TPTP Problem File: SEV096^5.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEV096^5 : 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_1072 [Bro09]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    7 (   0 unit;   6 type;   0 defn)
%            Number of atoms       :   42 (   0 equality;  27 variable)
%            Maximal formula depth :   12 (   4 average)
%            Number of connectives :   42 (   1   ~;   1   |;   7   &;  28   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6   :;   0   =)
%            Number of variables   :   15 (   0 sgn;  13   !;   2   ?;   0   ^)
%                                         (  15   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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/
%------------------------------------------------------------------------------
thf(a_type,type,(
    a: $tType )).

thf(b_type,type,(
    b: $tType )).

thf(z,type,(
    z: a )).

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

thf(f,type,(
    f: a > b > $o )).

thf(cS,type,(
    cS: b > b > $o )).

thf(cTHM552E_pme,conjecture,
    ( ( ! [Xu: a,Xv: a,Xw: a] :
          ( ( ( cR @ Xu @ Xv )
            & ( cR @ Xw @ Xv ) )
         => ( cR @ Xu @ Xw ) )
      & ! [Xx: a] :
          ( cR @ Xx @ Xx ) )
   => ( ( ! [Xx: a] :
          ? [Xy: b] :
            ( f @ Xx @ Xy )
        & ! [Xx: a,Xy1: b,Xy2: b] :
            ( ( ( f @ Xx @ Xy1 )
              & ( f @ Xx @ Xy2 ) )
           => ( cS @ Xy1 @ Xy2 ) )
        & ! [Xx1: a,Xx2: a,Xy: b] :
            ( ( ( f @ Xx1 @ Xy )
              & ( f @ Xx2 @ Xy ) )
           => ( cR @ Xx1 @ Xx2 ) ) )
     => ! [Xy: b] :
        ? [Xx: a] :
        ! [Xw: a] :
          ( ( f @ Xx @ Xy )
          | ( ~ ( f @ Xw @ Xy )
            & ( cR @ Xx @ z ) ) ) ) )).

%------------------------------------------------------------------------------