TPTP Problem File: SEV377^5.p

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```%------------------------------------------------------------------------------
% File     : SEV377^5 : 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_0813 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :   17 (   1 equality;   9 variable)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :   14 (   0   ~;   0   |;   1   &;  12   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   3   !;   0   ?;   0   ^)
%                                         (   3   :;   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
%------------------------------------------------------------------------------
thf(cGVB_COMPOSE,type,(
cGVB_COMPOSE: \$i > \$i > \$i )).

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_APP_PROP_1,conjecture,(
! [Xf: \$i,Xg: \$i,Xx: \$i] :
( ( ( cGVB_FUNCTION @ Xf )
& ( cGVB_IN @ Xx @ ( cGVB_DOMAIN @ Xf ) ) )
=> ( ( cGVB_APPLY @ Xg @ ( cGVB_APPLY @ Xf @ Xx ) )
= ( cGVB_APPLY @ ( cGVB_COMPOSE @ Xg @ Xf ) @ Xx ) ) ) )).

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