TSTP Solution File: LAT030-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT030-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:27:11 EDT 2023
% Result : Unsatisfiable 2.66s 0.74s
% Output : Proof 9.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT030-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 06:05:27 EDT 2023
% 0.14/0.34 % CPUTime :
% 2.66/0.74 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.66/0.74
% 2.66/0.74 % SZS status Unsatisfiable
% 2.66/0.74
% 7.23/1.26 % SZS output start Proof
% 7.23/1.26 Take the following subset of the input axioms:
% 7.23/1.26 fof(prove_wal_axioms, negated_conjecture, meet(a, a)!=a | (meet(b, a)!=meet(a, b) | (join(a, a)!=a | (join(b, a)!=join(a, b) | (meet(meet(join(a, b), join(c, b)), b)!=b | join(join(meet(a, b), meet(c, b)), b)!=b))))).
% 7.23/1.26 fof(single_axiom, axiom, ![X, Y, Z, X1, X2, U]: join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(join(meet(X, join(join(meet(Y, X1), meet(X2, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, X1), join(X2, Y)), Y)), meet(U, join(Y, meet(meet(join(Y, X1), join(X2, Y)), Y)))), join(X, join(join(meet(Y, X1), meet(X2, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))=Y).
% 7.23/1.26
% 7.23/1.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.23/1.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.23/1.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.23/1.26 fresh(y, y, x1...xn) = u
% 7.23/1.26 C => fresh(s, t, x1...xn) = v
% 7.23/1.26 where fresh is a fresh function symbol and x1..xn are the free
% 7.23/1.26 variables of u and v.
% 7.23/1.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.23/1.26 input problem has no model of domain size 1).
% 7.23/1.26
% 7.23/1.26 The encoding turns the above axioms into the following unit equations and goals:
% 7.23/1.26
% 7.23/1.27 Axiom 1 (single_axiom): join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(join(meet(X, join(join(meet(Y, W), meet(V, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, W), join(V, Y)), Y)), meet(U, join(Y, meet(meet(join(Y, W), join(V, Y)), Y)))), join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z))) = Y.
% 7.23/1.27
% 7.23/1.27 Lemma 2: join(meet(join(meet(X, join(meet(Y, Z), meet(Z, join(Y, Z)))), meet(join(meet(Y, Z), meet(Z, join(Y, Z))), join(X, join(meet(Y, Z), meet(Z, join(Y, Z)))))), W), meet(join(meet(X, join(join(meet(join(meet(Y, Z), meet(Z, join(Y, Z))), V), meet(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))), meet(Z, join(X, join(join(meet(join(meet(Y, Z), meet(Z, join(Y, Z))), V), meet(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))))), join(join(meet(X, join(meet(Y, Z), meet(Z, join(Y, Z)))), meet(join(meet(Y, Z), meet(Z, join(Y, Z))), join(X, join(meet(Y, Z), meet(Z, join(Y, Z)))))), W))) = join(meet(Y, Z), meet(Z, join(Y, Z))).
