## TPTP Problem File: SEV026^5.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEV026^5 : 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_1113 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   54 (   0 equality;  54 variable)
%            Maximal formula depth :   19 (  19 average)
%            Number of connectives :   53 (   0   ~;   0   |;   9   &;  36   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   21 (   0 sgn;  20   !;   1   ?;   0   ^)
%                                         (  21   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%------------------------------------------------------------------------------
thf(cTHM601_pme,conjecture,(
! [Xr: \$i > \$i > \$o] :
? [Xs: \$i > \$i > \$o] :
( ! [Xa: \$i,Xb: \$i] :
( ( Xr @ Xa @ Xb )
=> ( Xs @ Xa @ Xb ) )
& ! [Xx: \$i] :
( Xs @ Xx @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ( Xs @ Xx @ Xy )
=> ( Xs @ Xy @ Xx ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( Xs @ Xx @ Xy )
& ( Xs @ Xy @ Xz ) )
=> ( Xs @ Xx @ Xz ) )
& ! [Xt: \$i > \$i > \$o] :
( ( ! [Xa: \$i,Xb: \$i] :
( ( Xr @ Xa @ Xb )
=> ( Xt @ Xa @ Xb ) )
& ! [Xx: \$i] :
( Xt @ Xx @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ( Xt @ Xx @ Xy )
=> ( Xt @ Xy @ Xx ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( Xt @ Xx @ Xy )
& ( Xt @ Xy @ Xz ) )
=> ( Xt @ Xx @ Xz ) ) )
=> ! [Xa: \$i,Xb: \$i] :
( ( Xs @ Xa @ Xb )
=> ( Xt @ Xa @ Xb ) ) ) ) )).

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