0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.34	% Computer   : n010.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 180
0.12/0.34	% DateTime   : Thu Aug 29 12:11:21 EDT 2019
0.12/0.34	% CPUTime    : 
3.90/4.08	% SZS status Unsatisfiable
3.90/4.08	
3.90/4.08	% SZS output start Proof
3.90/4.08	Take the following subset of the input axioms:
3.90/4.08	  fof(prove_wal_axioms_5, negated_conjecture, meet(meet(join(a, b), join(c, b)), b)!=b).
3.90/4.08	  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)))).
3.90/4.08	
3.90/4.08	Now clausify the problem and encode Horn clauses using encoding 3 of
3.90/4.08	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
3.90/4.08	We repeatedly replace C & s=t => u=v by the two clauses:
3.90/4.08	  fresh(y, y, x1...xn) = u
3.90/4.08	  C => fresh(s, t, x1...xn) = v
3.90/4.08	where fresh is a fresh function symbol and x1..xn are the free
3.90/4.08	variables of u and v.
3.90/4.08	A predicate p(X) is encoded as p(X)=true (this is sound, because the
3.90/4.08	input problem has no model of domain size 1).
3.90/4.08	
3.90/4.08	The encoding turns the above axioms into the following unit equations and goals:
3.90/4.08	
5.32/5.53	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))).
5.32/5.53	
5.32/5.53	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))).
5.32/5.53	Proof:
5.32/5.53	  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)))
5.32/5.53	= { by axiom 1 (single_axiom) }
5.32/5.53	  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)))
5.32/5.53	= { by axiom 1 (single_axiom) }
5.60/5.83	  join(meet(X, Y), meet(Y, join(X, Y)))
5.60/5.83	
5.60/5.83	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))).
5.60/5.83	Proof:
5.60/5.83	  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)))
5.60/5.83	= { by lemma 2 }
5.60/5.83	  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)))
5.60/5.83	= { by lemma 2 }
5.60/5.83	  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)))
5.60/5.83	= { by lemma 2 }
5.60/5.83	  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)))
5.60/5.83	= { by lemma 2 }
5.60/5.84	  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)))
5.60/5.84	= { by lemma 2 }
5.60/5.85	  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)))
5.60/5.85	= { by lemma 2 }
5.60/5.85	  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)))
5.60/5.85	= { by lemma 2 }
5.70/5.86	  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)))
5.70/5.86	= { by lemma 2 }
5.70/5.87	  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)))
5.70/5.87	= { by lemma 2 }
5.70/5.87	  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), 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(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)))
5.70/5.88	= { by lemma 2 }
5.70/5.89	  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))))), 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(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)))
5.70/5.89	= { by lemma 2 }
5.73/5.90	  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)))), 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)))
5.73/5.90	= { by lemma 2 }
5.73/5.91	  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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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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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))), 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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)))
5.73/5.91	= { by lemma 2 }
5.73/5.92	  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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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), 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)))
5.73/5.92	= { by lemma 2 }
5.73/5.92	  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))))))))))
5.73/5.92	= { by lemma 2 }
5.73/5.93	  join(meet(X, Y), meet(Y, join(X, Y)))
5.73/5.93	
5.73/5.93	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))).
5.73/5.93	Proof:
5.73/5.93	  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)))
5.73/5.93	= { by lemma 3 }
5.73/5.93	  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)))
5.73/5.93	= { by lemma 3 }
5.73/5.93	  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)))
5.73/5.93	= { by lemma 3 }
5.77/5.93	  join(meet(X, Y), meet(Y, join(X, Y)))
5.77/5.93	
5.77/5.93	Lemma 5: join(meet(Y, U), meet(Y, join(Y, U))) = Y.
5.77/5.93	Proof:
5.77/5.93	  join(meet(Y, U), meet(Y, join(Y, U)))
5.77/5.93	= { by axiom 1 (single_axiom) }
5.77/5.93	  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)))
5.77/5.93	= { by axiom 1 (single_axiom) }
5.77/5.93	  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)))
5.77/5.93	= { by axiom 1 (single_axiom) }
5.77/5.93	  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)))
5.77/5.93	= { by lemma 4 }
5.77/5.93	  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)))))))
5.77/5.93	= { by axiom 1 (single_axiom) }
6.15/6.32	  Y
6.15/6.32	
6.15/6.32	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.
