TPTP Problem File: SEV249^5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEV249^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from SETS-OF-SETS-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0992 [Bro09]
% Status : Theorem
% Rating : 1.00 v6.2.0, 0.71 v6.0.0, 1.00 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% Number of atoms : 6 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 22 ( 0 ~; 2 |; 2 &; 12 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 5 ^; 7 !; 0 ?; 12 :)
% 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(cX,type,
cX: $i > $o ).
thf(cTHM626_pme,conjecture,
( ! [Xw: ( $i > $o ) > $o] :
( ( ( Xw
@ ^ [Xx: $i] : $false )
& ! [Xr: $i > $o,Xx: $i] :
( ( Xw @ Xr )
=> ( Xw
@ ^ [Xt: $i] :
( ( Xr @ Xt )
| ( Xt = Xx ) ) ) ) )
=> ( Xw @ cX ) )
=> ! [Xw: ( ( $i > $o ) > $o ) > $o] :
( ( ( Xw
@ ^ [Xx: $i > $o] : $false )
& ! [Xr: ( $i > $o ) > $o,Xx: $i > $o] :
( ( Xw @ Xr )
=> ( Xw
@ ^ [Xt: $i > $o] :
( ( Xr @ Xt )
| ( Xt = Xx ) ) ) ) )
=> ( Xw
@ ^ [R: $i > $o] :
! [Xx: $i] :
( ( R @ Xx )
=> ( cX @ Xx ) ) ) ) ) ).
%------------------------------------------------------------------------------