% 7.23/1.27 Proof:
% 7.23/1.27 join(meet(join(meet(X, join(meet(Y, Z), meet(Z, join(Y, Z)))), meet(join(meet(Y, Z), meet(Z, join(Y, Z))), join(X, join(meet(Y, Z), meet(Z, join(Y, Z)))))), W), meet(join(meet(X, join(join(meet(join(meet(Y, Z), meet(Z, join(Y, Z))), V), meet(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))), meet(Z, join(X, join(join(meet(join(meet(Y, Z), meet(Z, join(Y, Z))), V), meet(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))))), join(join(meet(X, join(meet(Y, Z), meet(Z, join(Y, Z)))), meet(join(meet(Y, Z), meet(Z, join(Y, Z))), join(X, join(meet(Y, Z), meet(Z, join(Y, Z)))))), W)))
% 7.23/1.27 = { by axiom 1 (single_axiom) R->L }
% 7.23/1.27 join(meet(join(meet(X, join(meet(Y, Z), meet(Z, join(Y, Z)))), meet(join(meet(Y, Z), meet(Z, join(Y, Z))), join(X, join(meet(Y, Z), meet(Z, join(Y, Z)))))), W), meet(join(meet(X, join(join(meet(join(meet(Y, Z), meet(Z, join(Y, Z))), V), meet(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))), meet(join(meet(join(meet(Y, Z), meet(Z, join(Y, Z))), meet(meet(join(join(meet(Y, Z), meet(Z, join(Y, Z))), V), join(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))), meet(join(meet(Y, join(join(meet(Z, T), meet(S, Z)), Z)), meet(join(meet(Z, meet(meet(join(Z, T), join(S, Z)), Z)), meet(X2, join(Z, meet(meet(join(Z, T), join(S, Z)), Z)))), join(Y, join(join(meet(Z, T), meet(S, Z)), Z)))), join(join(meet(Y, Z), meet(Z, join(Y, Z))), meet(meet(join(join(meet(Y, Z), meet(Z, join(Y, Z))), V), join(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))))), join(X, join(join(meet(join(meet(Y, Z), meet(Z, join(Y, Z))), V), meet(U, join(meet(Y, Z), meet(Z, join(Y, Z))))), join(meet(Y, Z), meet(Z, join(Y, Z))))))), join(join(meet(X, join(meet(Y, Z), meet(Z, join(Y, Z)))), meet(join(meet(Y, Z), meet(Z, join(Y, Z))), join(X, join(meet(Y, Z), meet(Z, join(Y, Z)))))), W)))
% 7.23/1.27 = { by axiom 1 (single_axiom) }
% 7.23/1.27 join(meet(Y, Z), meet(Z, join(Y, Z)))
% 7.23/1.27
% 7.23/1.27 Lemma 3: join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z), meet(Y, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z))) = Y.
% 7.23/1.27 Proof:
% 7.23/1.27 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z), meet(Y, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 7.23/1.27 = { by axiom 1 (single_axiom) R->L }
% 7.23/1.27 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 7.23/1.28 = { by axiom 1 (single_axiom) R->L }
% 7.23/1.28 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 7.23/1.29 = { by axiom 1 (single_axiom) R->L }
% 7.23/1.29 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 7.23/1.30 = { by axiom 1 (single_axiom) R->L }
% 7.23/1.30 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, Y)), Y)), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 7.23/1.31 = { by axiom 1 (single_axiom) R->L }
% 7.23/1.31 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), Y)), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 7.23/1.32 = { by axiom 1 (single_axiom) R->L }
% 7.23/1.33 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 7.78/1.34 = { by axiom 1 (single_axiom) R->L }
% 7.78/1.35 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, Y)), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 8.03/1.37 = { by axiom 1 (single_axiom) R->L }
% 8.03/1.37 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), Y)))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 8.03/1.40 = { by axiom 1 (single_axiom) R->L }
% 8.03/1.40 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 8.03/1.41 = { by axiom 1 (single_axiom) R->L }
% 8.03/1.42 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, 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% 8.03/1.43 = { by axiom 1 (single_axiom) R->L }
% 8.54/1.43 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), 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Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, 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% 8.54/1.44 = { by axiom 1 (single_axiom) R->L }
% 8.54/1.44 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), 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Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z)))
% 8.54/1.44 = { by axiom 1 (single_axiom) R->L }
% 8.54/1.45 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z)))
% 8.54/1.45 = { by lemma 2 }
% 8.54/1.45 join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))
% 8.54/1.45 = { by axiom 1 (single_axiom) }
% 8.54/1.46 Y
% 8.54/1.46
% 8.54/1.46 Lemma 4: join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(join(meet(X, join(join(meet(Y, W), meet(V, Y)), Y)), meet(Y, join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z))) = Y.