6.15/6.32	Proof:
6.15/6.32	  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)))
6.15/6.32	= { by axiom 1 (single_axiom) }
6.15/6.32	  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)))
6.15/6.32	= { by axiom 1 (single_axiom) }
6.15/6.32	  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)))
6.15/6.32	= { by axiom 1 (single_axiom) }
6.15/6.32	  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)))
6.15/6.32	= { by axiom 1 (single_axiom) }
6.15/6.32	  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)))
6.15/6.32	= { by axiom 1 (single_axiom) }
6.15/6.33	  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)))
6.15/6.33	= { by axiom 1 (single_axiom) }
6.15/6.33	  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)))
6.15/6.33	= { by axiom 1 (single_axiom) }
6.15/6.33	  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)))
6.15/6.33	= { by axiom 1 (single_axiom) }
6.15/6.34	  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)))
6.15/6.34	= { by axiom 1 (single_axiom) }
6.15/6.35	  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)))
6.15/6.35	= { by axiom 1 (single_axiom) }
6.15/6.35	  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)))
6.15/6.35	= { by axiom 1 (single_axiom) }
6.15/6.36	  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)))
6.15/6.36	= { by axiom 1 (single_axiom) }
6.15/6.36	  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)))
6.15/6.37	= { by axiom 1 (single_axiom) }
6.15/6.37	  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)))
6.15/6.37	= { by axiom 1 (single_axiom) }
6.22/6.38	  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)))
6.22/6.38	= { by axiom 1 (single_axiom) }
6.22/6.39	  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)))
6.22/6.39	= { by axiom 1 (single_axiom) }
6.22/6.40	  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)))
6.22/6.40	= { by axiom 1 (single_axiom) }
6.22/6.41	  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)))
6.22/6.41	= { by axiom 1 (single_axiom) }
6.22/6.42	  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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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(?, 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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, meet(meet(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)))
6.22/6.42	= { by axiom 1 (single_axiom) }
6.22/6.43	  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, 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Y)), meet(join(meet(Y, meet(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, 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)))
6.22/6.43	= { by lemma 3 }
6.22/6.43	  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)))))))
6.22/6.43	= { by axiom 1 (single_axiom) }
6.22/6.46	  Y
6.22/6.46	
6.22/6.46	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.
6.22/6.46	Proof:
6.22/6.46	  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)))
6.22/6.46	= { by lemma 6 }
6.22/6.46	  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)))
6.22/6.46	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.22/6.47	  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)))
6.22/6.47	= { by lemma 6 }
6.32/6.47	  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)))
6.32/6.47	= { by lemma 6 }
6.32/6.47	  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)))
6.32/6.48	= { by lemma 6 }
6.32/6.48	  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)))
6.32/6.48	= { by lemma 2 }
6.32/6.48	  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)))
6.32/6.48	= { by lemma 6 }
6.32/6.48	  Y
6.32/6.48	
6.32/6.48	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))).
6.32/6.48	Proof:
6.32/6.48	  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)))
6.32/6.48	= { by lemma 5 }
6.32/6.48	  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)))
6.32/6.48	= { by lemma 2 }
6.32/6.48	  join(meet(X, Y), meet(Y, join(X, Y)))
6.32/6.48	
6.32/6.48	Lemma 9: join(meet(Y, X), meet(X, join(Y, X))) = X.
6.32/6.48	Proof:
6.32/6.48	  join(meet(Y, X), meet(X, join(Y, X)))
6.32/6.48	= { by lemma 4 }
6.32/6.48	  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))), ?)))
6.32/6.48	= { by lemma 8 }
6.32/6.48	  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))), ?)))
6.32/6.48	= { by lemma 8 }
6.32/6.48	  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))), ?)))
6.32/6.48	= { by lemma 8 }
6.32/6.48	  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))), ?)))
