0.04/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.36	% Computer   : n016.cluster.edu
0.13/0.36	% Model      : x86_64 x86_64
0.13/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.36	% Memory     : 8042.1875MB
0.13/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.36	% CPULimit   : 180
0.13/0.36	% DateTime   : Thu Aug 29 12:20:53 EDT 2019
0.13/0.36	% CPUTime    : 
4.10/4.30	% SZS status Unsatisfiable
4.10/4.30	
4.10/4.31	% SZS output start Proof
4.10/4.31	Take the following subset of the input axioms:
4.10/4.31	  fof(prove_wal_axioms_4, negated_conjecture, join(b, a)!=join(a, b)).
4.10/4.31	  fof(single_axiom, axiom, ![B, A, C, D, E, F]: B=join(meet(join(meet(A, B), meet(B, join(A, B))), C), meet(join(meet(A, join(join(meet(B, D), meet(E, B)), B)), meet(join(meet(B, meet(meet(join(B, D), join(E, B)), B)), meet(F, join(B, meet(meet(join(B, D), join(E, B)), B)))), join(A, join(join(meet(B, D), meet(E, B)), B)))), join(join(meet(A, B), meet(B, join(A, B))), C)))).
4.10/4.31	
4.10/4.31	Now clausify the problem and encode Horn clauses using encoding 3 of
4.10/4.31	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
4.10/4.31	We repeatedly replace C & s=t => u=v by the two clauses:
4.10/4.31	  fresh(y, y, x1...xn) = u
4.10/4.31	  C => fresh(s, t, x1...xn) = v
4.10/4.31	where fresh is a fresh function symbol and x1..xn are the free
4.10/4.31	variables of u and v.
4.10/4.31	A predicate p(X) is encoded as p(X)=true (this is sound, because the
4.10/4.31	input problem has no model of domain size 1).
4.10/4.31	
4.10/4.31	The encoding turns the above axioms into the following unit equations and goals:
4.10/4.31	
5.62/5.83	Axiom 1 (single_axiom): X = join(meet(join(meet(Y, X), meet(X, join(Y, X))), Z), meet(join(meet(Y, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Y, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Y, X), meet(X, join(Y, X))), Z))).
5.62/5.83	
5.62/5.83	Lemma 2: join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), V), meet(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), V), meet(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W))) = join(meet(X, Y), meet(Y, join(X, Y))).
5.62/5.83	Proof:
5.62/5.83	  join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), V), meet(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), V), meet(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.62/5.83	= { by axiom 1 (single_axiom) }
5.62/5.83	  join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), V), meet(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), meet(meet(join(join(meet(X, Y), meet(Y, join(X, Y))), V), join(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(join(meet(X, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(X, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), meet(meet(join(join(meet(X, Y), meet(Y, join(X, Y))), V), join(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), V), meet(U, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.62/5.83	= { by axiom 1 (single_axiom) }
5.88/6.13	  join(meet(X, Y), meet(Y, join(X, Y)))
5.88/6.13	
5.88/6.13	Lemma 3: join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W))) = join(meet(X, Y), meet(Y, join(X, Y))).
5.88/6.13	Proof:
5.88/6.13	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.88/6.13	= { by lemma 2 }
5.88/6.13	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.88/6.13	= { by lemma 2 }
5.88/6.13	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.88/6.13	= { by lemma 2 }
5.88/6.13	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.88/6.13	= { by lemma 2 }
5.88/6.14	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.88/6.14	= { by lemma 2 }
5.88/6.15	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.88/6.15	= { by lemma 2 }
5.88/6.15	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.88/6.15	= { by lemma 2 }
5.99/6.16	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.99/6.16	= { by lemma 2 }
5.99/6.17	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.99/6.17	= { by lemma 2 }
5.99/6.18	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, 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Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), 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join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.99/6.18	= { by lemma 2 }
5.99/6.19	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), 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Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.99/6.19	= { by lemma 2 }
5.99/6.20	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, 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Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.99/6.20	= { by lemma 2 }
5.99/6.21	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, 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Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), 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join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, 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join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, 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?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), W)))
5.99/6.22	= { by lemma 2 }
6.05/6.22	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, 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Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?), meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))))))), join(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W)))
6.05/6.23	= { by lemma 2 }
6.05/6.23	  join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))))))
6.05/6.23	= { by lemma 2 }
6.05/6.23	  join(meet(X, Y), meet(Y, join(X, Y)))
6.05/6.23	
6.05/6.23	Lemma 4: join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z))) = join(meet(X, Y), meet(Y, join(X, Y))).
6.05/6.23	Proof:
6.05/6.23	  join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
6.05/6.23	= { by lemma 3 }
6.05/6.23	  join(meet(join(meet(join(meet(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), Z), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
6.05/6.23	= { by lemma 3 }
6.05/6.23	  join(meet(join(meet(join(meet(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), Z), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(?, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(X, Y), meet(Y, join(X, Y)))))), Z)))
6.05/6.23	= { by lemma 3 }
6.05/6.24	  join(meet(X, Y), meet(Y, join(X, Y)))
6.05/6.24	
6.05/6.24	Lemma 5: join(meet(Y, U), meet(Y, join(Y, U))) = Y.
