TPTP Problem File: SEU909^5.p

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```%------------------------------------------------------------------------------
% File     : SEU909^5 : TPTP v8.1.2. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SET-TOP-CATEGORY-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1161 [Bro09]

% Status   : Theorem
% Rating   : 0.38 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.22 v7.2.0, 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 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :   12 (   2 equ;   0 cnn)
%            Maximal formula atoms :   12 (  12 avg)
%            Number of connectives :   63 (   0   ~;   2   |;  12   &;  32   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  20 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1 usr;   1 con; 0-2 aty)
%            Number of variables   :   23 (   4   ^  17   !;   2   ?;  23   :)
% 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
%------------------------------------------------------------------------------
thf(a_type,type,
a: \$tType ).

thf(cA,type,
cA: ( a > \$o ) > \$o ).

thf(cDOMTHM8_pme,conjecture,
( ! [Xx: a > \$o] :
( ( cA @ Xx )
=> ( cA @ Xx ) )
& ! [Xe: a > \$o] :
( ( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: a] : \$false )
& ! [Xx: a > \$o] :
( ( X @ Xx )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: a] :
( ( Xe @ Xx )
=> ? [S: a > \$o] :
( ( cA @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) ) )
=> ( cA @ Xx ) )
& ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) ) )
=> ? [Xe_0: a > \$o] :
( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: a] : \$false )
& ! [Xx0: a > \$o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe_0 @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe_0 ) )
& ! [Xx0: a] :
( ( Xe_0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > \$o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe_0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) ) ) ) ) ) ) ) ).

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```