% 8.54/1.46 Proof:
% 8.54/1.46 join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(join(meet(X, join(join(meet(Y, W), meet(V, Y)), Y)), meet(Y, join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.54/1.46 = { by lemma 3 R->L }
% 8.54/1.46 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, Y))), Z), meet(join(meet(X, join(join(meet(Y, W), meet(V, Y)), Y)), meet(Y, join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.54/1.46 = { by lemma 3 R->L }
% 8.54/1.46 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(Y, W), meet(V, Y)), Y)), meet(Y, join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.54/1.46 = { by lemma 3 R->L }
% 8.54/1.46 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, Y)), Y)), meet(Y, join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.84/1.46 = { by lemma 3 R->L }
% 8.84/1.46 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), Y)), meet(Y, join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.84/1.47 = { by lemma 3 R->L }
% 8.84/1.47 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.84/1.47 = { by lemma 3 R->L }
% 8.84/1.47 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.84/1.48 = { by lemma 3 R->L }
% 8.84/1.48 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.84/1.48 = { by lemma 3 R->L }
% 8.84/1.49 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 8.84/1.49 = { by lemma 3 R->L }
% 8.84/1.49 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))))), join(join(meet(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))), meet(Y, join(X, Y))), Z)))
% 8.84/1.49 = { by lemma 3 R->L }
% 8.84/1.49 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))))), join(join(meet(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, Y))), Z)))
% 8.84/1.49 = { by lemma 3 R->L }
% 8.84/1.50 join(meet(join(meet(X, Y), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))))), join(join(meet(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z)))
% 8.84/1.50 = { by lemma 3 R->L }
% 8.84/1.50 join(meet(join(meet(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z), meet(join(meet(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), meet(Y, join(X, join(join(meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), W), meet(V, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))), join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))))))), join(join(meet(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))), meet(join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y))), join(X, join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))))), Z)))
% 8.84/1.50 = { by lemma 2 }
% 8.84/1.50 join(meet(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y), meet(Y, join(join(meet(join(meet(U, Y), meet(Y, join(U, Y))), Y), meet(Y, join(join(meet(U, Y), meet(Y, join(U, Y))), Y))), Y)))
% 8.84/1.50 = { by lemma 3 }
% 8.84/1.50 Y
% 8.84/1.50
% 8.84/1.50 Lemma 5: join(meet(X, Y), meet(X, join(X, Y))) = X.
% 8.84/1.50 Proof:
% 8.84/1.50 join(meet(X, Y), meet(X, join(X, Y)))
% 8.84/1.50 = { by lemma 3 R->L }
% 8.84/1.50 join(meet(X, Y), meet(X, join(join(meet(join(meet(join(meet(Z, X), meet(X, join(Z, X))), X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), X))), X), meet(X, join(join(meet(join(meet(Z, X), meet(X, join(Z, X))), X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), X))), X))), Y)))
% 8.84/1.50 = { by lemma 3 R->L }
% 8.84/1.50 join(meet(join(meet(join(meet(join(meet(Z, X), meet(X, join(Z, X))), X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), X))), X), meet(X, join(join(meet(join(meet(Z, X), meet(X, join(Z, X))), X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), X))), X))), Y), meet(X, join(join(meet(join(meet(join(meet(Z, X), meet(X, join(Z, X))), X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), X))), X), meet(X, join(join(meet(join(meet(Z, X), meet(X, join(Z, X))), X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), X))), X))), Y)))
% 8.84/1.50 = { by lemma 3 }
% 8.84/1.50 X
% 8.84/1.50
% 8.84/1.50 Lemma 6: join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))) = Y.
% 8.84/1.50 Proof:
% 8.84/1.50 join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))
% 8.84/1.50 = { by lemma 4 R->L }
% 8.84/1.51 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), U), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), T), meet(S, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), T), meet(S, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), U)))
% 8.84/1.51 = { by axiom 1 (single_axiom) }
% 8.84/1.51 join(meet(Y, U), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), T), meet(S, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), T), meet(S, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), U)))
% 8.84/1.51 = { by axiom 1 (single_axiom) }
% 8.84/1.51 join(meet(Y, U), meet(Y, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(V, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), U)))
% 8.84/1.51 = { by axiom 1 (single_axiom) }
% 8.84/1.51 join(meet(Y, U), meet(Y, join(Y, U)))
% 8.84/1.51 = { by lemma 5 }
% 8.84/1.51 Y
% 8.84/1.51
% 8.84/1.51 Lemma 7: join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))) = X.
