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   : n024.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 12:49:20 EDT 2019
0.12/0.34	% CPUTime    : 
2.48/2.65	% SZS status Unsatisfiable
2.48/2.65	
2.48/2.66	% SZS output start Proof
2.48/2.66	Take the following subset of the input axioms:
2.48/2.66	  fof(prove_normal_axioms_2, negated_conjecture, meet(a, b)!=meet(b, a)).
2.48/2.66	  fof(single_axiom, axiom, ![A, B, C, D, E, F, G]: join(meet(join(meet(A, B), meet(B, join(A, B))), C), meet(join(meet(A, join(join(meet(D, B), meet(B, E)), B)), meet(join(meet(B, meet(meet(join(D, join(B, E)), join(F, B)), B)), meet(G, join(B, meet(meet(join(D, join(B, E)), join(F, B)), B)))), join(A, join(join(meet(D, B), meet(B, E)), B)))), join(join(meet(A, B), meet(B, join(A, B))), C)))=B).
2.48/2.66	
2.48/2.66	Now clausify the problem and encode Horn clauses using encoding 3 of
2.48/2.66	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
2.48/2.66	We repeatedly replace C & s=t => u=v by the two clauses:
2.48/2.66	  fresh(y, y, x1...xn) = u
2.48/2.66	  C => fresh(s, t, x1...xn) = v
2.48/2.66	where fresh is a fresh function symbol and x1..xn are the free
2.48/2.66	variables of u and v.
2.48/2.66	A predicate p(X) is encoded as p(X)=true (this is sound, because the
2.48/2.66	input problem has no model of domain size 1).
2.48/2.66	
2.48/2.66	The encoding turns the above axioms into the following unit equations and goals:
2.48/2.66	
2.62/2.83	Axiom 1 (single_axiom): join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(join(meet(X, join(join(meet(W, Y), meet(Y, V)), Y)), meet(join(meet(Y, meet(meet(join(W, join(Y, V)), join(U, Y)), Y)), meet(T, join(Y, meet(meet(join(W, join(Y, V)), join(U, Y)), Y)))), join(X, join(join(meet(W, Y), meet(Y, V)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z))) = Y.
2.62/2.83	
2.62/2.83	Lemma 2: join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(Z, join(join(meet(V, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), U)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(V, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), U)), 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))).
2.62/2.83	Proof:
2.62/2.83	  join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(Z, join(join(meet(V, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), U)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(V, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), U)), 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)))
2.62/2.83	= { by axiom 1 (single_axiom) }
2.62/2.83	  join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), W), meet(join(meet(Z, join(join(meet(V, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), U)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), meet(meet(join(V, join(join(meet(X, Y), meet(Y, join(X, Y))), U)), join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(V, join(join(meet(X, Y), meet(Y, join(X, Y))), U)), join(?, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))))), join(Z, join(join(meet(V, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), U)), 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)))
2.62/2.83	= { by axiom 1 (single_axiom) }
2.94/3.11	  join(meet(X, Y), meet(Y, join(X, Y)))
2.94/3.11	
2.94/3.11	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))).
