## TPTP Problem File: SEV361^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV361^5 : 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_0859 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.4.0, 0.67 v5.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :   21 (   1 equality;   9 variable)
%            Maximal formula depth :   12 (   5 average)
%            Number of connectives :   18 (   0   ~;   0   |;   3   &;  12   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   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(x,type,(
x: \$i )).

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

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

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

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

thf(cGVB_AX_SING_VAL,conjecture,
( ( cGVB_SING_VAL @ x )
<=> ! [Xu: \$i,Xv: \$i,Xw: \$i] :
( ( ( cGVB_M @ Xu )
& ( cGVB_M @ Xv )
& ( cGVB_M @ Xw ) )
=> ( ( ( cGVB_IN @ ( cGVB_OP @ Xu @ Xv ) @ x )
& ( cGVB_IN @ ( cGVB_OP @ Xu @ Xw ) @ x ) )
=> ( Xv = Xw ) ) ) )).

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