6.05/6.24	Proof:
6.05/6.24	  join(meet(Y, U), meet(Y, join(Y, U)))
6.05/6.24	= { by axiom 1 (single_axiom) }
6.05/6.24	  join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), U), meet(Y, join(Y, U)))
6.05/6.24	= { by axiom 1 (single_axiom) }
6.05/6.24	  join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), U), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(Y, U)))
6.05/6.24	= { by axiom 1 (single_axiom) }
6.05/6.24	  join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), U), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), U)))
6.05/6.24	= { by lemma 4 }
6.05/6.24	  join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))
6.05/6.24	= { by axiom 1 (single_axiom) }
6.42/6.64	  Y
6.42/6.64	
6.42/6.64	Lemma 6: join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T))) = Y.
6.42/6.64	Proof:
6.42/6.64	  join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.64	= { by axiom 1 (single_axiom) }
6.42/6.64	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.64	= { by axiom 1 (single_axiom) }
6.42/6.64	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.64	= { by axiom 1 (single_axiom) }
6.42/6.64	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.64	= { by axiom 1 (single_axiom) }
6.42/6.65	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.65	= { by axiom 1 (single_axiom) }
6.42/6.65	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.65	= { by axiom 1 (single_axiom) }
6.42/6.65	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(Y, join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.65	= { by axiom 1 (single_axiom) }
6.42/6.66	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, Y))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.42/6.66	= { by axiom 1 (single_axiom) }
6.49/6.67	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), Y))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.49/6.67	= { by axiom 1 (single_axiom) }
6.49/6.67	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.49/6.67	= { by axiom 1 (single_axiom) }
6.49/6.67	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.49/6.67	= { by axiom 1 (single_axiom) }
6.49/6.68	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.49/6.68	= { by axiom 1 (single_axiom) }
6.49/6.69	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.49/6.69	= { by axiom 1 (single_axiom) }
6.53/6.70	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.53/6.70	= { by axiom 1 (single_axiom) }
6.53/6.71	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.53/6.71	= { by axiom 1 (single_axiom) }
6.53/6.71	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), T)))
6.53/6.71	= { by axiom 1 (single_axiom) }
6.53/6.72	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(Y, join(U, Y))), Y))), T)))
6.53/6.73	= { by axiom 1 (single_axiom) }
6.57/6.74	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, Y))), Y))), T)))
6.57/6.74	= { by axiom 1 (single_axiom) }
6.57/6.75	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, 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Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, 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?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, 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Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), Y))), T)))
6.57/6.75	= { by axiom 1 (single_axiom) }
6.57/6.76	  join(meet(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, 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meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(join(meet(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))), meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))))), join(U, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))))), T)))
6.57/6.76	= { by lemma 3 }
6.57/6.76	  join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y))))), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))))))
6.57/6.76	= { by axiom 1 (single_axiom) }
6.57/6.80	  Y
6.57/6.80	
6.57/6.80	Lemma 7: join(meet(join(meet(Z, Y), meet(Y, join(Z, Y))), W), meet(join(meet(Z, join(join(meet(Y, V), meet(U, Y)), Y)), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W))) = Y.
6.57/6.80	Proof:
6.57/6.80	  join(meet(join(meet(Z, Y), meet(Y, join(Z, Y))), W), meet(join(meet(Z, join(join(meet(Y, V), meet(U, Y)), Y)), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(Y, join(Z, Y))), W), meet(join(meet(Z, join(join(meet(Y, V), meet(U, Y)), Y)), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, Y))), W), meet(join(meet(Z, join(join(meet(Y, V), meet(U, Y)), Y)), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(Y, V), meet(U, Y)), Y)), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, Y)), Y)), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), Y)), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), meet(Y, join(Z, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), meet(Y, join(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), meet(Y, join(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.80	= { by lemma 6 }
6.57/6.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), meet(Y, join(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
6.57/6.81	= { by lemma 6 }
6.57/6.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), meet(Y, join(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))))), join(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(Y, join(Z, Y))), W)))
6.57/6.81	= { by lemma 6 }
6.57/6.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), meet(Y, join(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))))), join(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, Y))), W)))
6.57/6.81	= { by lemma 6 }
6.57/6.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), meet(Y, join(Z, join(join(meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), V), meet(U, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))), join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))))))), join(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W)))
6.57/6.81	= { by lemma 2 }
6.57/6.81	  join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))
6.57/6.81	= { by lemma 6 }
6.57/6.81	  Y
6.57/6.81	
6.57/6.81	Lemma 8: join(meet(join(meet(Y, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Y, join(meet(X, Y), meet(Y, join(X, Y)))))), Z), meet(Y, join(join(meet(Y, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Y, join(meet(X, Y), meet(Y, join(X, Y)))))), Z))) = join(meet(X, Y), meet(Y, join(X, Y))).
6.57/6.81	Proof:
6.57/6.81	  join(meet(join(meet(Y, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Y, join(meet(X, Y), meet(Y, join(X, Y)))))), Z), meet(Y, join(join(meet(Y, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Y, join(meet(X, Y), meet(Y, join(X, Y)))))), Z)))
6.57/6.81	= { by lemma 5 }
6.57/6.81	  join(meet(join(meet(Y, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Y, join(meet(X, Y), meet(Y, join(X, Y)))))), Z), meet(join(meet(Y, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Y, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), ?), meet(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Y, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Y, join(meet(X, Y), meet(Y, join(X, Y)))))), Z)))
6.57/6.81	= { by lemma 2 }
6.57/6.81	  join(meet(X, Y), meet(Y, join(X, Y)))
6.57/6.81	
6.57/6.81	Lemma 9: join(meet(Y, X), meet(X, join(Y, X))) = X.
