## TPTP Problem File: SEV381^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV381^5 : TPTP v7.2.0. 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_0975 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 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    :    7 (   0 unit;   6 type;   0 defn)
%            Number of atoms       :   37 (   4 equality;  21 variable)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :   28 (   0   ~;   0   |;   8   &;  18   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   2   !;   3   ?;   0   ^)
%                                         (   5   :;   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(cGVB_APPLY,type,(
cGVB_APPLY: \$i > \$i > \$i )).

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

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

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

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

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

thf(cGVB_THM15B_2,conjecture,(
! [Xf: \$i] :
( ( ( cGVB_M @ Xf )
& ( cGVB_FUNCTION @ Xf )
& ? [Xg: \$i] :
( ( cGVB_ITERATE @ Xf @ Xg )
& ( cGVB_M @ Xg )
& ( cGVB_FUNCTION @ Xg )
& ? [Xx: \$i] :
( ( cGVB_IN @ Xx @ ( cGVB_DOMAIN @ Xf ) )
& ( cGVB_IN @ Xx @ ( cGVB_DOMAIN @ Xg ) )
& ( ( cGVB_APPLY @ Xg @ Xx )
= Xx )
& ! [Xz: \$i] :
( ( ( cGVB_APPLY @ Xg @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) ) )
=> ? [Xy: \$i] :
( ( cGVB_APPLY @ Xf @ Xy )
= Xy ) ) )).

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