TPTP Problem File: SEV048^5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEV048^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Relations)
% Problem : TPS problem THM120
% Version : Especial.
% English : There exists a transitive relation on sets.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0107 [Bro09]
% : THM120 [TPS]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 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, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 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 : 8 ( 0 ~; 0 |; 1 &; 6 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 4 ( 0 ^; 3 !; 1 ?; 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/
% : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(cTHM120_pme,conjecture,
? [R: ( $i > $o ) > ( $i > $o ) > $o] :
! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) ).
%------------------------------------------------------------------------------