6.32/6.48	= { by lemma 7 }
6.32/6.48	  X
6.32/6.48	
6.32/6.48	Lemma 10: join(meet(X, W), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, W))) = X.
6.32/6.48	Proof:
6.32/6.48	  join(meet(X, W), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, W)))
6.32/6.48	= { by lemma 9 }
6.32/6.48	  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)))
6.32/6.48	= { by lemma 9 }
6.32/6.48	  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)))
6.32/6.48	= { by lemma 4 }
6.32/6.48	  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)))
6.32/6.48	= { by lemma 9 }
6.32/6.48	  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)))
6.32/6.48	= { by axiom 1 (single_axiom) }
6.32/6.49	  X
6.32/6.49	
6.32/6.49	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.
6.32/6.49	Proof:
6.32/6.49	  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))))
6.32/6.49	= { by lemma 7 }
6.32/6.49	  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))))))), ?)))
6.32/6.49	= { by lemma 7 }
6.32/6.49	  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))))))), ?)))
6.32/6.49	= { by lemma 7 }
6.32/6.49	  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))))))), ?)))
6.32/6.49	= { by lemma 7 }
6.32/6.49	  join(meet(Y, ?), meet(Y, join(Y, ?)))
6.32/6.49	= { by lemma 5 }
6.32/6.49	  Y
6.32/6.49	
6.32/6.49	Lemma 12: meet(meet(join(X, Y), join(Z, X)), X) = X.
6.32/6.49	Proof:
6.32/6.49	  meet(meet(join(X, Y), join(Z, X)), X)
6.32/6.49	= { by lemma 7 }
6.32/6.49	  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)))), ?)))
6.32/6.49	= { by lemma 10 }
6.32/6.49	  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)))), ?)))
6.32/6.49	= { by lemma 11 }
6.32/6.49	  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)))), ?)))
6.32/6.49	= { by lemma 10 }
6.32/6.49	  join(meet(X, ?), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, ?)))
6.32/6.49	= { by lemma 10 }
6.32/6.49	  X
6.32/6.49	
6.32/6.49	Lemma 13: meet(meet(Y, join(Z, meet(X, Y))), meet(X, Y)) = meet(X, Y).
6.32/6.49	Proof:
6.32/6.49	  meet(meet(Y, join(Z, meet(X, Y))), meet(X, Y))
6.32/6.49	= { by lemma 9 }
6.32/6.49	  meet(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, meet(X, Y))), meet(X, Y))
6.32/6.49	= { by lemma 12 }
6.32/6.49	  meet(X, Y)
6.32/6.49	
6.32/6.49	Lemma 14: meet(meet(X, join(W, X)), X) = X.
6.32/6.49	Proof:
6.32/6.49	  meet(meet(X, join(W, X)), X)
6.32/6.49	= { by lemma 12 }
6.32/6.49	  meet(meet(X, join(W, meet(meet(join(X, ?), join(?, X)), X))), X)
6.32/6.49	= { by lemma 12 }
6.32/6.49	  meet(meet(X, join(W, meet(meet(join(X, ?), join(?, X)), X))), meet(meet(join(X, ?), join(?, X)), X))
6.32/6.49	= { by lemma 13 }
6.32/6.49	  meet(meet(join(X, ?), join(?, X)), X)
6.32/6.49	= { by lemma 12 }
6.32/6.49	  X
6.32/6.49	
6.32/6.49	Lemma 15: meet(X, meet(X, join(Y, X))) = meet(X, join(Y, X)).
6.32/6.49	Proof:
6.32/6.49	  meet(X, meet(X, join(Y, X)))
6.32/6.49	= { by lemma 14 }
6.32/6.49	  meet(meet(meet(X, join(Y, X)), X), meet(X, join(Y, X)))
6.32/6.49	= { by lemma 9 }
6.32/6.49	  meet(meet(meet(X, join(Y, X)), join(meet(Y, X), meet(X, join(Y, X)))), meet(X, join(Y, X)))
6.32/6.49	= { by lemma 14 }
6.32/6.49	  meet(X, join(Y, X))
6.32/6.49	
6.32/6.49	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.