2.94/3.11	Proof:
2.94/3.11	  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)))
2.94/3.11	= { by lemma 2 }
2.94/3.12	  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)))
2.94/3.12	= { by lemma 2 }
2.94/3.12	  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)))
2.94/3.12	= { by lemma 2 }
2.94/3.12	  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)))
2.94/3.12	= { by lemma 2 }
2.94/3.12	  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)))
2.94/3.12	= { by lemma 2 }
2.94/3.13	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(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)))
2.94/3.13	= { by lemma 2 }
2.94/3.13	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(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)))
2.94/3.13	= { by lemma 2 }
2.94/3.14	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(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)))
2.94/3.14	= { by lemma 2 }
2.94/3.15	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?)), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(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)))
2.94/3.15	= { by lemma 2 }
2.94/3.16	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?)), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(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)))
2.94/3.16	= { by lemma 2 }
2.94/3.17	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?)), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(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)))
2.94/3.17	= { by lemma 2 }
3.02/3.18	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?)), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?)), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), 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(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)))
3.02/3.18	= { by lemma 2 }
3.02/3.19	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?)), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), ?)), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), 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(X, Y), meet(Y, join(X, Y)))))), W)))
3.02/3.19	= { by lemma 2 }
3.02/3.20	  join(meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))), join(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))))))))))), W), meet(join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(join(meet(?, join(meet(join(meet(Z, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), join(Z, join(meet(X, Y), meet(Y, join(X, Y)))))), join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y))))), meet(Y, join(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, Y)))), meet(join(meet(X, Y), meet(Y, join(X, Y))), ?)), join(meet(X, Y), meet(Y, join(X, Y)))))))), meet(join(meet(Z, join(join(meet(?, join(meet(X, Y), meet(Y, join(X, 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?)), 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)))
3.02/3.21	= { by lemma 2 }
3.02/3.21	  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))))))))))
3.02/3.21	= { by lemma 2 }
3.02/3.21	  join(meet(X, Y), meet(Y, join(X, Y)))
3.02/3.21	
3.02/3.21	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))).
3.02/3.21	Proof:
3.02/3.21	  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)))
3.02/3.21	= { by lemma 3 }
3.02/3.21	  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)))
3.02/3.21	= { by lemma 3 }
3.02/3.21	  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)))
3.02/3.21	= { by lemma 3 }
3.02/3.22	  join(meet(X, Y), meet(Y, join(X, Y)))
3.02/3.22	
3.02/3.22	Lemma 5: join(meet(Y, T), meet(Y, join(Y, T))) = Y.
3.02/3.22	Proof:
3.02/3.22	  join(meet(Y, T), meet(Y, join(Y, T)))
3.02/3.22	= { by axiom 1 (single_axiom) }
3.02/3.22	  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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), T), meet(Y, join(Y, T)))
3.02/3.22	= { by axiom 1 (single_axiom) }
3.02/3.22	  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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(Y, T)))
3.02/3.22	= { by axiom 1 (single_axiom) }
3.02/3.22	  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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), T)))
3.02/3.22	= { by lemma 4 }
3.02/3.22	  join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))
3.02/3.22	= { by axiom 1 (single_axiom) }
3.02/3.22	  Y
3.02/3.22	
3.02/3.22	Lemma 6: 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))).
3.02/3.22	Proof:
3.02/3.22	  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)))
3.02/3.22	= { by lemma 5 }
3.02/3.22	  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)))
3.02/3.22	= { by lemma 2 }
3.44/3.64	  join(meet(X, Y), meet(Y, join(X, Y)))
3.44/3.64	
3.44/3.64	Lemma 7: join(meet(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S))) = Y.