6.57/6.81	Proof:
6.57/6.81	  join(meet(Y, X), meet(X, join(Y, X)))
6.57/6.81	= { by lemma 4 }
6.57/6.81	  join(meet(join(meet(Y, X), meet(X, join(Y, X))), ?), meet(join(meet(Y, X), meet(X, join(Y, X))), join(join(meet(Y, X), meet(X, join(Y, X))), ?)))
6.57/6.81	= { by lemma 8 }
6.57/6.81	  join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?), meet(join(meet(Y, X), meet(X, join(Y, X))), join(join(meet(Y, X), meet(X, join(Y, X))), ?)))
6.57/6.81	= { by lemma 8 }
6.57/6.82	  join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?), meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(X, ?), meet(?, X)), X)))), join(join(meet(Y, X), meet(X, join(Y, X))), ?)))
6.57/6.82	= { by lemma 8 }
6.57/6.82	  join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?), meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(X, ?), meet(?, X)), X)))), join(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?)))
6.57/6.82	= { by lemma 7 }
6.57/6.82	  X
6.57/6.82	
6.57/6.82	Lemma 10: join(meet(X, W), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, W))) = X.
6.57/6.82	Proof:
6.57/6.82	  join(meet(X, W), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, W)))
6.57/6.82	= { by lemma 9 }
6.57/6.82	  join(meet(join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X))), W), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, W)))
6.57/6.82	= { by lemma 9 }
6.57/6.82	  join(meet(join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X))), W), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(X, W)))
6.57/6.82	= { by lemma 4 }
6.57/6.82	  join(meet(join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X))), W), meet(join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(X, Y), meet(Z, X)), X)), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(X, Y), meet(Z, X)), X)))), join(X, W)))
6.57/6.82	= { by lemma 9 }
6.57/6.82	  join(meet(join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X))), W), meet(join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(X, Y), meet(Z, X)), X)), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(X, Y), meet(Z, X)), X)))), join(join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), X))), W)))
6.57/6.82	= { by axiom 1 (single_axiom) }
6.57/6.82	  X
6.57/6.82	
6.57/6.82	Lemma 11: join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))) = Y.
6.57/6.82	Proof:
6.57/6.82	  join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))
6.57/6.82	= { by lemma 7 }
6.57/6.82	  join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), ?), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), ?), meet(?, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), ?), meet(?, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), ?)))
6.57/6.82	= { by lemma 7 }
6.57/6.82	  join(meet(Y, ?), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), ?), meet(?, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), ?), meet(?, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), ?)))
6.57/6.82	= { by lemma 7 }
6.57/6.82	  join(meet(Y, ?), meet(Y, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), ?)))
6.57/6.82	= { by lemma 7 }
6.57/6.82	  join(meet(Y, ?), meet(Y, join(Y, ?)))
6.57/6.82	= { by lemma 5 }
6.57/6.82	  Y
6.57/6.82	
6.57/6.82	Lemma 12: meet(meet(join(X, Y), join(Z, X)), X) = X.
6.57/6.82	Proof:
6.57/6.82	  meet(meet(join(X, Y), join(Z, X)), X)
6.57/6.82	= { by lemma 7 }
6.57/6.83	  join(meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), ?), meet(join(meet(X, join(join(meet(meet(meet(join(X, Y), join(Z, X)), X), ?), meet(?, meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, join(join(meet(meet(meet(join(X, Y), join(Z, X)), X), ?), meet(?, meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X))))), join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), ?)))
6.57/6.83	= { by lemma 10 }
6.57/6.83	  join(meet(X, ?), meet(join(meet(X, join(join(meet(meet(meet(join(X, Y), join(Z, X)), X), ?), meet(?, meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, join(join(meet(meet(meet(join(X, Y), join(Z, X)), X), ?), meet(?, meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X))))), join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), ?)))
6.57/6.83	= { by lemma 11 }
6.57/6.83	  join(meet(X, ?), meet(meet(meet(join(X, Y), join(Z, X)), X), join(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X)))), ?)))
6.57/6.83	= { by lemma 10 }
6.57/6.83	  join(meet(X, ?), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, ?)))
6.57/6.83	= { by lemma 10 }
6.57/6.83	  X
6.57/6.83	
6.57/6.83	Lemma 13: meet(meet(Y, join(Z, meet(X, Y))), meet(X, Y)) = meet(X, Y).
6.57/6.83	Proof:
6.57/6.83	  meet(meet(Y, join(Z, meet(X, Y))), meet(X, Y))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  meet(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, meet(X, Y))), meet(X, Y))
6.57/6.83	= { by lemma 12 }
6.57/6.83	  meet(X, Y)
6.57/6.83	
6.57/6.83	Lemma 14: meet(meet(X, join(W, X)), X) = X.