6.32/6.49	Proof:
6.32/6.49	  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)))
6.32/6.49	= { by lemma 9 }
6.32/6.49	  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)))
6.32/6.49	= { by lemma 12 }
6.32/6.49	  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)))
6.32/6.49	= { by lemma 12 }
6.32/6.49	  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)))
6.32/6.49	= { by lemma 9 }
6.32/6.49	  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)))
6.32/6.49	= { by axiom 1 (single_axiom) }
6.34/6.49	  X
6.34/6.49	
6.34/6.49	Lemma 17: join(join(meet(X, Y), meet(Z, X)), X) = X.
6.34/6.49	Proof:
6.34/6.49	  join(join(meet(X, Y), meet(Z, X)), X)
6.34/6.49	= { by lemma 16 }
6.34/6.49	  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))))
6.34/6.49	= { by lemma 16 }
6.34/6.49	  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))))
6.34/6.49	= { by lemma 11 }
6.34/6.49	  X
6.34/6.49	
6.34/6.49	Lemma 18: meet(meet(Y, join(W, meet(Y, Z))), meet(Y, Z)) = meet(Y, Z).
6.34/6.49	Proof:
6.34/6.49	  meet(meet(Y, join(W, meet(Y, Z))), meet(Y, Z))
6.34/6.49	= { by axiom 1 (single_axiom) }
6.34/6.49	  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))
6.34/6.49	= { by lemma 9 }
6.34/6.49	  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))
6.34/6.49	= { by lemma 9 }
6.34/6.49	  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))
6.34/6.49	= { by lemma 12 }
6.34/6.49	  meet(join(meet(?, Y), meet(Y, join(?, Y))), Z)
6.34/6.49	= { by lemma 9 }
6.34/6.49	  meet(Y, Z)
6.34/6.49	
6.34/6.49	Lemma 19: meet(X, X) = X.
6.34/6.49	Proof:
6.34/6.49	  meet(X, X)
6.34/6.49	= { by lemma 12 }
6.34/6.49	  meet(meet(meet(join(X, ?), join(?, X)), X), X)
6.34/6.49	= { by lemma 17 }
6.34/6.49	  meet(meet(meet(join(X, ?), join(?, X)), join(join(meet(X, ?), meet(?, X)), X)), X)
6.34/6.49	= { by lemma 12 }
6.34/6.49	  meet(meet(meet(join(X, ?), join(?, X)), join(join(meet(X, ?), meet(?, X)), meet(meet(join(X, ?), join(?, X)), X))), X)
6.34/6.49	= { by lemma 12 }
6.34/6.49	  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))
6.34/6.49	= { by lemma 18 }
6.34/6.49	  meet(meet(join(X, ?), join(?, X)), X)
6.34/6.49	= { by lemma 12 }
6.34/6.49	  X
6.34/6.49	
6.34/6.49	Lemma 20: meet(meet(X, X), meet(X, join(Y, X))) = meet(X, join(Y, X)).
6.34/6.49	Proof:
6.34/6.49	  meet(meet(X, X), meet(X, join(Y, X)))
6.34/6.49	= { by lemma 9 }
6.34/6.49	  meet(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(X, join(Y, X)))
6.34/6.49	= { by lemma 18 }
6.34/6.49	  meet(X, join(Y, X))
6.34/6.49	
6.34/6.49	Lemma 21: join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), Y)) = meet(X, Y).
6.34/6.49	Proof:
6.34/6.49	  join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), Y))
6.34/6.49	= { by lemma 9 }
6.34/6.49	  join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(X, Y)))))
6.34/6.49	= { by lemma 5 }
7.67/7.87	  meet(X, Y)
7.67/7.87	
7.67/7.87	Lemma 22: join(X, X) = X.