% 8.84/1.51 Proof:
% 8.84/1.51 join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))
% 8.84/1.51 = { by lemma 3 R->L }
% 8.84/1.51 join(meet(join(meet(join(meet(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))))), join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))))), join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))))), join(join(meet(X, Y), meet(Z, X)), X)), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(join(meet(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))))), join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(join(meet(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))), meet(join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X)))), join(V, join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))))), join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(W, join(X, meet(meet(join(X, Y), join(Z, X)), X))))))), join(join(meet(X, Y), meet(Z, X)), X))))
% 8.84/1.51 = { by lemma 6 }
% 8.84/1.51 X
% 8.84/1.51
% 8.84/1.51 Lemma 8: join(meet(X, Y), meet(Y, join(X, Y))) = Y.
% 8.84/1.51 Proof:
% 8.84/1.51 join(meet(X, Y), meet(Y, join(X, Y)))
% 8.84/1.51 = { by lemma 7 R->L }
% 8.84/1.51 join(meet(join(meet(X, Y), meet(Y, join(X, Y))), meet(meet(join(join(meet(X, Y), meet(Y, join(X, Y))), Z), join(W, 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, V), meet(U, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, V), join(U, Y)), Y)), meet(T, join(Y, meet(meet(join(Y, V), join(U, Y)), Y)))), join(X, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), meet(meet(join(join(meet(X, Y), meet(Y, join(X, Y))), Z), join(W, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))
% 8.84/1.51 = { by axiom 1 (single_axiom) }
% 8.84/1.51 Y
% 8.84/1.51
% 8.84/1.51 Lemma 9: meet(meet(join(X, Y), join(Z, X)), X) = X.
% 8.84/1.51 Proof:
% 8.84/1.51 meet(meet(join(X, Y), join(Z, X)), X)
% 8.84/1.51 = { by lemma 8 R->L }
% 8.84/1.51 join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X))))
% 8.84/1.51 = { by lemma 7 }
% 8.84/1.51 X
% 8.84/1.51
% 8.84/1.51 Lemma 10: join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))) = Y.
% 8.84/1.51 Proof:
% 8.84/1.51 join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))
% 8.84/1.51 = { by lemma 4 R->L }
% 8.84/1.51 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), V), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), U), meet(T, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), U), meet(T, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), V)))
% 8.84/1.51 = { by lemma 4 }
% 8.84/1.51 join(meet(Y, V), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), U), meet(T, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), U), meet(T, join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))))))), join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), V)))
% 8.84/1.51 = { by lemma 4 }
% 8.84/1.52 join(meet(Y, V), meet(Y, join(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y))))))), V)))
% 8.84/1.52 = { by lemma 4 }
% 8.84/1.52 join(meet(Y, V), meet(Y, join(Y, V)))
% 8.84/1.52 = { by lemma 5 }
% 8.84/1.52 Y
% 8.84/1.52
% 8.84/1.52 Lemma 11: join(join(meet(X, Y), meet(Z, X)), X) = X.