6.57/6.83	Proof:
6.57/6.83	  meet(meet(X, join(W, X)), X)
6.57/6.83	= { by lemma 12 }
6.57/6.83	  meet(meet(X, join(W, meet(meet(join(X, ?), join(?, X)), X))), X)
6.57/6.83	= { by lemma 12 }
6.57/6.83	  meet(meet(X, join(W, meet(meet(join(X, ?), join(?, X)), X))), meet(meet(join(X, ?), join(?, X)), X))
6.57/6.83	= { by lemma 13 }
6.57/6.83	  meet(meet(join(X, ?), join(?, X)), X)
6.57/6.83	= { by lemma 12 }
6.57/6.83	  X
6.57/6.83	
6.57/6.83	Lemma 15: meet(X, meet(X, join(Y, X))) = meet(X, join(Y, X)).
6.57/6.83	Proof:
6.57/6.83	  meet(X, meet(X, join(Y, X)))
6.57/6.83	= { by lemma 14 }
6.57/6.83	  meet(meet(meet(X, join(Y, X)), X), meet(X, join(Y, X)))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  meet(meet(meet(X, join(Y, X)), join(meet(Y, X), meet(X, join(Y, X)))), meet(X, join(Y, X)))
6.57/6.83	= { by lemma 14 }
6.57/6.83	  meet(X, join(Y, X))
6.57/6.83	
6.57/6.83	Lemma 16: join(meet(X, Z), meet(join(meet(Y, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, X), meet(U, join(X, X))), join(Y, join(join(meet(X, W), meet(V, X)), X)))), join(X, Z))) = X.
6.57/6.83	Proof:
6.57/6.83	  join(meet(X, Z), meet(join(meet(Y, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, X), meet(U, join(X, X))), join(Y, join(join(meet(X, W), meet(V, X)), X)))), join(X, Z)))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  join(meet(join(meet(Y, X), meet(X, join(Y, X))), Z), meet(join(meet(Y, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, X), meet(U, join(X, X))), join(Y, join(join(meet(X, W), meet(V, X)), X)))), join(X, Z)))
6.57/6.83	= { by lemma 12 }
6.57/6.83	  join(meet(join(meet(Y, X), meet(X, join(Y, X))), Z), meet(join(meet(Y, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, X))), join(Y, join(join(meet(X, W), meet(V, X)), X)))), join(X, Z)))
6.57/6.83	= { by lemma 12 }
6.57/6.83	  join(meet(join(meet(Y, X), meet(X, join(Y, X))), Z), meet(join(meet(Y, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Y, join(join(meet(X, W), meet(V, X)), X)))), join(X, Z)))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  join(meet(join(meet(Y, X), meet(X, join(Y, X))), Z), meet(join(meet(Y, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Y, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Y, X), meet(X, join(Y, X))), Z)))
6.57/6.83	= { by axiom 1 (single_axiom) }
6.57/6.83	  X
6.57/6.83	
6.57/6.83	Lemma 17: join(join(meet(X, Y), meet(Z, X)), X) = X.
6.57/6.83	Proof:
6.57/6.83	  join(join(meet(X, Y), meet(Z, X)), X)
6.57/6.83	= { by lemma 16 }
6.57/6.83	  join(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, ?), meet(?, X)), X)), meet(join(meet(X, join(join(meet(join(join(meet(X, Y), meet(Z, X)), X), ?), meet(?, join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X))), meet(join(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X)), meet(join(meet(X, X), meet(?, join(X, X))), join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X)))), join(X, join(join(meet(join(join(meet(X, Y), meet(Z, X)), X), ?), meet(?, join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X))))), join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, ?), meet(?, X)), X))))
6.57/6.83	= { by lemma 16 }
6.57/6.83	  join(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, ?), meet(?, X)), X))))
6.57/6.83	= { by lemma 11 }
6.57/6.83	  X
6.57/6.83	
6.57/6.83	Lemma 18: meet(meet(Y, join(W, meet(Y, Z))), meet(Y, Z)) = meet(Y, Z).
6.57/6.83	Proof:
6.57/6.83	  meet(meet(Y, join(W, meet(Y, Z))), meet(Y, Z))
6.57/6.83	= { by axiom 1 (single_axiom) }
6.57/6.83	  meet(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Z), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), Z))), join(W, meet(Y, Z))), meet(Y, Z))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  meet(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Z), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), Z))), join(W, meet(join(meet(?, Y), meet(Y, join(?, Y))), Z))), meet(Y, Z))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  meet(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Z), meet(join(meet(?, join(join(meet(Y, ?), meet(?, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, ?), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(Y, ?), join(?, Y)), Y)))), join(?, join(join(meet(Y, ?), meet(?, Y)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), Z))), join(W, meet(join(meet(?, Y), meet(Y, join(?, Y))), Z))), meet(join(meet(?, Y), meet(Y, join(?, Y))), Z))
6.57/6.83	= { by lemma 12 }
6.57/6.83	  meet(join(meet(?, Y), meet(Y, join(?, Y))), Z)
6.57/6.83	= { by lemma 9 }
6.57/6.83	  meet(Y, Z)
6.57/6.83	
6.57/6.83	Lemma 19: meet(X, X) = X.
