TPTP Problem File: SEV165^5.p
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% File : SEV165^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory
% Problem : TPS problem EXISTS-CART-SET-PROD
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0457 [Bro09]
% : EXISTS-CART-SET-PROD [TPS]
% Status : Theorem
% Rating : 0.67 v8.2.0, 0.64 v8.1.0, 0.75 v7.4.0, 0.67 v7.3.0, 0.70 v7.2.0, 0.62 v7.1.0, 0.71 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 0.80 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 9 ( 0 ~; 0 |; 1 &; 7 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 6 ( 1 ^; 4 !; 1 ?; 6 :)
% 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(cEXISTS_CART_SET_PROD_pme,conjecture,
? [CROSS: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
! [A: $i > $o,B: $i > $o,Xa: $i,Xb: $i] :
( ( CROSS @ A @ B
@ ^ [G: $i > $i > $i] : ( G @ Xa @ Xb ) )
<=> ( ( A @ Xa )
& ( B @ Xb ) ) ) ).
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