% 8.84/1.52 Proof:
% 8.84/1.52 join(join(meet(X, Y), meet(Z, X)), X)
% 8.84/1.52 = { by lemma 7 R->L }
% 8.84/1.52 join(meet(join(join(meet(X, Y), meet(Z, X)), X), meet(meet(join(join(join(meet(X, Y), meet(Z, X)), X), W), join(V, join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X))), meet(X, join(join(join(meet(X, Y), meet(Z, X)), X), meet(meet(join(join(join(meet(X, Y), meet(Z, X)), X), W), join(V, join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X)))))
% 8.84/1.52 = { by lemma 9 }
% 8.84/1.52 join(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X)), meet(X, join(join(join(meet(X, Y), meet(Z, X)), X), meet(meet(join(join(join(meet(X, Y), meet(Z, X)), X), W), join(V, join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X)))))
% 8.84/1.52 = { by lemma 9 }
% 8.84/1.52 join(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X)), meet(X, join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X))))
% 8.84/1.52 = { by lemma 10 }
% 8.84/1.52 X
% 8.84/1.52
% 8.84/1.52 Lemma 12: meet(meet(X, join(Y, meet(Z, X))), meet(Z, X)) = meet(Z, X).
% 8.84/1.52 Proof:
% 8.84/1.52 meet(meet(X, join(Y, meet(Z, X))), meet(Z, X))
% 8.84/1.52 = { by lemma 8 R->L }
% 8.84/1.52 meet(meet(join(meet(Z, X), meet(X, join(Z, X))), join(Y, meet(Z, X))), meet(Z, X))
% 8.84/1.52 = { by lemma 9 }
% 8.84/1.52 meet(Z, X)
% 8.84/1.52
% 8.84/1.52 Lemma 13: meet(meet(X, join(Y, X)), X) = X.
% 8.84/1.52 Proof:
% 8.84/1.52 meet(meet(X, join(Y, X)), X)
% 8.84/1.52 = { by lemma 9 R->L }
% 8.84/1.52 meet(meet(X, join(Y, X)), meet(meet(join(X, Z), join(W, X)), X))
% 8.84/1.52 = { by lemma 9 R->L }
% 8.84/1.52 meet(meet(X, join(Y, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(join(X, Z), join(W, X)), X))
% 8.84/1.52 = { by lemma 12 }
% 8.84/1.52 meet(meet(join(X, Z), join(W, X)), X)
% 8.84/1.52 = { by lemma 9 }
% 8.84/1.52 X
% 8.84/1.52
% 8.84/1.52 Lemma 14: meet(meet(X, X), X) = X.
% 8.84/1.52 Proof:
% 8.84/1.52 meet(meet(X, X), X)
% 8.84/1.52 = { by lemma 11 R->L }
% 8.84/1.52 meet(meet(X, join(join(meet(X, Y), meet(Z, X)), X)), X)
% 8.84/1.52 = { by lemma 13 }
% 8.84/1.52 X
% 8.84/1.52
% 8.84/1.52 Lemma 15: join(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))) = X.
% 8.84/1.52 Proof:
% 8.84/1.52 join(X, meet(X, join(meet(join(X, Y), join(Z, X)), X)))
% 8.84/1.52 = { by lemma 9 R->L }
% 8.84/1.52 join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))
% 8.84/1.52 = { by lemma 8 }
% 8.84/1.52 X
% 8.84/1.52
% 8.84/1.52 Lemma 16: meet(meet(join(meet(X, join(X, Y)), Z), X), meet(X, join(X, Y))) = meet(X, join(X, Y)).
% 8.84/1.52 Proof:
% 8.84/1.52 meet(meet(join(meet(X, join(X, Y)), Z), X), meet(X, join(X, Y)))
% 8.84/1.52 = { by lemma 8 R->L }
% 8.84/1.52 meet(meet(join(meet(X, join(join(meet(W, X), meet(X, join(W, X))), Y)), Z), X), meet(X, join(X, Y)))
% 8.84/1.52 = { by lemma 8 R->L }
% 8.84/1.52 meet(meet(join(meet(X, join(join(meet(W, X), meet(X, join(W, X))), Y)), Z), X), meet(X, join(join(meet(W, X), meet(X, join(W, X))), Y)))
% 8.84/1.52 = { by lemma 6 R->L }
% 8.84/1.52 meet(meet(join(meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Y)), Z), X), meet(X, join(join(meet(W, X), meet(X, join(W, X))), Y)))
% 8.84/1.52 = { by lemma 6 R->L }
% 8.84/1.52 meet(meet(join(meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Y)), Z), X), meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Y)))
% 8.84/1.52 = { by axiom 1 (single_axiom) R->L }
% 8.84/1.52 meet(meet(join(meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Y)), Z), join(meet(join(meet(W, X), meet(X, join(W, X))), Y), meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Y)))), meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Y)))
% 8.84/1.52 = { by lemma 9 }
% 8.84/1.52 meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Y))
% 8.84/1.52 = { by lemma 6 }
% 8.84/1.52 meet(X, join(join(meet(W, X), meet(X, join(W, X))), Y))
% 8.84/1.52 = { by lemma 8 }
% 8.84/1.52 meet(X, join(X, Y))
% 8.84/1.52
% 8.84/1.52 Lemma 17: meet(meet(join(meet(X, X), Y), X), meet(X, X)) = meet(X, X).
