## TPTP Problem File: SEV104^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV104^5 : 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_1108 [Bro09]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    7 (   0 unit;   6 type;   0 defn)
%            Number of atoms       :   54 (   0 equality;  34 variable)
%            Maximal formula depth :   14 (   5 average)
%            Number of connectives :   55 (   2   ~;   2   |;   9   &;  36   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6   :;   0   =)
%            Number of variables   :   17 (   0 sgn;  16   !;   1   ?;   0   ^)
%                                         (  17   :;   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
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(b_type,type,(
b: \$tType )).

thf(cR,type,(
cR: a > a > \$o )).

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

thf(f,type,(
f: a > b > \$o )).

thf(cS,type,(
cS: b > b > \$o )).

thf(cTHM552D_pme,conjecture,
( ( ! [Xu: a,Xv: a,Xw: a] :
( ( ( cR @ Xu @ Xv )
& ( cR @ Xw @ Xv ) )
=> ( cR @ Xu @ Xw ) )
& ! [Xx: a] :
( cR @ Xx @ Xx ) )
=> ( ( ! [Xx: a] :
? [Xy: b] :
( f @ Xx @ Xy )
& ! [Xx: a,Xy1: b,Xy2: b] :
( ( ( f @ Xx @ Xy1 )
& ( f @ Xx @ Xy2 ) )
=> ( cS @ Xy1 @ Xy2 ) )
& ! [Xx1: a,Xx2: a,Xy: b] :
( ( ( f @ Xx1 @ Xy )
& ( f @ Xx2 @ Xy ) )
=> ( cR @ Xx1 @ Xx2 ) ) )
=> ! [Xy: b,Xx1: a,Xx2: a] :
( ( ! [Xw: a] :
( ( f @ Xx1 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx1 @ z ) ) )
& ! [Xw: a] :
( ( f @ Xx2 @ Xy )
| ( ~ ( f @ Xw @ Xy )
& ( cR @ Xx2 @ z ) ) ) )
=> ( cR @ Xx1 @ Xx2 ) ) ) )).

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