3.44/3.64	Proof:
3.44/3.64	  join(meet(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.64	= { by axiom 1 (single_axiom) }
3.44/3.64	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.64	= { by axiom 1 (single_axiom) }
3.44/3.64	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.64	= { by axiom 1 (single_axiom) }
3.44/3.65	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.65	= { by axiom 1 (single_axiom) }
3.44/3.65	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.65	= { by axiom 1 (single_axiom) }
3.44/3.65	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.65	= { by axiom 1 (single_axiom) }
3.44/3.65	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))), meet(Y, join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.65	= { by axiom 1 (single_axiom) }
3.44/3.66	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, Y))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.66	= { by axiom 1 (single_axiom) }
3.44/3.67	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), Y))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.67	= { by axiom 1 (single_axiom) }
3.44/3.67	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), meet(Y, join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.44/3.67	= { by axiom 1 (single_axiom) }
3.52/3.68	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(join(meet(T, Y), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.52/3.68	= { by axiom 1 (single_axiom) }
3.53/3.68	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))), meet(Y, join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.53/3.68	= { by axiom 1 (single_axiom) }
3.53/3.69	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, Y))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.53/3.69	= { by axiom 1 (single_axiom) }
3.53/3.70	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), Y), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.55/3.70	= { by axiom 1 (single_axiom) }
3.55/3.71	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))), meet(Y, join(join(meet(T, Y), meet(Y, join(T, Y))), Y))), S)))
3.55/3.71	= { by axiom 1 (single_axiom) }
3.57/3.72	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), 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3.57/3.72	= { by axiom 1 (single_axiom) }
3.57/3.73	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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, 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3.57/3.73	= { by axiom 1 (single_axiom) }
3.57/3.74	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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, 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join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), 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join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, Y))), Y))), S)))
3.57/3.74	= { by axiom 1 (single_axiom) }
3.57/3.75	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), Y))), S)))
3.57/3.75	= { by axiom 1 (single_axiom) }
3.57/3.76	  join(meet(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S), 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(join(meet(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))))), join(T, join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, 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(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))))), S)))
3.57/3.76	= { by lemma 3 }
3.57/3.76	  join(meet(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y))))), meet(join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))), join(join(meet(?, Y), meet(Y, join(?, Y))), join(meet(?, join(join(meet(?, Y), meet(Y, ?)), Y)), meet(join(meet(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)), meet(?, join(Y, meet(meet(join(?, join(Y, ?)), join(?, Y)), Y)))), join(?, join(join(meet(?, Y), meet(Y, ?)), Y)))))))
3.57/3.76	= { by axiom 1 (single_axiom) }
3.57/3.80	  Y
3.57/3.80	
3.57/3.80	Lemma 8: join(meet(join(meet(Z, Y), meet(Y, join(Z, Y))), W), meet(join(meet(Z, join(join(meet(V, Y), meet(Y, U)), Y)), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W))) = Y.
3.57/3.80	Proof:
3.57/3.80	  join(meet(join(meet(Z, Y), meet(Y, join(Z, Y))), W), meet(join(meet(Z, join(join(meet(V, Y), meet(Y, U)), Y)), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.80	= { by lemma 7 }
3.57/3.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(Y, join(Z, Y))), W), meet(join(meet(Z, join(join(meet(V, Y), meet(Y, U)), Y)), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.80	= { by lemma 7 }
3.57/3.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, Y))), W), meet(join(meet(Z, join(join(meet(V, Y), meet(Y, U)), Y)), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.80	= { by lemma 7 }
3.57/3.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, Y), meet(Y, U)), Y)), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.80	= { by lemma 7 }
3.57/3.80	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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, U)), Y)), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.80	= { by lemma 7 }
3.57/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), U)), Y)), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.81	= { by lemma 7 }
3.57/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), 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))))), meet(Y, join(Z, join(join(meet(V, Y), meet(Y, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.81	= { by lemma 7 }
3.57/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), 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))))), meet(Y, join(Z, join(join(meet(V, 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, U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.81	= { by lemma 7 }
3.57/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), 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))))), meet(Y, join(Z, join(join(meet(V, 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))), U)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.81	= { by lemma 7 }
3.57/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), 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))))), meet(Y, join(Z, join(join(meet(V, 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))), 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(join(meet(Z, Y), meet(Y, join(Z, Y))), W)))
3.57/3.81	= { by lemma 7 }
3.57/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), 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))))), meet(Y, join(Z, join(join(meet(V, 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))), 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(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)))
3.57/3.81	= { by lemma 7 }
3.57/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), 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))))), meet(Y, join(Z, join(join(meet(V, 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))), 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(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)))
3.57/3.81	= { by lemma 7 }
3.66/3.81	  join(meet(join(meet(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y))), join(Z, join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))))), W), meet(join(meet(Z, join(join(meet(V, 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))), 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))))), meet(Y, join(Z, join(join(meet(V, 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))), 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(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)))
3.66/3.81	= { by lemma 2 }
3.66/3.81	  join(meet(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(?, Y), meet(Y, join(?, Y))), Y), meet(Y, join(join(meet(?, Y), meet(Y, join(?, Y))), Y))), Y)))
3.66/3.81	= { by lemma 7 }
3.66/3.82	  Y
3.66/3.82	
3.66/3.82	Lemma 9: join(meet(Y, X), meet(X, join(Y, X))) = X.
