TPTP Problem File: SEV399^5.p
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% File : SEV399^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory
% Problem : TPS problem THM597
% Version : Especial.
% English : If K and L are order reversing, K o L has a fixed point.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0447 [Bro09]
% : THM597 [TPS]
% Status : Theorem
% Rating : 1.00 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 1 ( 1 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 22 ( 0 ~; 0 |; 1 &; 14 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 11 ( 0 ^; 10 !; 1 ?; 11 :)
% 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/
% : Polymorphic definitions expanded.
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thf(cTHM597_pme,conjecture,
! [K: ( $i > $o ) > $i > $o,L: ( $i > $o ) > $i > $o] :
( ( ! [Xu: $i > $o,Xv: $i > $o] :
( ! [Xx: $i] :
( ( Xu @ Xx )
=> ( Xv @ Xx ) )
=> ! [Xx: $i] :
( ( K @ Xv @ Xx )
=> ( K @ Xu @ Xx ) ) )
& ! [Xu: $i > $o,Xv: $i > $o] :
( ! [Xx: $i] :
( ( Xu @ Xx )
=> ( Xv @ Xx ) )
=> ! [Xx: $i] :
( ( L @ Xv @ Xx )
=> ( L @ Xu @ Xx ) ) ) )
=> ? [Xw: $i > $o] :
( ( K @ ( L @ Xw ) )
= Xw ) ) ).
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