TPTP Problem File: SEV365^5.p

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% 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
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
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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 ) ) ) ) ) )).

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