TPTP Problem File: SEV144^5.p
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% File : SEV144^5 : TPTP v9.0.0. Bugfixed v5.2.0.
% Domain : Set Theory (Relations)
% Problem : TPS problem from TRANSITIVE-CLOSURE
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0933 [Bro09]
% Status : Theorem
% Rating : 1.00 v7.3.0, 0.89 v7.2.0, 0.88 v7.1.0, 1.00 v5.2.0
% Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% Number of atoms : 4 ( 1 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 31 ( 0 ~; 0 |; 3 &; 22 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 14 ( 2 ^; 12 !; 0 ?; 14 :)
% 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/
% Bugfixes : v5.2.0 - Added missing type declarations.
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thf(cTCLOSED_type,type,
cTCLOSED: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(cTCLOSED_def,definition,
( cTCLOSED
= ( ^ [Xp: $i > $i > $o,Xs: $i > $i > $o] :
! [Xu: $i,Xv: $i,Xw: $i] :
( ( ( Xp @ Xu @ Xv )
& ( Xs @ Xv @ Xw ) )
=> ( Xp @ Xu @ Xw ) ) ) ) ).
thf(cTHM146B_pme,conjecture,
! [Xr: $i > $i > $o,Xx: $i,Xy: $i] :
( ! [Xp: $i > $i > $o] :
( ( ! [Xx0: $i,Xy0: $i] :
( ( Xr @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( cTCLOSED @ Xp @ Xr ) )
=> ( Xp @ Xx @ Xy ) )
<=> ! [Xp: $i > $i > $o] :
( ( ! [Xx0: $i,Xy0: $i] :
( ( Xr @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( cTCLOSED @ Xp @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ) ).
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