## TPTP Problem File: SYO269^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO269^5 : TPTP v8.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM112D
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0277 [Bro09]
%          : THM112C [TPS]
%          : THM112D [TPS]

% Status   : Theorem
% Rating   : 0.67 v7.5.0, 0.75 v7.4.0, 0.67 v7.3.0, 0.70 v7.2.0, 0.62 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.57 v6.3.0, 0.83 v6.1.0, 0.67 v5.5.0, 0.80 v5.4.0, 0.75 v5.2.0, 0.50 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 typ;   0 def)
%            Number of atoms       :    0 (   0 equ;   0 cnn)
%            Maximal formula atoms :    0 (   0 avg)
%            Number of connectives :   38 (   0   ~;   5   |;   4   &;  27   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  16 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   15 (   4   ^   9   !;   2   ?;  15   :)
% 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(cTHM112D,conjecture,
! [P: \$i > \$o] :
? [Xm_9: ( \$i > \$i ) > \$i > \$o,Xm_10: ( \$i > \$i ) > \$i > \$o] :
( ! [Xw_1: \$i] :
( ( Xm_9
@ ^ [Xx: \$i] : Xx
@ Xw_1 )
| ( Xm_10
@ ^ [Xx: \$i] : Xx
@ Xw_1 ) )
& ! [G: \$i > \$i,H: \$i > \$i] :
( ( ! [Xw_1: \$i] :
( ( Xm_9 @ G @ Xw_1 )
| ( Xm_10 @ G @ Xw_1 ) )
& ! [Xw_1: \$i] :
( ( Xm_9 @ G @ Xw_1 )
| ( Xm_10 @ G @ Xw_1 ) )
& ! [Xw_1: \$i] :
( ( Xm_9 @ H @ Xw_1 )
| ( Xm_10 @ H @ Xw_1 ) ) )
=> ( ! [Xw_1: \$i] :
( ( Xm_9
@ ^ [Xx: \$i] : ( G @ ( H @ Xx ) )
@ Xw_1 )
| ( Xm_10
@ ^ [Xx: \$i] : ( G @ ( H @ Xx ) )
@ Xw_1 ) )
& ! [Y: \$i] :
( ( P @ Y )
=> ( P @ ( G @ Y ) ) ) ) ) ) ).

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