3.66/3.82	Proof:
3.66/3.82	  join(meet(Y, X), meet(X, join(Y, X)))
3.66/3.82	= { by lemma 4 }
3.66/3.82	  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))), ?)))
3.66/3.82	= { by lemma 6 }
3.66/3.82	  join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?), meet(join(meet(Y, X), meet(X, join(Y, X))), join(join(meet(Y, X), meet(X, join(Y, X))), ?)))
3.66/3.82	= { by lemma 6 }
3.66/3.82	  join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?), meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(?, X), meet(X, ?)), X)), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(?, X), meet(X, ?)), X)))), join(join(meet(Y, X), meet(X, join(Y, X))), ?)))
3.66/3.82	= { by lemma 6 }
3.66/3.82	  join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?), meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(?, X), meet(X, ?)), X)), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(?, X), meet(X, ?)), X)))), join(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), X))), ?)))
3.66/3.82	= { by lemma 8 }
3.66/3.82	  X
3.66/3.82	
3.66/3.82	Lemma 10: join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))) = Z.
3.66/3.82	Proof:
3.66/3.82	  join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))
3.66/3.82	= { by lemma 8 }
3.66/3.82	  join(meet(join(meet(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), join(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))))), ?), meet(join(meet(join(meet(X, Z), meet(Z, join(X, Z))), join(join(meet(?, join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), ?)), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), join(join(meet(X, Z), meet(Z, join(X, Z))), join(join(meet(?, join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), ?)), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))))))), join(join(meet(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), join(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))))), ?)))
3.66/3.82	= { by lemma 8 }
3.66/3.82	  join(meet(Z, ?), meet(join(meet(join(meet(X, Z), meet(Z, join(X, Z))), join(join(meet(?, join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), ?)), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), join(join(meet(X, Z), meet(Z, join(X, Z))), join(join(meet(?, join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), ?)), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))))))), join(join(meet(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), join(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))))), ?)))
3.66/3.82	= { by lemma 8 }
3.66/3.82	  join(meet(Z, ?), meet(Z, join(join(meet(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))), meet(join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z)))), join(join(meet(X, Z), meet(Z, join(X, Z))), join(meet(X, join(join(meet(Y, Z), meet(Z, W)), Z)), meet(Z, join(X, join(join(meet(Y, Z), meet(Z, W)), Z))))))), ?)))
3.66/3.82	= { by lemma 8 }
3.66/3.82	  join(meet(Z, ?), meet(Z, join(Z, ?)))
3.66/3.82	= { by lemma 5 }
3.66/3.82	  Z
3.66/3.82	
3.66/3.82	Lemma 11: join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))) = X.
3.66/3.82	Proof:
3.66/3.82	  join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))
3.66/3.82	= { by lemma 10 }
3.66/3.83	  join(meet(X, join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(X, join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))))))
3.66/3.83	= { by lemma 9 }
3.66/3.83	  join(meet(join(meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X))), join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(X, join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))))))
3.66/3.83	= { by lemma 5 }
3.66/3.83	  join(meet(join(meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X))), join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))))), meet(join(meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(join(meet(Y, X), meet(X, Z)), X)), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(join(meet(Y, X), meet(X, Z)), X)))), join(X, join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))))))
3.66/3.83	= { by lemma 9 }
3.66/3.83	  join(meet(join(meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X))), join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))))), meet(join(meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(join(meet(Y, X), meet(X, Z)), X)), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), join(join(meet(Y, X), meet(X, Z)), X)))), join(join(meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X), meet(X, join(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), X))), join(join(meet(?, join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))), meet(join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)))), ?)), join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(V, join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))))))
3.66/3.83	= { by axiom 1 (single_axiom) }
3.66/3.83	  X
3.66/3.83	
3.66/3.83	Lemma 12: meet(meet(join(Y, join(X, Z)), join(W, X)), X) = X.