6.57/6.83	Proof:
6.57/6.83	  meet(X, X)
6.57/6.83	= { by lemma 12 }
6.57/6.83	  meet(meet(meet(join(X, ?), join(?, X)), X), X)
6.57/6.83	= { by lemma 17 }
6.57/6.83	  meet(meet(meet(join(X, ?), join(?, X)), join(join(meet(X, ?), meet(?, X)), X)), X)
6.57/6.83	= { by lemma 12 }
6.57/6.83	  meet(meet(meet(join(X, ?), join(?, X)), join(join(meet(X, ?), meet(?, X)), meet(meet(join(X, ?), join(?, X)), X))), X)
6.57/6.83	= { by lemma 12 }
6.57/6.83	  meet(meet(meet(join(X, ?), join(?, X)), join(join(meet(X, ?), meet(?, X)), meet(meet(join(X, ?), join(?, X)), X))), meet(meet(join(X, ?), join(?, X)), X))
6.57/6.83	= { by lemma 18 }
6.57/6.83	  meet(meet(join(X, ?), join(?, X)), X)
6.57/6.83	= { by lemma 12 }
6.57/6.83	  X
6.57/6.83	
6.57/6.83	Lemma 20: meet(meet(X, X), meet(X, join(Y, X))) = meet(X, join(Y, X)).
6.57/6.83	Proof:
6.57/6.83	  meet(meet(X, X), meet(X, join(Y, X)))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  meet(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(X, join(Y, X)))
6.57/6.83	= { by lemma 18 }
6.57/6.83	  meet(X, join(Y, X))
6.57/6.83	
6.57/6.83	Lemma 21: join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), Y)) = meet(X, Y).
6.57/6.83	Proof:
6.57/6.83	  join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), Y))
6.57/6.83	= { by lemma 9 }
6.57/6.83	  join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(X, Y)))))
6.57/6.83	= { by lemma 5 }
8.09/8.26	  meet(X, Y)
8.09/8.26	
8.09/8.26	Lemma 22: join(X, X) = X.
8.09/8.26	Proof:
8.09/8.26	  join(X, X)
8.09/8.26	= { by lemma 14 }
8.09/8.26	  join(meet(meet(X, join(X, X)), X), X)
8.09/8.26	= { by lemma 15 }
8.09/8.26	  join(meet(meet(X, meet(X, join(X, X))), X), X)
8.09/8.26	= { by lemma 19 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), X), X)
8.09/8.26	= { by lemma 19 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(X, X)), X)
8.09/8.26	= { by lemma 19 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), X)
8.09/8.26	= { by lemma 19 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(X, X))
8.09/8.26	= { by lemma 14 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(X, join(X, X)), meet(X, X))), meet(X, X)))
8.09/8.26	= { by lemma 15 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(X, meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.26	= { by lemma 14 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(X, join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.26	= { by lemma 11 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), X)))), join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.26	= { by lemma 9 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), X)))), join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.26	= { by lemma 9 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), X)))), join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.26	= { by lemma 9 }
8.09/8.26	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), X)))), join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.26	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, X)), X)))), join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), X)))), join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(X, X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, X), meet(X, join(?, X))), X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 18 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(join(meet(?, join(join(meet(X, ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), join(meet(?, X), meet(X, join(?, X))))))), join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), X)))), join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 11 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 2 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(join(meet(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(join(meet(?, join(join(meet(X, ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), join(meet(?, X), meet(X, join(?, X))))), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(join(meet(?, X), meet(X, join(?, X))), ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, join(meet(?, X), meet(X, join(?, X))))), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), join(meet(?, X), meet(X, join(?, X))))))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(join(meet(?, join(join(meet(X, ?), meet(?, X)), X)), meet(X, join(?, join(join(meet(X, ?), meet(?, X)), X)))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 11 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(join(meet(?, X), meet(X, join(?, X))), X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), X), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 14 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(X, join(X, X))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 15 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(X, meet(X, join(X, X)))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 14 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), meet(X, join(X, X)))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), meet(join(meet(?, X), meet(X, join(?, X))), join(X, X)))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.27	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, X), meet(X, join(?, X))), X)))), meet(X, X))), meet(X, X)))
8.09/8.27	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)))), meet(X, X))), meet(X, X)))
8.09/8.28	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))), meet(meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.28	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(join(meet(?, X), meet(X, join(?, X))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))), meet(meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.28	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))), meet(meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.28	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))), meet(meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.28	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(join(meet(?, X), meet(X, join(?, X))), X))), meet(meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.28	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.28	= { by lemma 9 }
8.09/8.28	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(join(meet(?, X), meet(X, join(?, X))), X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), join(meet(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(join(meet(?, X), meet(X, join(?, X))), join(?, join(meet(?, X), meet(X, join(?, X)))))), join(meet(?, X), meet(X, join(?, X)))))), X))))))), meet(X, X))), meet(X, X)))
8.09/8.29	= { by lemma 3 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), join(meet(?, X), meet(X, join(?, X))))))), meet(X, X))), meet(X, X)))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)))), meet(X, X))), meet(X, X)))
8.09/8.29	= { by lemma 14 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)))), meet(meet(meet(X, join(X, X)), X), X))), meet(X, X)))
8.09/8.29	= { by lemma 20 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)))), meet(meet(meet(meet(X, X), meet(X, join(X, X))), X), X))), meet(X, X)))
8.09/8.29	= { by lemma 14 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)))), meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), X))), meet(X, X)))
8.09/8.29	= { by lemma 14 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), join(meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(meet(X, join(X, X)), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)))), meet(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X)), meet(meet(X, join(X, X)), X)))), meet(X, X)))
8.09/8.29	= { by lemma 21 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, join(X, X)), X))), meet(X, X)))
8.09/8.29	= { by lemma 20 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(meet(X, join(X, X)), meet(meet(X, join(X, X)), X))), meet(X, X)))
8.09/8.29	= { by lemma 14 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(meet(X, join(X, X)), X)), meet(X, X)))
8.09/8.29	= { by lemma 14 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), X), meet(X, X)))
8.09/8.29	= { by lemma 5 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), join(meet(X, X), meet(X, join(X, X)))))))
8.09/8.29	= { by lemma 5 }
8.09/8.29	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(meet(meet(X, X), X), join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X))))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  meet(meet(X, X), X)
8.09/8.29	= { by lemma 19 }
8.09/8.29	  meet(X, X)
8.09/8.29	= { by lemma 19 }
8.09/8.29	  X
8.09/8.29	
8.09/8.29	Lemma 23: join(join(meet(X, Y), X), X) = X.