% 8.84/1.52 Proof:
% 8.84/1.52 meet(meet(join(meet(X, X), Y), X), meet(X, X))
% 8.84/1.52 = { by lemma 15 R->L }
% 8.84/1.52 meet(meet(join(meet(X, X), Y), X), meet(X, join(X, meet(X, join(meet(join(X, Z), join(W, X)), X)))))
% 8.84/1.52 = { by lemma 15 R->L }
% 8.84/1.52 meet(meet(join(meet(X, join(X, meet(X, join(meet(join(X, Z), join(W, X)), X)))), Y), X), meet(X, join(X, meet(X, join(meet(join(X, Z), join(W, X)), X)))))
% 8.84/1.52 = { by lemma 16 }
% 8.84/1.52 meet(X, join(X, meet(X, join(meet(join(X, Z), join(W, X)), X))))
% 8.84/1.52 = { by lemma 15 }
% 8.84/1.52 meet(X, X)
% 8.84/1.52
% 8.84/1.52 Lemma 18: meet(X, meet(X, X)) = meet(X, X).
% 8.84/1.52 Proof:
% 8.84/1.52 meet(X, meet(X, X))
% 8.84/1.52 = { by lemma 14 R->L }
% 8.84/1.52 meet(meet(meet(X, X), X), meet(X, X))
% 8.84/1.52 = { by lemma 15 R->L }
% 8.84/1.52 meet(meet(join(meet(X, X), meet(meet(X, X), join(meet(join(meet(X, X), Y), join(Z, meet(X, X))), meet(X, X)))), X), meet(X, X))
% 8.84/1.52 = { by lemma 17 }
% 8.84/1.52 meet(X, X)
% 8.84/1.52
% 8.84/1.52 Lemma 19: meet(meet(X, join(Y, meet(X, Z))), meet(X, Z)) = meet(X, Z).
% 8.84/1.52 Proof:
% 8.84/1.52 meet(meet(X, join(Y, meet(X, Z))), meet(X, Z))
% 8.84/1.52 = { by lemma 8 R->L }
% 8.84/1.52 meet(meet(X, join(Y, meet(join(meet(W, X), meet(X, join(W, X))), Z))), meet(X, Z))
% 8.84/1.52 = { by lemma 8 R->L }
% 8.84/1.52 meet(meet(X, join(Y, meet(join(meet(W, X), meet(X, join(W, X))), Z))), meet(join(meet(W, X), meet(X, join(W, X))), Z))
% 8.84/1.52 = { by axiom 1 (single_axiom) R->L }
% 8.84/1.52 meet(meet(join(meet(join(meet(W, X), meet(X, join(W, X))), Z), meet(join(meet(W, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(T, join(X, meet(meet(join(X, V), join(U, X)), X)))), join(W, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(W, X), meet(X, join(W, X))), Z))), join(Y, meet(join(meet(W, X), meet(X, join(W, X))), Z))), meet(join(meet(W, X), meet(X, join(W, X))), Z))
% 8.84/1.52 = { by lemma 9 }
% 8.84/1.52 meet(join(meet(W, X), meet(X, join(W, X))), Z)
% 8.84/1.52 = { by lemma 8 }
% 8.84/1.52 meet(X, Z)
% 8.84/1.52
% 8.84/1.52 Lemma 20: meet(meet(X, X), meet(X, join(X, Y))) = meet(X, join(X, Y)).
