TPTP Problem File: SEV106^5.p

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% File     : SEV106^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from RELN-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1130 [Bro09]

% Status   : Theorem
% Rating   : 0.82 v7.5.0, 0.86 v7.4.0, 0.89 v7.2.0, 0.88 v7.1.0, 1.00 v6.1.0, 0.86 v5.5.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   66 (   9 equality;  57 variable)
%            Maximal formula depth :   18 (  10 average)
%            Number of connectives :   47 (   0   ~;   0   |;  13   &;  24   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   18 (   0 sgn;  12   !;   6   ?;   0   ^)
%                                         (  18   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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(a_type,type,(
    a: $tType )).

thf(cEQP1_1C_pme,conjecture,(
    ! [Xx: a > $o,Xy: a > $o,Xz: a > $o] :
      ( ( ? [Xs: a > a] :
            ( ! [Xx0: a] :
                ( ( Xx @ Xx0 )
               => ( Xy @ ( Xs @ Xx0 ) ) )
            & ! [Xy0: a] :
                ( ( Xy @ Xy0 )
               => ? [Xx0: a] :
                    ( ( Xx @ Xx0 )
                    & ( Xy0
                      = ( Xs @ Xx0 ) )
                    & ! [Xz0: a] :
                        ( ( ( Xx @ Xz0 )
                          & ( Xy0
                            = ( Xs @ Xz0 ) ) )
                       => ( Xz0 = Xx0 ) ) ) ) )
        & ? [Xs: a > a] :
            ( ! [Xx0: a] :
                ( ( Xy @ Xx0 )
               => ( Xz @ ( Xs @ Xx0 ) ) )
            & ! [Xy0: a] :
                ( ( Xz @ Xy0 )
               => ? [Xx0: a] :
                    ( ( Xy @ Xx0 )
                    & ( Xy0
                      = ( Xs @ Xx0 ) )
                    & ! [Xz0: a] :
                        ( ( ( Xy @ Xz0 )
                          & ( Xy0
                            = ( Xs @ Xz0 ) ) )
                       => ( Xz0 = Xx0 ) ) ) ) ) )
     => ? [Xs: a > a] :
          ( ! [Xx0: a] :
              ( ( Xx @ Xx0 )
             => ( Xz @ ( Xs @ Xx0 ) ) )
          & ! [Xy0: a] :
              ( ( Xz @ Xy0 )
             => ? [Xx0: a] :
                  ( ( Xx @ Xx0 )
                  & ( Xy0
                    = ( Xs @ Xx0 ) )
                  & ! [Xz0: a] :
                      ( ( ( Xx @ Xz0 )
                        & ( Xy0
                          = ( Xs @ Xz0 ) ) )
                     => ( Xz0 = Xx0 ) ) ) ) ) ) )).

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