TPTP Problem File: SEV332^5.p

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%------------------------------------------------------------------------------
% File     : SEV332^5 : 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_0638 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.4.0, 0.67 v5.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    7 (   0 unit;   6 type;   0 defn)
%            Number of atoms       :   10 (   1 equality;   0 variable)
%            Maximal formula depth :    5 (   3 average)
%            Number of connectives :    7 (   0   ~;   0   |;   0   &;   7   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   6   :;   0   =)
%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?;   0   ^)
%                                         (   0   :;   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(y,type,(
    y: $i )).

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

thf(f,type,(
    f: $i )).

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

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

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

thf(cGVB_AX_APP2,conjecture,
    ( ( cGVB_APP2 @ f @ x @ y )
    = ( cGVB_APPLY @ f @ ( cGVB_OP @ x @ y ) ) )).

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