## TPTP Problem File: SEV410^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV410^5 : TPTP v7.5.0. 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_0790 [Bro09]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   11 (   0 equality;   6 variable)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :   10 (   0   ~;   1   |;   1   &;   6   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   1   !;   1   ?;   1   ^)
%                                         (   3   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%------------------------------------------------------------------------------
thf(cA,type,(
cA: \$i > \$o )).

thf(cP,type,(
cP: ( \$i > \$o ) > \$o )).

thf(cB,type,(
cB: \$i > \$o )).

thf(cSV1_pme,conjecture,
( ( cP
@ ^ [Xx: \$i] :
( ( cA @ Xx )
| ( cB @ Xx ) ) )
=> ? [Xu: \$i > \$o] :
( ( cP @ Xu )
& ! [Xx: \$i] :
( ( cA @ Xx )
=> ( Xu @ Xx ) ) ) )).

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