7.67/7.87	Proof:
7.67/7.87	  join(X, X)
7.67/7.87	= { by lemma 14 }
7.67/7.87	  join(meet(meet(X, join(X, X)), X), X)
7.67/7.87	= { by lemma 15 }
7.67/7.87	  join(meet(meet(X, meet(X, join(X, X))), X), X)
7.67/7.87	= { by lemma 19 }
7.67/7.87	  join(meet(meet(meet(X, X), meet(X, join(X, X))), X), X)
7.67/7.87	= { by lemma 19 }
7.67/7.87	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(X, X)), X)
7.67/7.87	= { by lemma 19 }
7.67/7.87	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), X)
7.67/7.87	= { by lemma 19 }
7.67/7.87	  join(meet(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X)), meet(X, X))
7.67/7.87	= { by lemma 14 }
7.67/7.87	  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)))
7.67/7.87	= { by lemma 15 }
7.67/7.87	  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)))
7.67/7.87	= { by lemma 14 }
7.67/7.87	  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)))
7.67/7.87	= { by lemma 11 }
7.67/7.87	  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)))
7.67/7.87	= { by lemma 9 }
7.67/7.87	  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)))
7.67/7.87	= { by lemma 9 }
7.67/7.88	  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)))
7.67/7.88	= { by lemma 9 }
7.67/7.88	  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)))
7.67/7.88	= { by lemma 9 }
7.67/7.88	  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)))
7.67/7.88	= { by lemma 9 }
7.67/7.88	  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)))
7.67/7.88	= { by lemma 9 }
7.67/7.88	  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)))
7.67/7.88	= { by lemma 9 }
7.67/7.88	  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)))
7.67/7.88	= { by lemma 9 }
7.67/7.88	  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)))
7.67/7.88	= { by lemma 18 }
7.72/7.88	  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)))
7.72/7.88	= { by lemma 9 }
7.72/7.88	  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)))
7.72/7.88	= { by lemma 9 }
7.72/7.88	  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)))
7.72/7.88	= { by lemma 9 }
7.72/7.88	  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)))
7.72/7.88	= { by lemma 9 }
7.72/7.88	  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)))
7.72/7.88	= { by lemma 9 }
7.72/7.88	  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)))
7.72/7.88	= { by lemma 9 }
7.72/7.88	  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)))
7.72/7.89	= { by lemma 11 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 2 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 11 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 14 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 15 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 14 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.89	  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)))
7.72/7.89	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 3 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 14 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 20 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 14 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 14 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 21 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 20 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 14 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 14 }
7.72/7.90	  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)))
7.72/7.90	= { by lemma 5 }
7.72/7.90	  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)))))))
7.72/7.90	= { by lemma 5 }
7.72/7.90	  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))))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  meet(meet(X, X), X)
7.72/7.90	= { by lemma 19 }
7.72/7.90	  meet(X, X)
7.72/7.90	= { by lemma 19 }
7.72/7.90	  X
7.72/7.90	
7.72/7.90	Lemma 23: meet(join(meet(X, Y), X), X) = join(meet(X, Y), X).
7.72/7.90	Proof:
7.72/7.90	  meet(join(meet(X, Y), X), X)
7.72/7.90	= { by lemma 22 }
7.72/7.90	  join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), X))
7.72/7.90	= { by lemma 17 }
7.72/7.90	  join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), meet(meet(join(X, ?), join(?, X)), X)), X)))
7.72/7.90	= { by lemma 12 }
7.72/7.90	  join(meet(join(meet(X, Y), X), X), meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))
7.72/7.90	= { by lemma 5 }
7.72/7.90	  join(meet(X, Y), X)
7.72/7.90	
7.72/7.90	Lemma 24: join(meet(meet(Y, X), meet(X, join(Y, X))), X) = meet(X, join(Y, X)).
7.72/7.90	Proof:
7.72/7.90	  join(meet(meet(Y, X), meet(X, join(Y, X))), X)
7.72/7.90	= { by lemma 14 }
7.72/7.90	  join(meet(meet(Y, X), meet(X, join(Y, X))), meet(meet(X, join(Y, X)), X))
7.72/7.90	= { by lemma 9 }
7.72/7.90	  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)))))
7.72/7.90	= { by lemma 9 }
7.72/7.91	  meet(X, join(Y, X))
7.72/7.91	
7.72/7.91	Lemma 25: meet(X, join(meet(X, join(Y, X)), X)) = X.
