,Xy1: a] :
                              ! [Xp0: a > a > $o] :
                                ( ( ! [Xx2: a,Xy2: a] :
                                      ( ( Q @ Xx2 @ Xy2 )
                                     => ( Xp0 @ Xx2 @ Xy2 ) )
                                  & ( PROP @ Xp0 ) )
                               => ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
                    & ( R @ Xx0 @ Xy0 ) )
               => ( Xp @ Xx0 @ Xy0 ) )
            & ( PROP @ Xp ) )
         => ( Xp @ Xx @ Xy ) )
     => ! [Xp: a > a > $o] :
          ( ( ! [Xx0: a,Xy0: a] :
                ( ? [R: a > a > $o] :
                    ( ( S @ R )
                    & ( R @ Xx0 @ Xy0 ) )
               => ( Xp @ Xx0 @ Xy0 ) )
            & ( PROP @ Xp ) )
         => ( Xp @ Xx @ Xy ) ) ) ).

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