8.09/8.29	Proof:
8.09/8.29	  join(join(meet(X, Y), X), X)
8.09/8.29	= { by lemma 12 }
8.09/8.29	  join(join(meet(X, Y), meet(meet(join(X, ?), join(?, X)), X)), X)
8.09/8.29	= { by lemma 17 }
8.09/8.29	  X
8.09/8.29	
8.09/8.29	Lemma 24: meet(join(meet(X, Y), X), X) = join(meet(X, Y), X).
8.09/8.29	Proof:
8.09/8.29	  meet(join(meet(X, Y), X), X)
8.09/8.29	= { by lemma 22 }
8.09/8.29	  join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), X))
8.09/8.29	= { by lemma 23 }
8.09/8.29	  join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))
8.09/8.29	= { by lemma 5 }
8.09/8.29	  join(meet(X, Y), X)
8.09/8.29	
8.09/8.29	Lemma 25: join(meet(meet(Y, X), meet(X, join(Y, X))), X) = meet(X, join(Y, X)).
8.09/8.29	Proof:
8.09/8.29	  join(meet(meet(Y, X), meet(X, join(Y, X))), X)
8.09/8.29	= { by lemma 14 }
8.09/8.29	  join(meet(meet(Y, X), meet(X, join(Y, X))), meet(meet(X, join(Y, X)), X))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  join(meet(meet(Y, X), meet(X, join(Y, X))), meet(meet(X, join(Y, X)), join(meet(Y, X), meet(X, join(Y, X)))))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  meet(X, join(Y, X))
8.09/8.29	
8.09/8.29	Lemma 26: meet(X, join(join(X, Y), X)) = meet(join(X, Y), X).
8.09/8.29	Proof:
8.09/8.29	  meet(X, join(join(X, Y), X))
8.09/8.29	= { by lemma 25 }
8.09/8.29	  join(meet(meet(join(X, Y), X), meet(X, join(join(X, Y), X))), X)
8.09/8.29	= { by lemma 12 }
8.09/8.29	  join(meet(meet(join(X, Y), X), meet(X, join(join(X, Y), X))), meet(meet(join(X, Y), join(join(meet(X, ?), meet(?, X)), X)), X))
8.09/8.29	= { by lemma 17 }
8.09/8.29	  join(meet(meet(join(X, Y), X), meet(X, join(join(X, Y), X))), meet(meet(join(X, Y), X), X))
8.09/8.29	= { by lemma 21 }
8.09/8.29	  meet(join(X, Y), X)
8.09/8.29	
8.09/8.29	Lemma 27: meet(join(X, Y), X) = X.
8.09/8.29	Proof:
8.09/8.29	  meet(join(X, Y), X)
8.09/8.29	= { by lemma 22 }
8.09/8.29	  join(meet(join(X, Y), X), meet(join(X, Y), X))
8.09/8.29	= { by lemma 26 }
8.09/8.29	  join(meet(join(X, Y), X), meet(X, join(join(X, Y), X)))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  X
8.09/8.29	
8.09/8.29	Lemma 28: meet(X, join(meet(X, join(Y, X)), X)) = X.
8.09/8.29	Proof:
8.09/8.29	  meet(X, join(meet(X, join(Y, X)), X))
8.09/8.29	= { by lemma 14 }
8.09/8.29	  meet(meet(meet(X, join(Y, X)), X), join(meet(X, join(Y, X)), X))
8.09/8.29	= { by lemma 14 }
8.09/8.29	  meet(meet(meet(X, join(Y, X)), X), join(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)))
8.09/8.29	= { by lemma 25 }
8.09/8.29	  join(meet(meet(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)), meet(meet(meet(X, join(Y, X)), X), join(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)))), meet(meet(X, join(Y, X)), X))
8.09/8.29	= { by lemma 18 }
8.09/8.29	  join(meet(meet(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)), meet(meet(meet(X, join(Y, X)), X), join(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)))), meet(meet(meet(X, join(Y, X)), join(join(meet(meet(meet(X, join(Y, X)), X), ?), meet(?, meet(meet(X, join(Y, X)), X))), meet(meet(X, join(Y, X)), X))), meet(meet(X, join(Y, X)), X)))
8.09/8.29	= { by lemma 17 }
8.09/8.29	  join(meet(meet(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)), meet(meet(meet(X, join(Y, X)), X), join(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)))), meet(meet(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)), meet(meet(X, join(Y, X)), X)))
8.09/8.29	= { by lemma 21 }
8.09/8.29	  meet(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X))
8.09/8.29	= { by lemma 5 }
8.09/8.29	  meet(join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(meet(X, join(Y, X)), X))), meet(meet(X, join(Y, X)), X))
8.09/8.29	= { by lemma 27 }
8.09/8.29	  meet(meet(X, join(Y, X)), X)
8.09/8.29	= { by lemma 14 }
8.09/8.29	  X
8.09/8.29	
8.09/8.29	Lemma 29: meet(X, join(Y, X)) = X.