% 8.84/1.52 Proof:
% 8.84/1.52 meet(meet(X, X), meet(X, join(X, Y)))
% 8.84/1.52 = { by lemma 8 R->L }
% 8.84/1.52 meet(meet(X, X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), Y)))
% 8.84/1.52 = { by lemma 6 R->L }
% 8.84/1.52 meet(meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), X), meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), Y)))
% 8.84/1.52 = { by lemma 6 R->L }
% 8.84/1.52 meet(meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), X), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)))
% 8.84/1.52 = { by axiom 1 (single_axiom) R->L }
% 8.84/1.53 meet(meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(meet(join(meet(Z, X), meet(X, join(Z, X))), Y), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)))), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)))
% 8.84/1.53 = { by lemma 19 }
% 8.84/1.53 meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))
% 8.84/1.53 = { by lemma 6 }
% 8.84/1.53 meet(X, join(join(meet(Z, X), meet(X, join(Z, X))), Y))
% 8.84/1.53 = { by lemma 8 }
% 8.84/1.53 meet(X, join(X, Y))
% 8.84/1.53
% 8.84/1.53 Lemma 21: join(meet(meet(X, Y), meet(X, join(X, Y))), meet(meet(X, Y), X)) = meet(X, Y).
% 8.84/1.53 Proof:
% 8.84/1.53 join(meet(meet(X, Y), meet(X, join(X, Y))), meet(meet(X, Y), X))
% 8.84/1.53 = { by lemma 5 R->L }
% 8.84/1.53 join(meet(meet(X, Y), meet(X, join(X, Y))), meet(meet(X, Y), join(meet(X, Y), meet(X, join(X, Y)))))
% 8.84/1.53 = { by lemma 5 }
% 8.84/1.53 meet(X, Y)
% 8.84/1.53
% 8.84/1.53 Lemma 22: join(meet(X, join(X, X)), X) = meet(X, X).
% 8.84/1.53 Proof:
% 8.84/1.53 join(meet(X, join(X, X)), X)
% 8.84/1.53 = { by lemma 14 R->L }
% 8.84/1.53 join(meet(X, join(X, X)), meet(meet(X, X), X))
% 8.84/1.53 = { by lemma 20 R->L }
% 8.84/1.53 join(meet(meet(X, X), meet(X, join(X, X))), meet(meet(X, X), X))
% 8.84/1.53 = { by lemma 21 }
% 8.84/1.53 meet(X, X)
% 8.84/1.53
% 8.84/1.53 Lemma 23: join(X, meet(X, X)) = X.
% 8.84/1.53 Proof:
% 8.84/1.53 join(X, meet(X, X))
% 8.84/1.53 = { by lemma 18 R->L }
% 8.84/1.53 join(X, meet(X, meet(X, X)))
% 8.84/1.53 = { by lemma 11 R->L }
% 8.84/1.53 join(join(join(meet(X, Y), meet(Z, X)), X), meet(X, meet(X, X)))
% 8.84/1.53 = { by lemma 11 R->L }
% 8.84/1.53 join(join(join(meet(X, Y), meet(Z, X)), X), meet(X, meet(join(join(meet(X, Y), meet(Z, X)), X), X)))
% 8.84/1.53 = { by lemma 11 R->L }
% 8.84/1.53 join(join(join(meet(X, Y), meet(Z, X)), X), meet(X, meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X))))
% 8.84/1.53 = { by lemma 13 R->L }
% 8.84/1.53 join(meet(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X)), meet(X, meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X))))
% 8.84/1.53 = { by lemma 22 R->L }
% 8.84/1.53 join(meet(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X)), meet(X, join(meet(join(join(meet(X, Y), meet(Z, X)), X), join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X))), join(join(meet(X, Y), meet(Z, X)), X))))
% 8.84/1.53 = { by lemma 10 }
% 8.84/1.53 X
% 8.84/1.53
% 8.84/1.53 Lemma 24: meet(X, X) = X.
