## TPTP Problem File: SEV105^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV105^5 : 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_1109 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   54 (   1 equality;  47 variable)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :   52 (   1   ~;   0   |;   9   &;  34   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :   18 (   0 sgn;  17   !;   1   ?;   0   ^)
%                                         (  18   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_EQU_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,(
atype: \$tType )).

thf(a,type,(
a: atype )).

thf(b,type,(
b: atype )).

thf(cTC_INTERP_OTHER_pme,conjecture,(
! [Xr: atype > atype > \$o,T: atype > atype > \$o] :
( ( ! [Xx: atype] :
( T @ Xx @ Xx )
& ! [Xx: atype,Xy: atype,Xz: atype] :
( ( ( T @ Xx @ Xy )
& ( T @ Xy @ Xz ) )
=> ( T @ Xx @ Xz ) )
& ! [Xx: atype,Xy: atype] :
( ( Xr @ Xx @ Xy )
=> ( T @ Xx @ Xy ) )
& ! [S: atype > atype > \$o] :
( ( ! [Xx: atype] :
( S @ Xx @ Xx )
& ! [Xx: atype,Xy: atype,Xz: atype] :
( ( ( S @ Xx @ Xy )
& ( S @ Xy @ Xz ) )
=> ( S @ Xx @ Xz ) )
& ! [Xx: atype,Xy: atype] :
( ( Xr @ Xx @ Xy )
=> ( S @ Xx @ Xy ) ) )
=> ! [Xx: atype,Xy: atype] :
( ( T @ Xx @ Xy )
=> ( S @ Xx @ Xy ) ) ) )
=> ( ( ( a != b )
& ( T @ a @ b ) )
=> ? [Xc: atype] :
( ( Xr @ a @ Xc )
& ( T @ Xc @ b ) ) ) ) )).

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