## TPTP Problem File: SEV133^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV133^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from TC-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1062 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   43 (   1 equality;  33 variable)
%            Maximal formula depth :   16 (   5 average)
%            Number of connectives :   41 (   1   ~;   0   |;   7   &;  25   @)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   12 (   0 sgn;  11   !;   1   ?;   0   ^)
%                                         (  12   :;   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(cSTAR,type,(
cSTAR: ( atype > atype > \$o ) > atype > atype > \$o )).

thf(cTC_INTERP_THIRD_pme,conjecture,(
! [Xr: atype > atype > \$o] :
( ( ! [Xx: atype > \$o] :
( ! [Xy: atype,Xz: atype] :
( ( ( Xr @ Xy @ Xz )
& ( Xx @ Xy ) )
=> ( Xx @ Xz ) )
<=> ! [Xy: atype,Xz: atype] :
( ( ( Xr @ Xy @ Xz )
& ( Xx @ Xy ) )
=> ( Xx @ Xz ) ) )
& ! [Xa0: atype,Xb0: atype] :
( ( cSTAR @ Xr @ Xa0 @ Xb0 )
<=> ! [Xx: atype > \$o] :
( ! [Xy: atype,Xz: atype] :
( ( ( Xr @ Xy @ Xz )
& ( Xx @ Xy ) )
=> ( Xx @ Xz ) )
=> ( ( Xx @ Xa0 )
=> ( Xx @ Xb0 ) ) ) )
& ( a != b )
& ( cSTAR @ Xr @ a @ b ) )
=> ? [Xc: atype] :
( ( Xr @ a @ Xc )
& ( cSTAR @ Xr @ Xc @ b ) ) ) )).

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