TPTP Problem File: SEV155^5.p
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% File : SEV155^5 : TPTP v9.0.0. 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_1232 [Bro09]
% Status : Theorem
% Rating : 0.50 v9.0.0, 0.42 v8.2.0, 0.27 v8.1.0, 0.42 v7.5.0, 0.58 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 161 ( 0 ~; 7 |; 18 &; 108 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 23 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 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/
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thf(a_type,type,
a: $tType ).
thf(cTHM250D_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ( ( ! [Xx0: a,Xy0: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) )
& ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xx1 @ Xy1 )
& ( Xp1 @ Xy1 @ Xz ) )
=> ( Xp1 @ Xx1 @ Xz ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
| ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) )
& ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xx1 @ Xy1 )
& ( Xp1 @ Xy1 @ Xz ) )
=> ( Xp1 @ Xx1 @ Xz ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( ( R @ Xx1 @ Xy1 )
| ( S @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) )
& ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xx1 @ Xy1 )
& ( Xp1 @ Xy1 @ Xz ) )
=> ( Xp1 @ Xx1 @ Xz ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( ( R @ Xx1 @ Xy1 )
| ( S @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) )
& ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xx1 @ Xy1 )
& ( Xp1 @ Xy1 @ Xz0 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
& ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( ( R @ Xx1 @ Xy1 )
| ( S @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) )
& ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xx1 @ Xy1 )
& ( Xp1 @ Xy1 @ Xz0 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) ) )
=> ( Xp1 @ Xy0 @ Xz ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a] :
( ( ( R @ Xx1 @ Xy1 )
| ( S @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) )
& ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xx1 @ Xy1 )
& ( Xp1 @ Xy1 @ Xz0 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) ) )
=> ( Xp1 @ Xx0 @ Xz ) ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( R @ Xx0 @ Xy0 )
| ( S @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xx0 @ Xy0 )
& ( Xp1 @ Xy0 @ Xz ) )
=> ( Xp1 @ Xx0 @ Xz ) ) )
=> ( Xp1 @ Xx @ Xy ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( R @ Xx0 @ Xy0 )
| ( S @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xx0 @ Xy0 )
& ( Xp1 @ Xy0 @ Xz ) )
=> ( Xp1 @ Xx0 @ Xz ) ) )
=> ( Xp1 @ Xx @ Xy ) ) ) ).
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