3.66/3.83	Proof:
3.66/3.83	  meet(meet(join(Y, join(X, Z)), join(W, X)), X)
3.66/3.83	= { by lemma 9 }
3.66/3.83	  join(meet(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X)), meet(meet(meet(join(Y, join(X, Z)), join(W, X)), X), join(X, meet(meet(join(Y, join(X, Z)), join(W, X)), X))))
3.66/3.83	= { by lemma 11 }
3.66/3.83	  X
3.66/3.83	
3.66/3.83	Lemma 13: join(meet(X, X), meet(Y, join(X, X))) = X.
3.66/3.83	Proof:
3.66/3.83	  join(meet(X, X), meet(Y, join(X, X)))
3.66/3.83	= { by lemma 12 }
3.66/3.83	  join(meet(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)), meet(Y, join(X, X)))
3.66/3.83	= { by lemma 12 }
3.66/3.83	  join(meet(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)), meet(Y, join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X))))
3.66/3.83	= { by lemma 11 }
3.66/3.83	  X
3.66/3.83	
3.66/3.83	Lemma 14: join(join(meet(X, Y), meet(Y, Z)), Y) = Y.
3.66/3.83	Proof:
3.66/3.83	  join(join(meet(X, Y), meet(Y, Z)), Y)
3.66/3.83	= { by lemma 13 }
3.66/3.83	  join(meet(join(join(meet(X, Y), meet(Y, Z)), Y), join(join(meet(X, Y), meet(Y, Z)), Y)), meet(Y, join(join(join(meet(X, Y), meet(Y, Z)), Y), join(join(meet(X, Y), meet(Y, Z)), Y))))
3.66/3.83	= { by lemma 10 }
3.74/3.96	  Y
3.74/3.96	
3.74/3.96	Lemma 15: join(X, X) = X.
3.74/3.96	Proof:
3.74/3.96	  join(X, X)
3.74/3.96	= { by lemma 13 }
3.74/3.96	  join(meet(join(X, X), join(X, X)), meet(X, join(join(X, X), join(X, X))))
3.74/3.96	= { by lemma 9 }
3.74/3.96	  join(meet(join(X, X), join(join(meet(?, X), meet(X, join(?, X))), X)), meet(X, join(join(X, X), join(X, X))))
3.74/3.96	= { by lemma 2 }
3.74/3.96	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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)))))))))), X)), meet(X, join(join(X, X), join(X, X))))
3.74/3.96	= { by lemma 10 }
3.74/3.96	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(join(meet(?, X), meet(X, ?)), X)), meet(X, join(?, join(join(meet(?, X), meet(X, ?)), X)))))), meet(X, join(join(X, X), join(X, X))))
3.74/3.96	= { by lemma 9 }
3.74/3.96	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(X, ?)), X)), meet(X, join(?, join(join(meet(?, X), meet(X, ?)), X)))))), meet(X, join(join(X, X), join(X, X))))
3.74/3.96	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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)))))), meet(X, join(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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)))))), meet(X, join(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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)))))), meet(X, join(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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)))))), meet(X, join(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), meet(X, join(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 10 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), meet(join(meet(?, join(join(meet(?, X), meet(X, ?)), X)), meet(X, join(?, join(join(meet(?, X), meet(X, ?)), X)))), join(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.74/3.97	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(join(X, X), join(X, X))))
3.74/3.97	= { by lemma 9 }
3.82/3.98	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(join(X, X), join(X, X))))
3.82/3.98	= { by lemma 9 }
3.82/3.98	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, X), join(X, X))))
3.82/3.98	= { by lemma 9 }
3.82/3.98	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, X), join(join(meet(?, X), meet(X, join(?, X))), X))))
3.82/3.98	= { by lemma 2 }
3.82/3.98	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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)))))))))), X))))
