TPTP Problem File: SET796+4.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SET796+4 : TPTP v8.2.0. Bugfixed v4.0.0.
% Domain : Set Theory (Order relations)
% Problem : If R(a,b) then a is the greatest lower bound of unordered_pair(a,b)
% Version : [Pas05] axioms.
% English :
% Refs : [Pas05] Pastre (2005), Email to G. Sutcliffe
% Source : [Pas05]
% Names :
% Status : Theorem
% Rating : 0.53 v8.2.0, 0.58 v8.1.0, 0.56 v7.5.0, 0.62 v7.4.0, 0.47 v7.3.0, 0.52 v7.1.0, 0.48 v7.0.0, 0.57 v6.4.0, 0.58 v6.3.0, 0.54 v6.2.0, 0.60 v6.1.0, 0.67 v6.0.0, 0.70 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0, 0.80 v5.1.0, 0.81 v5.0.0, 0.79 v4.1.0, 0.78 v4.0.1, 0.83 v4.0.0
% Syntax : Number of formulae : 22 ( 1 unt; 0 def)
% Number of atoms : 90 ( 6 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 70 ( 2 ~; 3 |; 28 &)
% ( 20 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 0 prp; 2-4 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 77 !; 1 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v4.0.0 - removed duplicate include of SET006+3.ax
%------------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%----Include order relation axioms
include('Axioms/SET006+3.ax').
%------------------------------------------------------------------------------
fof(thIV8,conjecture,
! [R,E,A,B] :
( ( order(R,E)
& member(A,E)
& member(B,E)
& apply(R,A,B) )
=> greatest_lower_bound(A,unordered_pair(A,B),R,E) ) ).
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