8.09/8.29	Proof:
8.09/8.29	  meet(X, join(Y, X))
8.09/8.29	= { by lemma 5 }
8.09/8.29	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(meet(X, join(Y, X)), X)))
8.09/8.29	= { by lemma 24 }
8.09/8.29	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), meet(join(meet(X, join(Y, X)), X), X)))
8.09/8.29	= { by lemma 24 }
8.09/8.29	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), meet(meet(join(meet(X, join(Y, X)), X), X), X)))
8.09/8.29	= { by lemma 9 }
8.09/8.29	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), meet(meet(join(meet(X, join(Y, X)), X), join(meet(meet(X, join(Y, X)), X), meet(X, join(meet(X, join(Y, X)), X)))), X)))
8.09/8.29	= { by lemma 28 }
8.09/8.29	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), meet(meet(join(meet(X, join(Y, X)), X), join(meet(meet(X, join(Y, X)), X), meet(X, join(meet(X, join(Y, X)), X)))), meet(X, join(meet(X, join(Y, X)), X)))))
8.09/8.29	= { by lemma 13 }
8.09/8.29	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), meet(X, join(meet(X, join(Y, X)), X))))
8.09/8.29	= { by lemma 28 }
8.09/8.29	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), X))
8.09/8.29	= { by lemma 22 }
8.09/8.29	  meet(meet(X, join(Y, X)), X)
8.09/8.29	= { by lemma 14 }
8.09/8.29	  X
8.09/8.29	
8.09/8.29	Lemma 30: meet(join(Y, X), X) = X.
8.09/8.29	Proof:
8.09/8.29	  meet(join(Y, X), X)
8.09/8.29	= { by lemma 9 }
8.09/8.29	  meet(join(meet(X, join(Y, X)), meet(join(Y, X), join(X, join(Y, X)))), X)
8.09/8.29	= { by lemma 29 }
8.09/8.29	  meet(join(meet(X, join(Y, X)), meet(join(Y, X), join(X, join(Y, X)))), meet(X, join(Y, X)))
8.09/8.29	= { by lemma 27 }
8.09/8.29	  meet(X, join(Y, X))
8.09/8.29	= { by lemma 29 }
8.09/8.29	  X
8.09/8.29	
8.09/8.29	Lemma 31: join(X, meet(Y, X)) = X.
8.09/8.29	Proof:
8.09/8.29	  join(X, meet(Y, X))
8.09/8.29	= { by lemma 5 }
8.09/8.29	  join(meet(join(X, meet(Y, X)), X), meet(join(X, meet(Y, X)), join(join(X, meet(Y, X)), X)))
8.09/8.29	= { by lemma 19 }
8.09/8.29	  join(meet(join(X, meet(Y, X)), X), meet(join(X, meet(Y, X)), join(join(meet(X, X), meet(Y, X)), X)))
8.09/8.29	= { by lemma 17 }
8.09/8.29	  join(meet(join(X, meet(Y, X)), X), meet(join(X, meet(Y, X)), X))
8.09/8.29	= { by lemma 22 }
8.09/8.29	  meet(join(X, meet(Y, X)), X)
8.09/8.29	= { by lemma 27 }
8.09/8.29	  X
8.09/8.29	
8.09/8.29	Lemma 32: join(join(X, Y), X) = join(X, Y).
8.09/8.29	Proof:
8.09/8.29	  join(join(X, Y), X)
8.09/8.29	= { by lemma 5 }
8.09/8.29	  join(join(X, Y), join(meet(X, join(X, Y)), meet(X, join(X, join(X, Y)))))
8.09/8.29	= { by lemma 31 }
8.09/8.29	  join(join(X, Y), join(meet(X, join(X, Y)), meet(X, join(join(X, join(X, Y)), meet(join(X, Y), join(X, join(X, Y)))))))
8.09/8.29	= { by lemma 27 }
8.09/8.29	  join(join(X, Y), join(meet(X, join(X, Y)), meet(X, join(join(meet(join(X, Y), X), join(X, Y)), meet(join(X, Y), join(X, join(X, Y)))))))
8.09/8.29	= { by lemma 29 }
8.09/8.29	  join(join(X, Y), join(meet(X, join(X, Y)), meet(X, join(join(meet(join(X, Y), X), join(X, Y)), join(X, Y)))))
8.09/8.29	= { by lemma 23 }
8.09/8.29	  join(join(X, Y), join(meet(X, join(X, Y)), meet(X, join(X, Y))))
8.09/8.29	= { by lemma 22 }
8.09/8.29	  join(join(X, Y), meet(X, join(X, Y)))
8.09/8.29	= { by lemma 31 }
8.09/8.29	  join(X, Y)
8.09/8.29	
8.09/8.29	Lemma 33: meet(join(X, Y), join(Y, X)) = join(X, Y).