3.82/3.98	= { by lemma 10 }
3.82/3.98	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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(join(meet(?, X), meet(X, ?)), X)), meet(X, join(?, join(join(meet(?, X), meet(X, ?)), X))))))))
3.82/3.98	= { by lemma 9 }
3.82/3.98	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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(join(meet(?, join(meet(?, X), meet(X, join(?, X)))), meet(X, ?)), X)), meet(X, join(?, join(join(meet(?, X), meet(X, ?)), X))))))))
3.82/3.98	= { by lemma 9 }
3.82/3.99	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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(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))))))))
3.82/3.99	= { by lemma 9 }
3.82/3.99	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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(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))))))))
3.82/3.99	= { by lemma 9 }
3.82/3.99	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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(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))))))))
3.82/3.99	= { by lemma 9 }
3.82/3.99	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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(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))))))))
3.82/3.99	= { by lemma 9 }
3.82/4.00	  join(meet(join(X, 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(?, 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)))))))), 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)))))), 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(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))))))))), 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(X, 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(?, 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)))))))), 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)))))), 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(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)))))))))))
3.82/4.00	= { by lemma 10 }
3.82/4.00	  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)))))))
3.82/4.00	= { by lemma 9 }
3.82/4.00	  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)))))))
3.82/4.00	= { by lemma 9 }
3.82/4.00	  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)))))))
3.82/4.00	= { by lemma 9 }
3.82/4.00	  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)))))))
3.82/4.00	= { by lemma 9 }
3.82/4.00	  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)))))))
3.82/4.00	= { by lemma 9 }
3.82/4.00	  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)))))))
3.82/4.00	= { by lemma 9 }
3.82/4.00	  join(meet(?, join(join(meet(?, X), meet(X, ?)), X)), meet(X, join(?, join(join(meet(?, X), meet(X, ?)), X))))
3.82/4.00	= { by lemma 10 }
3.82/4.00	  X
3.82/4.00	
3.82/4.00	Lemma 16: meet(X, X) = X.
3.82/4.00	Proof:
3.82/4.00	  meet(X, X)
3.82/4.00	= { by lemma 15 }
3.82/4.00	  join(meet(X, X), meet(X, X))
3.82/4.00	= { by lemma 15 }
3.82/4.00	  join(meet(X, X), meet(X, join(X, X)))
3.82/4.00	= { by lemma 5 }
3.82/4.00	  X
3.82/4.00	
3.82/4.00	Lemma 17: meet(join(X, Y), X) = X.
3.82/4.00	Proof:
3.82/4.00	  meet(join(X, Y), X)
3.82/4.00	= { by lemma 5 }
3.82/4.00	  join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), X)))
3.82/4.00	= { by lemma 13 }
3.82/4.00	  join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(join(meet(meet(join(X, Y), X), meet(join(X, Y), X)), meet(X, join(meet(join(X, Y), X), meet(join(X, Y), X)))), X)))
3.82/4.00	= { by lemma 16 }
3.82/4.00	  join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(join(meet(join(X, Y), X), meet(X, join(meet(join(X, Y), X), meet(join(X, Y), X)))), X)))
