TPTP Problem File: SEU926^5.p
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% File : SEU926^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory
% Problem : TPS problem THM113
% Version : Especial.
% English : There is a set of functions on P closed under composition.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0214 [Bro09]
% : THM113 [TPS]
% Status : Theorem
% Rating : 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.50 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 10 ( 0 ~; 0 |; 1 &; 7 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 5 ( 1 ^; 3 !; 1 ?; 5 :)
% SPC : TH0_THM_NEQ_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/
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thf(cTHM113,conjecture,
! [P: $i > $o] :
? [M: ( $i > $i ) > $o] :
! [G: $i > $i] :
( ( M @ G )
=> ( ( M
@ ^ [Z: $i] : ( G @ ( G @ Z ) ) )
& ! [Y: $i] :
( ( P @ Y )
=> ( P @ ( G @ Y ) ) ) ) ) ).
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