## TPTP Problem File: SEV156^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV156^5 : TPTP v8.1.2. 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_1233 [Bro09]

% Status   : Theorem
% Rating   : 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 :  162 (   1   ~;   8   |;  19   &; 108   @)
%                                         (   0 <=>;  26  =>;   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
%------------------------------------------------------------------------------
thf(a_type,type,
a: \$tType ).

thf(cTHM250H_pme,conjecture,
! [R: a > a > \$o,S: a > a > \$o,Xx: a,Xy: a] :
( ! [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 ) )
& ! [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 ) ) ) ) ) ).

%------------------------------------------------------------------------------
```