TPTP Problem File: SET046^5.p
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% File : SET046^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory
% Problem : TPS problem PELL42
% Version : Especial.
% English : There is no set of non-circular sets (where a circular set is a
% set x s.t. there is a set y, s.t. x belongs to y and reversely).
% Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0525 [Bro09]
% : PELL42 [TPS]
% : Pelletier 42 [Pel86]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% Number of atoms : 6 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 20 ( 3 ~; 0 |; 3 &; 12 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 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/
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thf(cF,type,
cF: $i > $i > $o ).
thf(cPELL42,conjecture,
~ ? [Xy: $i] :
! [Xx: $i] :
( ( ( cF @ Xx @ Xy )
=> ~ ? [Xz: $i] :
( ( cF @ Xx @ Xz )
& ( cF @ Xz @ Xx ) ) )
& ( ~ ? [Xz: $i] :
( ( cF @ Xx @ Xz )
& ( cF @ Xz @ Xx ) )
=> ( cF @ Xx @ Xy ) ) ) ).
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