TPTP Problem File: SEV150^5.p
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% File : SEV150^5 : TPTP v8.2.0. Released v4.0.0.
% 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_1188 [Bro09]
% : tps_1189 [Bro09]
% Status : Theorem
% Rating : 0.90 v8.2.0, 0.92 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 1.00 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% Number of atoms : 1 ( 1 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 82 ( 0 ~; 4 |; 12 &; 48 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 30 ( 4 ^; 26 !; 0 ?; 30 :)
% 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/
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thf(a_type,type,
a: $tType ).
thf(cTHM251A_pme,conjecture,
! [R: a > a > $o,S: a > a > $o] :
( ( ^ [Xp: a,Xq: a] :
! [Xq0: a > $o] :
( ( ! [Xw: a] :
( ( ( R @ Xp @ Xw )
| ( S @ Xp @ Xw ) )
=> ( Xq0 @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq0 @ Xu )
& ( ( R @ Xu @ Xv )
| ( S @ Xu @ Xv ) ) )
=> ( Xq0 @ Xv ) ) )
=> ( Xq0 @ Xq ) ) )
= ( ^ [Xp: a,Xq: a] :
! [Xq0: a > $o] :
( ( ! [Xw: a] :
( ( ! [Xq1: a > $o] :
( ( ! [Xw0: a] :
( ( R @ Xp @ Xw0 )
=> ( Xq1 @ Xw0 ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq1 @ Xu )
& ( R @ Xu @ Xv ) )
=> ( Xq1 @ Xv ) ) )
=> ( Xq1 @ Xw ) )
| ! [Xq1: a > $o] :
( ( ! [Xw0: a] :
( ( S @ Xp @ Xw0 )
=> ( Xq1 @ Xw0 ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq1 @ Xu )
& ( S @ Xu @ Xv ) )
=> ( Xq1 @ Xv ) ) )
=> ( Xq1 @ Xw ) ) )
=> ( Xq0 @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq0 @ Xu )
& ( ! [Xq1: a > $o] :
( ( ! [Xw: a] :
( ( R @ Xu @ Xw )
=> ( Xq1 @ Xw ) )
& ! [Xu0: a,Xv0: a] :
( ( ( Xq1 @ Xu0 )
& ( R @ Xu0 @ Xv0 ) )
=> ( Xq1 @ Xv0 ) ) )
=> ( Xq1 @ Xv ) )
| ! [Xq1: a > $o] :
( ( ! [Xw: a] :
( ( S @ Xu @ Xw )
=> ( Xq1 @ Xw ) )
& ! [Xu0: a,Xv0: a] :
( ( ( Xq1 @ Xu0 )
& ( S @ Xu0 @ Xv0 ) )
=> ( Xq1 @ Xv0 ) ) )
=> ( Xq1 @ Xv ) ) ) )
=> ( Xq0 @ Xv ) ) )
=> ( Xq0 @ Xq ) ) ) ) ).
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