TPTP Problem File: SEU922^5.p
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% File : SEU922^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Functions)
% Problem : TPS problem THM128
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0118 [Bro09]
% : THM128 [TPS]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% Number of atoms : 3 ( 1 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 14 ( 0 ~; 0 |; 0 &; 12 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 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(a,type,
a: $i ).
thf(f,type,
f: $i > $i ).
thf(g,type,
g: $i > $i ).
thf(cP,type,
cP: $i > $o ).
thf(cTHM128_pme,conjecture,
( ( ( ^ [Xx: $i] : ( f @ ( g @ Xx ) ) )
= ( ^ [Xx: $i] : ( g @ ( f @ Xx ) ) ) )
=> ( ( cP @ ( f @ ( f @ ( g @ a ) ) ) )
=> ( cP @ ( g @ ( f @ ( f @ a ) ) ) ) ) ) ).
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