TPTP Problem File: SET066+1.p
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%------------------------------------------------------------------------------
% File : SET066+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Domain : Set Theory
% Problem : Unordered pair is commutative
% Version : [Qua92] axioms : Reduced & Augmented > Complete.
% English :
% Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% Source : [Qua92]
% Names :
% Status : Theorem
% Rating : 0.75 v8.2.0, 0.78 v8.1.0, 0.75 v7.5.0, 0.81 v7.4.0, 0.77 v7.3.0, 0.76 v7.1.0, 0.74 v7.0.0, 0.77 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.87 v5.5.0, 0.85 v5.4.0
% Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% Number of atoms : 101 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 62 ( 5 ~; 3 |; 26 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% Number of variables : 88 ( 83 !; 5 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
%------------------------------------------------------------------------------
%----Include set theory axioms
include('Axioms/SET005+0.ax').
%------------------------------------------------------------------------------
%----UP1: Unordered pair is commutative
fof(commutativity_of_unordered_pair,conjecture,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X) ).
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