7.72/7.91	Proof:
7.72/7.91	  meet(X, join(meet(X, join(Y, X)), X))
7.72/7.91	= { by lemma 14 }
7.72/7.91	  meet(meet(meet(X, join(Y, X)), X), join(meet(X, join(Y, X)), X))
7.72/7.91	= { by lemma 14 }
7.72/7.91	  meet(meet(meet(X, join(Y, X)), X), join(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X)))
7.72/7.91	= { by lemma 24 }
7.72/7.91	  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))
7.72/7.91	= { by lemma 18 }
7.72/7.91	  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)))
7.72/7.91	= { by lemma 17 }
7.72/7.91	  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)))
7.72/7.91	= { by lemma 21 }
7.72/7.91	  meet(meet(X, join(Y, X)), meet(meet(X, join(Y, X)), X))
7.72/7.91	= { by lemma 5 }
7.72/7.91	  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))
7.72/7.91	= { by lemma 22 }
7.72/7.91	  join(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)), 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)))
7.72/7.91	= { by lemma 21 }
7.72/7.91	  join(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)), join(meet(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)), meet(meet(meet(X, join(Y, X)), X), join(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)))), meet(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)), meet(meet(X, join(Y, X)), X))))
7.72/7.91	= { by lemma 17 }
7.72/7.91	  join(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)), join(meet(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)), meet(meet(meet(X, join(Y, X)), X), join(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)))), meet(meet(join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(meet(X, join(Y, X)), 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))))
7.72/7.91	= { by lemma 12 }
7.72/7.91	  join(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)), join(meet(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)), meet(meet(meet(X, join(Y, X)), X), join(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)))), meet(meet(X, join(Y, X)), X)))
7.72/7.91	= { by lemma 24 }
7.72/7.91	  join(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)), meet(meet(meet(X, join(Y, X)), X), join(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))))
7.72/7.91	= { by lemma 9 }
7.72/7.91	  meet(meet(X, join(Y, X)), X)
7.72/7.91	= { by lemma 14 }
7.72/7.91	  X
7.72/7.91	
7.72/7.91	Lemma 26: meet(X, join(Y, X)) = X.
7.72/7.91	Proof:
7.72/7.91	  meet(X, join(Y, X))
7.72/7.91	= { by lemma 5 }
7.72/7.91	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(meet(X, join(Y, X)), X)))
7.72/7.91	= { by lemma 23 }
7.72/7.91	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), meet(join(meet(X, join(Y, X)), X), X)))
7.72/7.91	= { by lemma 23 }
7.72/7.91	  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)))
7.72/7.91	= { by lemma 9 }
7.72/7.91	  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)))
7.72/7.91	= { by lemma 25 }
7.72/7.91	  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)))))
7.72/7.91	= { by lemma 13 }
7.72/7.91	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), meet(X, join(meet(X, join(Y, X)), X))))
7.72/7.91	= { by lemma 25 }
7.72/7.91	  join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), X))
7.72/7.91	= { by lemma 22 }
7.72/7.91	  meet(meet(X, join(Y, X)), X)
7.72/7.91	= { by lemma 14 }
7.72/7.91	  X
7.72/7.91	
7.72/7.91	Goal 1 (prove_wal_axioms_5): meet(meet(join(a, b), join(c, b)), b) = b.
7.72/7.91	Proof:
7.72/7.91	  meet(meet(join(a, b), join(c, b)), b)
7.72/7.91	= { by lemma 26 }
7.72/7.91	  meet(meet(join(a, b), join(c, meet(b, join(a, b)))), b)
7.72/7.91	= { by lemma 26 }
7.72/7.91	  meet(meet(join(a, b), join(c, meet(b, join(a, b)))), meet(b, join(a, b)))
7.72/7.91	= { by lemma 13 }
7.72/7.91	  meet(b, join(a, b))
7.72/7.91	= { by lemma 26 }
7.72/7.91	  b
7.72/7.91	% SZS output end Proof
7.72/7.91	
7.72/7.91	RESULT: Unsatisfiable (the axioms are contradictory).
7.72/7.91	EOF