## TPTP Problem File: SEV099^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV099^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from RELN-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1080 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   42 (   0 equality;  42 variable)
%            Maximal formula depth :   17 (  10 average)
%            Number of connectives :   42 (   1   ~;   0   |;   6   &;  28   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   16 (   0 sgn;  15   !;   1   ?;   0   ^)
%                                         (  16   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_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(cTC_INTERP_pme,conjecture,(
! [Xr: a > a > \$o,Xs: a,Xt: a] :
( ( ~ ( Xr @ Xs @ Xt )
& ! [Xp: a > a > \$o] :
( ( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xp @ Xx @ Xy ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xy )
& ( Xp @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xz ) ) )
=> ( Xp @ Xs @ Xt ) ) )
=> ? [Xz: a] :
( ( Xr @ Xs @ Xz )
& ! [Xp: a > a > \$o] :
( ( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xp @ Xx @ Xy ) )
& ! [Xx: a,Xy: a,Xz0: a] :
( ( ( Xp @ Xx @ Xy )
& ( Xp @ Xy @ Xz0 ) )
=> ( Xp @ Xx @ Xz0 ) ) )
=> ( Xp @ Xz @ Xt ) ) ) ) )).

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