## TPTP Problem File: SEV094^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV094^5 : 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_1063 [Bro09]

% Status   : Theorem
% Rating   : 0.36 v7.5.0, 0.29 v7.4.0, 0.56 v7.3.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 1.00 v6.1.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   44 (   6 equality;  38 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   31 (   0   ~;   0   |;   8   &;  16   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   12 (   0 sgn;   8   !;   4   ?;   0   ^)
%                                         (  12   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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,(
a: \$tType )).

thf(cEQP1_1B_pme,conjecture,(
! [Xx: a > \$o,Xy: a > \$o] :
( ? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ( Xy @ ( Xs @ Xx0 ) ) )
& ! [Xy0: a] :
( ( Xy @ Xy0 )
=> ? [Xx0: a] :
( ( Xx @ Xx0 )
& ( Xy0
= ( Xs @ Xx0 ) )
& ! [Xz: a] :
( ( ( Xx @ Xz )
& ( Xy0
= ( Xs @ Xz ) ) )
=> ( Xz = Xx0 ) ) ) ) )
=> ? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xy @ Xx0 )
=> ( Xx @ ( Xs @ Xx0 ) ) )
& ! [Xy0: a] :
( ( Xx @ Xy0 )
=> ? [Xx0: a] :
( ( Xy @ Xx0 )
& ( Xy0
= ( Xs @ Xx0 ) )
& ! [Xz: a] :
( ( ( Xy @ Xz )
& ( Xy0
= ( Xs @ Xz ) ) )
=> ( Xz = Xx0 ) ) ) ) ) ) )).

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