3.82/4.00	= { by lemma 15 }
3.82/4.00	  join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(join(meet(join(X, Y), X), meet(X, meet(join(X, Y), X))), X)))
3.82/4.00	= { by lemma 14 }
3.82/4.00	  join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), X))
3.82/4.00	= { by lemma 15 }
3.82/4.00	  meet(meet(join(X, Y), X), X)
3.82/4.00	= { by lemma 15 }
3.82/4.00	  meet(meet(join(join(X, X), Y), X), X)
3.82/4.00	= { by lemma 15 }
3.82/4.00	  meet(meet(join(join(join(X, X), Y), join(join(X, X), Y)), X), X)
3.82/4.00	= { by lemma 11 }
3.82/4.00	  meet(meet(join(join(join(X, X), Y), join(join(X, X), Y)), join(meet(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)), meet(meet(join(?, join(join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)), ?)), join(?, join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)))), join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X))))), X)
3.82/4.00	= { by lemma 12 }
3.82/4.00	  meet(meet(join(join(join(X, X), Y), join(join(X, X), Y)), join(meet(X, X), meet(meet(join(?, join(join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)), ?)), join(?, join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)))), join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X))))), X)
3.82/4.00	= { by lemma 12 }
3.82/4.00	  meet(meet(join(join(join(X, X), Y), join(join(X, X), Y)), join(meet(X, X), join(X, meet(meet(join(?, join(X, ?)), join(?, X)), X)))), X)
3.82/4.00	= { by lemma 12 }
3.82/4.00	  meet(meet(join(join(join(X, X), Y), join(join(X, X), Y)), join(meet(X, X), join(X, X))), X)
3.82/4.00	= { by lemma 15 }
3.82/4.00	  meet(meet(join(join(join(X, X), Y), join(join(X, X), Y)), join(meet(X, X), join(X, X))), join(X, X))
3.82/4.00	= { by lemma 12 }
3.82/4.00	  join(X, X)
3.82/4.00	= { by lemma 15 }
3.82/4.00	  X
3.82/4.00	
3.82/4.00	Lemma 18: join(X, meet(X, Y)) = X.
3.82/4.00	Proof:
3.82/4.00	  join(X, meet(X, Y))
3.82/4.00	= { by lemma 5 }
3.82/4.00	  join(meet(join(X, meet(X, Y)), X), meet(join(X, meet(X, Y)), join(join(X, meet(X, Y)), X)))
3.82/4.00	= { by lemma 12 }
3.82/4.00	  join(meet(join(X, meet(X, Y)), X), meet(join(X, meet(X, Y)), join(join(meet(meet(join(?, join(X, ?)), join(?, X)), X), meet(X, Y)), X)))
3.82/4.00	= { by lemma 14 }
3.82/4.00	  join(meet(join(X, meet(X, Y)), X), meet(join(X, meet(X, Y)), X))
3.82/4.00	= { by lemma 15 }
3.82/4.00	  meet(join(X, meet(X, Y)), X)
3.82/4.00	= { by lemma 17 }
3.82/4.00	  X
3.82/4.00	
3.82/4.00	Lemma 19: meet(X, meet(X, Y)) = meet(X, Y).
3.82/4.00	Proof:
3.82/4.00	  meet(X, meet(X, Y))
3.82/4.00	= { by lemma 5 }
3.82/4.00	  meet(join(meet(X, Y), meet(X, join(X, Y))), meet(X, Y))
3.82/4.00	= { by lemma 17 }
3.82/4.00	  meet(X, Y)
3.82/4.00	
3.82/4.00	Lemma 20: meet(meet(X, Y), X) = meet(X, Y).
3.82/4.00	Proof:
3.82/4.00	  meet(meet(X, Y), X)
3.82/4.00	= { by lemma 15 }
3.82/4.00	  join(meet(meet(X, Y), X), meet(meet(X, Y), X))
3.82/4.00	= { by lemma 19 }
3.82/4.00	  join(meet(meet(X, meet(X, Y)), X), meet(meet(X, Y), X))
3.82/4.00	= { by lemma 16 }
3.82/4.00	  join(meet(meet(X, meet(X, Y)), meet(X, X)), meet(meet(X, Y), X))
3.82/4.00	= { by lemma 18 }
3.82/4.00	  join(meet(meet(X, meet(X, Y)), meet(X, join(X, meet(X, Y)))), meet(meet(X, Y), X))
3.82/4.00	= { by lemma 19 }
3.82/4.00	  join(meet(meet(X, meet(X, Y)), meet(X, join(X, meet(X, Y)))), meet(meet(X, meet(X, Y)), X))
3.82/4.00	= { by lemma 5 }
3.82/4.00	  join(meet(meet(X, meet(X, Y)), meet(X, join(X, meet(X, Y)))), meet(meet(X, meet(X, Y)), join(meet(X, meet(X, Y)), meet(X, join(X, meet(X, Y))))))
3.82/4.00	= { by lemma 5 }
3.82/4.00	  meet(X, meet(X, Y))
3.82/4.00	= { by lemma 19 }
3.82/4.00	  meet(X, Y)
3.82/4.00	
3.82/4.00	Lemma 21: meet(X, join(X, Y)) = X.
