## TPTP Problem File: SEV351^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV351^5 : 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_0786 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.4.0, 0.67 v5.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :   10 (   0 unit;   9 type;   0 defn)
%            Number of atoms       :   17 (   0 equality;   0 variable)
%            Maximal formula depth :    8 (   3 average)
%            Number of connectives :   16 (   0   ~;   0   |;   3   &;  12   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9   :;   0   =)
%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?;   0   ^)
%                                         (   0   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%------------------------------------------------------------------------------
thf(y,type,(
y: \$i )).

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

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

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

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

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

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

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

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

thf(cGVB_B5,conjecture,
( ( cGVB_IN @ z @ ( cGVB_CROSS @ x @ y ) )
<=> ( ( cGVB_M @ z )
& ( cGVB_OPP @ z )
& ( cGVB_IN @ ( cGVB_FIRST @ z ) @ x )
& ( cGVB_IN @ ( cGVB_SECOND @ z ) @ y ) ) )).

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