## TPTP Problem File: SEV414^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV414^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0869 [Bro09]
%          : tps_0870 [Bro09]

% Status   : Theorem
% Rating   : 0.75 v7.1.0, 0.71 v7.0.0, 0.75 v6.4.0, 0.71 v6.3.0, 0.67 v6.2.0, 0.83 v5.5.0, 0.80 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   18 (   0 equality;  14 variable)
%            Maximal formula depth :   11 (   5 average)
%            Number of connectives :   17 (   0   ~;   0   |;   3   &;  10   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   4   !;   1   ?;   0   ^)
%                                         (   5   :;   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(cS,type,(
cS: \$i > \$i )).

thf(c0,type,(
c0: \$i )).

thf(cTHM594_pme,conjecture,(
? [Xv: \$i > \$o] :
( ( Xv @ c0 )
& ! [Xw: \$i] :
( ( Xv @ Xw )
=> ( Xv @ ( cS @ Xw ) ) )
& ! [Xp: \$i > \$o] :
( ( ( Xp @ c0 )
& ! [Xw: \$i] :
( ( Xp @ Xw )
=> ( Xp @ ( cS @ Xw ) ) ) )
=> ! [Xx: \$i] :
( ( Xv @ Xx )
=> ( Xp @ Xx ) ) ) ) )).

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