TPTP Problem File: SEV365^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV365^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (GvNB)
% Problem  : TPS problem from GVB-MB-AXIOMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0924 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.4.0, 0.67 v5.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :   12 (   0 unit;  11 type;   0 defn)
%            Number of atoms       :   37 (   1 equality;   6 variable)
%            Maximal formula depth :   13 (   4 average)
%            Number of connectives :   34 (   0   ~;   0   |;   4   &;  28   @)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11   :;   0   =)
%            Number of variables   :    2 (   0 sgn;   2   !;   0   ?;   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
%------------------------------------------------------------------------------
thf(h,type,(
h: \$i )).

thf(f2,type,(
f2: \$i )).

thf(f1,type,(
f1: \$i )).

thf(s1,type,(
s1: \$i )).

thf(s2,type,(
s2: \$i )).

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

thf(cGVB_APP2,type,(
cGVB_APP2: \$i > \$i > \$i > \$i )).

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

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

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

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

thf(cGVB_AX_HOMOM,conjecture,
( ( cGVB_HOMOM @ h @ s1 @ f1 @ s2 @ f2 )
<=> ( ( cGVB_CLOSED @ s1 @ f1 )
& ( cGVB_CLOSED @ s2 @ f2 )
& ( cGVB_MAPS @ h @ s1 @ s2 )
& ! [Xx: \$i,Xy: \$i] :
( ( ( cGVB_IN @ Xx @ s1 )
& ( cGVB_IN @ Xy @ s1 ) )
=> ( ( cGVB_APPLY @ h @ ( cGVB_APP2 @ f1 @ Xx @ Xy ) )
= ( cGVB_APP2 @ f2 @ ( cGVB_APPLY @ h @ Xx ) @ ( cGVB_APPLY @ h @ Xy ) ) ) ) ) )).

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