TPTP Problem File: SEV040^5.p

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% File     : SEV040^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from EQUIVALENCE-RELATIONS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1214 [Bro09]

% Status   : Theorem
% Rating   : 0.18 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :  127 (   8 equality; 119 variable)
%            Maximal formula depth :   19 (  10 average)
%            Number of connectives :  110 (   0   ~;   0   |;  24   &;  70   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   44 (   0 sgn;  40   !;   0   ?;   4   ^)
%                                         (  44   :;   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
%          : May require description or choice.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM515_pme,conjecture,
( ! [Xx: a > a > \$o,Xy: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xx @ Xx0 @ Xy0 )
=> ( Xx @ Xy0 @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xx @ Xx0 @ Xy0 )
& ( Xx @ Xy0 @ Xz ) )
=> ( Xx @ Xx0 @ Xz ) )
& ( Xx = Xy ) )
=> ( ! [Xx0: a,Xy0: a] :
( ( Xy @ Xx0 @ Xy0 )
=> ( Xy @ Xy0 @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xy @ Xx0 @ Xy0 )
& ( Xy @ Xy0 @ Xz ) )
=> ( Xy @ Xx0 @ Xz ) )
& ( Xy = Xx ) ) )
& ! [Xx: a > a > \$o,Xy: a > a > \$o,Xz: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xx @ Xx0 @ Xy0 )
=> ( Xx @ Xy0 @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xx @ Xx0 @ Xy0 )
& ( Xx @ Xy0 @ Xz0 ) )
=> ( Xx @ Xx0 @ Xz0 ) )
& ( Xx = Xy )
& ! [Xx0: a,Xy0: a] :
( ( Xy @ Xx0 @ Xy0 )
=> ( Xy @ Xy0 @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xy @ Xx0 @ Xy0 )
& ( Xy @ Xy0 @ Xz0 ) )
=> ( Xy @ Xx0 @ Xz0 ) )
& ( Xy = Xz ) )
=> ( ! [Xx0: a,Xy0: a] :
( ( Xx @ Xx0 @ Xy0 )
=> ( Xx @ Xy0 @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xx @ Xx0 @ Xy0 )
& ( Xx @ Xy0 @ Xz0 ) )
=> ( Xx @ Xx0 @ Xz0 ) )
& ( Xx = Xz ) ) )
& ( ( ^ [Xp: a > a > \$o,Xq: a > a > \$o] :
( ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xp @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xy )
& ( Xp @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xz ) )
& ( Xp = Xq ) ) )
= ( ^ [Xp: a > a > \$o,Xq: a > a > \$o] :
( ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xp @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xy )
& ( Xp @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xz ) )
& ( Xp = Xq ) ) ) ) )).

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