TPTP Problem File: SEU987^5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEU987^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Relations)
% Problem : TPS problem from FUNS-AND-RELNS-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0910 [Bro09]
% Status : Theorem
% Rating : 0.88 v9.0.0, 1.00 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v4.0.0
% Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% Number of atoms : 5 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 15 ( 0 ~; 0 |; 1 &; 10 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 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/
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(g,type,
g: b > b ).
thf(f,type,
f: a > a ).
thf(cS,type,
cS: a > b > $o ).
thf(cSV7_pme,conjecture,
( ( ! [Xx: a,Xy: a] :
( ( ( f @ Xx )
= ( f @ Xy ) )
=> ( Xx = Xy ) )
& ! [Xx: b,Xy: b] :
( ( ( g @ Xx )
= ( g @ Xy ) )
=> ( Xx = Xy ) ) )
=> ? [Xu: a > b > $o] :
! [Xx: a,Xy: b] :
( ( cS @ Xx @ Xy )
<=> ( Xu @ ( f @ Xx ) @ ( g @ Xy ) ) ) ) ).
%------------------------------------------------------------------------------