## TPTP Problem File: SEV375^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV375^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (GvNB)
% Problem  : TPS problem from GVB-MB-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0751 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v5.4.0, 1.00 v5.0.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   12 (   1 equality;   5 variable)
%            Maximal formula depth :    8 (   4 average)
%            Number of connectives :    9 (   0   ~;   0   |;   1   &;   7   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    2 (   0 sgn;   1   !;   1   ?;   0   ^)
%                                         (   2   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_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(f,type,(
f: \$i )).

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

thf(cGVB_COMPOSE,type,(
cGVB_COMPOSE: \$i > \$i > \$i )).

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

thf(cTHM15B_EXISTS,conjecture,(
? [P: \$i] :
! [Xg: \$i] :
( ( cGVB_IN @ Xg @ P )
<=> ( ( ( cGVB_COMPOSE @ f @ Xg )
= ( cGVB_COMPOSE @ Xg @ f ) )
& ( cGVB_M @ Xg ) ) ) )).

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