TPTP Problem File: SEU933^5.p
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% File : SEU933^5 : TPTP v7.1.0. Released v4.0.0.
% Domain : Set Theory (Functions)
% Problem : TPS problem THM196B
% Version : Especial.
% English : It is not true that if [k COMPOSE j] is an iterate of j, then k
% must be an iterate of j, provided we have distinct elements a
% and b.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0273 [Bro09]
% : THM196B [TPS]
% Status : Theorem
% Rating : 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax : Number of formulae : 3 ( 0 unit; 2 type; 0 defn)
% Number of atoms : 25 ( 1 equality; 22 variable)
% Maximal formula depth : 15 ( 6 average)
% Number of connectives : 24 ( 2 ~; 0 |; 2 &; 14 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% ( 0 ~|; 0 ~&)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 :; 0 =)
% Number of variables : 9 ( 0 sgn; 6 !; 0 ?; 3 ^)
% ( 9 :; 0 !>; 0 ?*)
% ( 0 @-; 0 @+)
% 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(b,type,(
b: $i )).
thf(a,type,(
a: $i )).
thf(cTHM196B_pme,conjecture,
( ( a != b )
=> ~ ( ! [Xj: $i > $i,Xk: $i > $i] :
( ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_2: $i > $i] :
( ( Xp @ Xj_2 )
=> ( Xp
@ ^ [Xx: $i] :
( Xj @ ( Xj_2 @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: $i] :
( Xk @ ( Xj @ Xx ) ) ) )
=> ! [Xp: ( $i > $i ) > $o] :
( ( ( Xp @ Xj )
& ! [Xj_3: $i > $i] :
( ( Xp @ Xj_3 )
=> ( Xp
@ ^ [Xx: $i] :
( Xj @ ( Xj_3 @ Xx ) ) ) ) )
=> ( Xp @ Xk ) ) ) ) )).
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