TPTP Problem File: SEV175^5.p
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% File : SEV175^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem THM144A
% Version : Especial.
% English : A lemma for the Injective Cantor Theorem X5309.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0230 [Bro09]
% : THM144A [TPS]
% Status : Theorem
% Rating : 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 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, 0.40 v5.3.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 2 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 11 ( 2 ~; 0 |; 2 &; 7 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 4 ( 1 ^; 1 !; 2 ?; 4 :)
% 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(cTHM144A_pme,conjecture,
! [Xh: ( $i > $o ) > $i] :
? [Xt: $i > $o] :
( ~ ( Xt @ ( Xh @ Xt ) )
& ( ( Xh
@ ^ [Xz: $i] :
? [Xt0: $i > $o] :
( ~ ( Xt0 @ ( Xh @ Xt0 ) )
& ( Xz
= ( Xh @ Xt0 ) ) ) )
= ( Xh @ Xt ) ) ) ).
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