## TPTP Problem File: SEV157^5.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEV157^5 : TPTP v7.2.0. 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_1234 [Bro09]

% Status   : Theorem
% Rating   : 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 unit;   1 type;   0 defn)
%            Number of atoms       :  162 (   0 equality; 162 variable)
%            Maximal formula depth :   24 (  13 average)
%            Number of connectives :  162 (   1   ~;   8   |;  18   &; 108   @)
%                                         (   0 <=>;  27  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   57 (   0 sgn;  57   !;   0   ?;   0   ^)
%                                         (  57   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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
%          :
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thf(a_type,type,(
a: \$tType )).

thf(cTHM250G_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 ) )
| ~ ( ( ! [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 ) ) ) ) )).

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