%------------------------------------------------------------------------------
% File     : SEV046^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from PERS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1181 [Bro09]

% Status   : Theorem
% Rating   : 0.10 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   1 unt;   2 typ;   0 def)
%            Number of atoms       :    1 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   88 (   0   ~;   0   |;   8   &;  66   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (  18 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :   30 (   0   ^;  30   !;   0   ?;  30   :)
% 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(b_type,type,
    b: $tType ).

thf(cTHM507_pme,conjecture,
    ! [Xp: a > a > $o,Xp2: a > b > b > $o] :
      ( ( ! [Xx: a,Xy: a] :
            ( ( Xp @ Xx @ Xy )
           => ( Xp @ Xy @ Xx ) )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( ( Xp @ Xx @ Xy )
              & ( Xp @ Xy @ Xz ) )
           => ( Xp @ Xx @ Xz ) )
        & ! [Xx: a] :
            ( ( Xp @ Xx @ Xx )
           => ( ! [Xx0: b,Xy: b] :
                  ( ( Xp2 @ Xx @ Xx0 @ Xy )
                 => ( Xp2 @ Xx @ Xy @ Xx0 ) )
              & ! [Xx0: b,Xy: b,Xz: b] :
                  ( ( ( Xp2 @ Xx @ Xx0 @ Xy )
                    & ( Xp2 @ Xx @ Xy @ Xz ) )
                 => ( Xp2 @ Xx @ Xx0 @ Xz ) ) ) )
        & ! [Xx: a,Xy: a] :
            ( ( Xp @ Xx @ Xy )
           => ( ( Xp2 @ Xx )
              = ( Xp2 @ Xy ) ) ) )
     => ( ! [Xx: a > b,Xy: a > b] :
            ( ! [Xx0: a,Xy0: a] :
                ( ( Xp @ Xx0 @ Xy0 )
               => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
           => ! [Xx0: a,Xy0: a] :
                ( ( Xp @ Xx0 @ Xy0 )
               => ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) )
        & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
            ( ( ! [Xx0: a,Xy0: a] :
                  ( ( Xp @ Xx0 @ Xy0 )
                 => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
              & ! [Xx0: a,Xy0: a] :
                  ( ( Xp @ Xx0 @ Xy0 )
                 => ( Xp2 @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
           => ! [Xx0: a,Xy0: a] :
                ( ( Xp @ Xx0 @ Xy0 )
               => ( Xp2 @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) ) ) ) ).

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