TPTP Problem File: SEU948^5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEU948^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Functions)
% Problem : TPS problem THM135
% Version : Especial.
% English : The composition of iterates of a function is also an iterate of
% that function.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0547 [Bro09]
% : THM135 [TPS]
% : tps_1048 [Bro09]
% Status : Theorem
% : Without eta : CounterSatisfiable
% Rating : 0.38 v9.0.0, 0.42 v8.2.0, 0.36 v8.1.0, 0.50 v7.4.0, 0.33 v7.3.0, 0.50 v7.2.0, 0.38 v7.1.0, 0.29 v7.0.0, 0.38 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v5.5.0, 0.60 v5.4.0, 0.75 v5.3.0, 1.00 v5.2.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 31 ( 0 ~; 0 |; 4 &; 20 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 15 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 16 ( 7 ^; 9 !; 0 ?; 16 :)
% 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/
% : Polymorphic definitions expanded.
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thf(a_type,type,
a: $tType ).
thf(cTHM135_pme,conjecture,
! [Xf: a > a,Xg1: a > a,Xg2: a > a] :
( ( ! [Xp: ( a > a ) > $o] :
( ( ( Xp
@ ^ [Xu: a] : Xu )
& ! [Xj: a > a] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: a] : ( Xf @ ( Xj @ Xx ) ) ) ) )
=> ( Xp @ Xg1 ) )
& ! [Xp: ( a > a ) > $o] :
( ( ( Xp
@ ^ [Xu: a] : Xu )
& ! [Xj: a > a] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: a] : ( Xf @ ( Xj @ Xx ) ) ) ) )
=> ( Xp @ Xg2 ) ) )
=> ! [Xp: ( a > a ) > $o] :
( ( ( Xp
@ ^ [Xu: a] : Xu )
& ! [Xj: a > a] :
( ( Xp @ Xj )
=> ( Xp
@ ^ [Xx: a] : ( Xf @ ( Xj @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: a] : ( Xg1 @ ( Xg2 @ Xx ) ) ) ) ) ).
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