TPTP Problem File: SYO341^5.p

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% File     : SYO341^5 : TPTP v7.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1175 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v6.2.0, 0.67 v5.2.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :  101 (   0 equality;  66 variable)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :  112 (  12   ~;  17   |;   8   &;  74   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   6   !;   3   ?;   0   ^)
%                                         (   9   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_NEQ_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(cG,type,(
    cG: $i > $i )).

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

thf(cR,type,(
    cR: $i > $i > $o )).

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

thf(cP,type,(
    cP: $i > $o )).

thf(cTHM74A,conjecture,(
    ! [X: $i,Y: $i,Q: $i > $i > $o] :
      ( ? [Q1: $i > $i > $o,Q2: $i > $i > $o] :
          ( ( Q1 @ ( cF @ X @ ( cG @ X ) ) @ Y )
          & ! [Y0: $i] :
              ( ( ~ ( Q1 @ X @ Y0 )
                | ( cP @ X )
                | ( Q @ X @ ( cG @ Y0 ) ) )
              & ( ~ ( Q1 @ X @ Y0 )
                | ~ ( cR @ ( cG @ Y0 ) @ cK )
                | ( Q @ X @ ( cG @ Y0 ) ) )
              & ( ~ ( Q1 @ X @ Y0 )
                | ~ ( cP @ X )
                | ( cR @ ( cG @ Y0 ) @ cK )
                | ( Q2 @ X @ Y0 ) ) )
          & ! [Y0: $i] :
              ( ( ~ ( Q2 @ X @ Y0 )
                | ( cP @ X )
                | ( Q2 @ X @ ( cG @ Y0 ) ) )
              & ( ~ ( Q2 @ X @ Y0 )
                | ~ ( cP @ X )
                | ( Q1 @ X @ ( cG @ Y0 ) ) ) ) )
    <=> ? [Q1: $i > $i > $o] :
          ( ( ( cP @ ( cF @ X @ ( cG @ Y ) ) )
            | ( Q @ ( cF @ X @ ( cG @ Y ) ) @ ( cG @ Y ) ) )
          & ( ~ ( cP @ ( cF @ X @ ( cG @ Y ) ) )
            | ( Q1 @ ( cF @ X @ ( cG @ Y ) ) @ Y ) )
          & ! [Y0: $i] :
              ( ( ~ ( Q1 @ X @ Y0 )
                | ~ ( cR @ ( cG @ Y0 ) @ cK )
                | ( Q @ X @ ( cG @ Y0 ) ) )
              & ( ~ ( Q1 @ X @ Y0 )
                | ( cR @ ( cG @ Y0 ) @ cK )
                | ( Q1 @ X @ ( cG @ Y0 ) ) ) ) ) ) )).

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