3.82/4.00	Proof:
3.82/4.00	  meet(X, join(X, Y))
3.82/4.00	= { by lemma 17 }
3.82/4.00	  meet(meet(join(X, Y), X), join(X, Y))
3.82/4.00	= { by lemma 20 }
3.82/4.00	  meet(join(X, Y), X)
3.82/4.00	= { by lemma 17 }
3.82/4.00	  X
3.82/4.00	
3.82/4.00	Lemma 22: meet(meet(Y, X), meet(X, Y)) = meet(X, Y).
3.82/4.00	Proof:
3.82/4.00	  meet(meet(Y, X), meet(X, Y))
3.82/4.00	= { by lemma 5 }
3.82/4.00	  meet(meet(join(meet(Y, ?), meet(Y, join(Y, ?))), X), meet(X, Y))
3.82/4.00	= { by lemma 9 }
3.82/4.00	  meet(meet(join(meet(Y, ?), join(meet(X, meet(Y, join(Y, ?))), meet(meet(Y, join(Y, ?)), join(X, meet(Y, join(Y, ?)))))), X), meet(X, Y))
3.82/4.00	= { by lemma 18 }
3.82/4.00	  meet(meet(join(meet(Y, ?), join(meet(X, meet(Y, join(Y, ?))), meet(meet(Y, join(Y, ?)), join(X, meet(Y, join(Y, ?)))))), join(X, meet(X, Y))), meet(X, Y))
3.82/4.00	= { by lemma 21 }
3.82/4.00	  meet(meet(join(meet(Y, ?), join(meet(X, meet(Y, join(Y, ?))), meet(meet(Y, join(Y, ?)), join(X, meet(Y, join(Y, ?)))))), join(X, meet(X, meet(Y, join(Y, ?))))), meet(X, Y))
3.82/4.00	= { by lemma 21 }
3.82/4.00	  meet(meet(join(meet(Y, ?), join(meet(X, meet(Y, join(Y, ?))), meet(meet(Y, join(Y, ?)), join(X, meet(Y, join(Y, ?)))))), join(X, meet(X, meet(Y, join(Y, ?))))), meet(X, meet(Y, join(Y, ?))))
3.82/4.00	= { by lemma 12 }
3.82/4.00	  meet(X, meet(Y, join(Y, ?)))
3.82/4.00	= { by lemma 21 }
3.82/4.00	  meet(X, Y)
3.82/4.00	
3.82/4.00	Goal 1 (prove_normal_axioms_2): meet(a, b) = meet(b, a).
3.82/4.00	Proof:
3.82/4.00	  meet(a, b)
3.82/4.00	= { by lemma 22 }
3.82/4.00	  meet(meet(b, a), meet(a, b))
3.82/4.00	= { by lemma 22 }
3.82/4.00	  meet(meet(meet(a, b), meet(b, a)), meet(a, b))
3.82/4.00	= { by lemma 20 }
3.82/4.00	  meet(meet(a, b), meet(b, a))
3.82/4.00	= { by lemma 22 }
3.82/4.00	  meet(b, a)
3.82/4.00	% SZS output end Proof
3.82/4.00	
3.82/4.00	RESULT: Unsatisfiable (the axioms are contradictory).
3.82/4.00	EOF