TPTP Problem File: SEV153^5.p
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% File : SEV153^5 : 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_1220 [Bro09]
% Status : Theorem
% Rating : 0.42 v8.2.0, 0.36 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, 0.62 v6.4.0, 0.71 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v5.2.0, 0.75 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 : 148 ( 1 ~; 14 |; 19 &; 88 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 23 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% 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(cTHM251H_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( ( R @ Xx @ Xw )
| ( S @ Xx @ Xw ) )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( ( R @ Xu @ Xv )
| ( S @ Xu @ Xv ) ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xy ) )
| ( ~ ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( ( R @ Xx @ Xw )
| ( S @ Xx @ Xw ) )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( ( R @ Xu @ Xv )
| ( S @ Xu @ Xv ) ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xy ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( R @ Xx0 @ Xw )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( R @ Xu @ Xv ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xy0 ) )
| ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( S @ Xx0 @ Xw )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( S @ Xu @ Xv ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( ( R @ Xx0 @ Xw )
| ( S @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( ( R @ Xu @ Xv )
| ( S @ Xu @ Xv ) ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( ( R @ Xx0 @ Xw )
| ( S @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( ( R @ Xu @ Xv )
| ( S @ Xu @ Xv ) ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xy0 ) )
& ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( ( R @ Xy0 @ Xw )
| ( S @ Xy0 @ Xw ) )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( ( R @ Xu @ Xv )
| ( S @ Xu @ Xv ) ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xz ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xw: a] :
( ( ( R @ Xx0 @ Xw )
| ( S @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( ( R @ Xu @ Xv )
| ( S @ Xu @ Xv ) ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xz ) ) ) ) ) ).
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