TPTP Problem File: SEV360^5.p

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% File     : SEV360^5 : 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_0843 [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       :   22 (   1 equality;   5 variable)
%            Maximal formula depth :   10 (   4 average)
%            Number of connectives :   19 (   0   ~;   0   |;   5   &;  13   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9   :;   0   =)
%            Number of variables   :    1 (   0 sgn;   0   !;   1   ?;   0   ^)
%                                         (   1   :;   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(z,type,(
    z: $i )).

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

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

thf(cGVB_AX_APPLY,conjecture,
    ( ( cGVB_IN @ z @ ( cGVB_APPLY @ f @ y ) )
  <=> ( ( cGVB_M @ z )
      & ? [Xw: $i] :
          ( ( cGVB_M @ Xw )
          & ( cGVB_OPP @ Xw )
          & ( cGVB_IN @ Xw @ f )
          & ( ( cGVB_FIRST @ Xw )
            = y )
          & ( cGVB_IN @ z @ ( cGVB_SECOND @ Xw ) ) ) ) )).

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