8.09/8.29	Proof:
8.09/8.29	  meet(join(X, Y), join(Y, X))
8.09/8.29	= { by lemma 30 }
8.09/8.29	  meet(join(meet(join(Y, X), X), Y), join(Y, X))
8.09/8.29	= { by lemma 32 }
8.09/8.29	  meet(join(meet(join(join(Y, X), Y), X), Y), join(Y, X))
8.09/8.29	= { by lemma 27 }
8.09/8.29	  meet(join(meet(join(join(Y, X), Y), X), meet(join(Y, X), Y)), join(Y, X))
8.09/8.29	= { by lemma 26 }
8.09/8.29	  meet(join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y))), join(Y, X))
8.09/8.29	= { by lemma 32 }
8.09/8.29	  meet(join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y))), join(join(Y, X), Y))
8.09/8.29	= { by lemma 22 }
8.09/8.29	  join(meet(join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y))), join(join(Y, X), Y)), meet(join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y))), join(join(Y, X), Y)))
8.09/8.29	= { by lemma 17 }
8.09/8.29	  join(meet(join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y))), join(join(Y, X), Y)), meet(join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y))), join(join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y))), join(join(Y, X), Y))))
8.09/8.29	= { by lemma 5 }
8.09/8.29	  join(meet(join(join(Y, X), Y), X), meet(Y, join(join(Y, X), Y)))
8.09/8.29	= { by lemma 32 }
8.09/8.29	  join(meet(join(Y, X), X), meet(Y, join(join(Y, X), Y)))
8.09/8.29	= { by lemma 30 }
8.09/8.29	  join(X, meet(Y, join(join(Y, X), Y)))
8.09/8.29	= { by lemma 26 }
8.09/8.29	  join(X, meet(join(Y, X), Y))
8.09/8.29	= { by lemma 27 }
8.09/8.30	  join(X, Y)
8.09/8.30	
8.09/8.30	Goal 1 (prove_wal_axioms_4): join(b, a) = join(a, b).
8.09/8.30	Proof:
8.09/8.30	  join(b, a)
8.09/8.30	= { by lemma 33 }
8.09/8.30	  meet(join(b, a), join(a, b))
8.09/8.30	= { by lemma 21 }
8.09/8.30	  join(meet(meet(join(b, a), join(a, b)), meet(join(a, b), join(join(b, a), join(a, b)))), meet(meet(join(b, a), join(a, b)), join(a, b)))
8.09/8.30	= { by lemma 29 }
8.09/8.30	  join(meet(meet(join(b, a), join(a, b)), join(a, b)), meet(meet(join(b, a), join(a, b)), join(a, b)))
8.09/8.30	= { by lemma 22 }
8.09/8.30	  meet(meet(join(b, a), join(a, b)), join(a, b))
8.09/8.30	= { by lemma 9 }
8.09/8.30	  meet(meet(join(meet(join(a, b), join(b, a)), meet(join(b, a), join(join(a, b), join(b, a)))), join(a, b)), join(a, b))
8.09/8.30	= { by lemma 14 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), meet(join(a, b), join(b, a))), meet(join(b, a), join(join(a, b), join(b, a)))), join(a, b)), join(a, b))
8.09/8.30	= { by lemma 9 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), join(a, b)), join(a, b))
8.09/8.30	= { by lemma 29 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), meet(join(a, b), join(?, join(a, b)))), join(a, b))
8.09/8.30	= { by lemma 33 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), meet(meet(join(a, b), join(b, a)), join(?, join(a, b)))), join(a, b))
8.09/8.30	= { by lemma 33 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a))))), join(a, b))
8.09/8.30	= { by lemma 9 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), join(meet(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a))))), meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))))), join(a, b))
8.09/8.30	= { by lemma 33 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), join(meet(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a))))), meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))))), meet(join(a, b), join(b, a)))
8.09/8.30	= { by lemma 14 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), join(meet(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a))))), meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))))), meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), meet(join(a, b), join(b, a))))
8.09/8.30	= { by lemma 9 }
8.09/8.30	  meet(meet(join(meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))), meet(join(b, a), join(join(a, b), join(b, a)))), join(meet(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a))))), meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))))), meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))))))
8.09/8.30	= { by lemma 12 }
8.09/8.30	  meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), join(meet(?, meet(join(a, b), join(b, a))), meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a))))))
8.09/8.30	= { by lemma 9 }
8.09/8.30	  meet(meet(meet(join(a, b), join(b, a)), join(?, meet(join(a, b), join(b, a)))), meet(join(a, b), join(b, a)))
8.09/8.30	= { by lemma 14 }
8.09/8.30	  meet(join(a, b), join(b, a))
8.09/8.30	= { by lemma 33 }
8.09/8.30	  join(a, b)
8.09/8.30	% SZS output end Proof
8.09/8.30	
8.09/8.30	RESULT: Unsatisfiable (the axioms are contradictory).
8.09/8.30	EOF