TPTP Problem File: SEV381^5.p

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%------------------------------------------------------------------------------
% File     : SEV381^5 : TPTP v7.1.0. 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   : 0.33 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
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%          : 
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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 ) ) )).

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