% 8.84/1.53 Proof:
% 8.84/1.53 meet(X, X)
% 8.84/1.53 = { by lemma 23 R->L }
% 8.84/1.53 meet(X, join(X, meet(X, X)))
% 8.84/1.53 = { by lemma 20 R->L }
% 8.84/1.53 meet(meet(X, X), meet(X, join(X, meet(X, X))))
% 8.84/1.53 = { by lemma 18 R->L }
% 8.84/1.53 meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X))))
% 8.84/1.53 = { by lemma 5 R->L }
% 8.84/1.53 join(meet(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), meet(meet(X, meet(X, X)), X)), meet(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), join(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), meet(meet(X, meet(X, X)), X))))
% 8.84/1.53 = { by lemma 21 }
% 8.84/1.53 join(meet(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), meet(meet(X, meet(X, X)), X)), meet(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), meet(X, meet(X, X))))
% 8.84/1.53 = { by lemma 23 }
% 8.84/1.53 join(meet(meet(meet(X, meet(X, X)), meet(X, X)), meet(meet(X, meet(X, X)), X)), meet(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), meet(X, meet(X, X))))
% 8.84/1.53 = { by lemma 18 }
% 8.84/1.53 join(meet(meet(meet(X, X), meet(X, X)), meet(meet(X, meet(X, X)), X)), meet(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), meet(X, meet(X, X))))
% 8.84/1.53 = { by lemma 18 }
% 8.84/1.53 join(meet(meet(meet(X, X), meet(X, X)), meet(meet(X, X), X)), meet(meet(meet(X, meet(X, X)), meet(X, join(X, meet(X, X)))), meet(X, meet(X, X))))
% 8.84/1.53 = { by lemma 18 }
% 8.84/1.53 join(meet(meet(meet(X, X), meet(X, X)), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, meet(X, X))))
% 8.84/1.53 = { by lemma 18 }
% 8.84/1.53 join(meet(meet(meet(X, X), meet(X, X)), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 8 R->L }
% 9.33/1.53 join(meet(meet(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(X, X)), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 8 R->L }
% 9.33/1.53 join(meet(meet(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), X)), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 8 R->L }
% 9.33/1.53 join(meet(meet(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(meet(Y, X), meet(X, join(Y, X))))), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by axiom 1 (single_axiom) R->L }
% 9.33/1.53 join(meet(meet(meet(join(meet(join(meet(Y, X), meet(X, join(Y, X))), join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(join(meet(Y, X), meet(X, join(Y, X))), join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(meet(Y, X), meet(X, join(Y, X))))), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 17 }
% 9.33/1.53 join(meet(meet(join(meet(Y, X), meet(X, join(Y, X))), join(meet(Y, X), meet(X, join(Y, X)))), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 8 }
% 9.33/1.53 join(meet(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 8 }
% 9.33/1.53 join(meet(meet(X, X), meet(meet(X, X), X)), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 14 }
% 9.33/1.53 join(meet(meet(X, X), X), meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 14 }
% 9.33/1.53 join(X, meet(meet(meet(X, X), meet(X, join(X, meet(X, X)))), meet(X, X)))
% 9.33/1.53 = { by lemma 20 }
% 9.33/1.53 join(X, meet(meet(X, join(X, meet(X, X))), meet(X, X)))
% 9.33/1.53 = { by lemma 19 }
% 9.33/1.53 join(X, meet(X, X))
% 9.33/1.53 = { by lemma 23 }
% 9.33/1.53 X
% 9.33/1.53
% 9.33/1.53 Lemma 25: join(join(meet(X, Y), X), X) = X.
% 9.33/1.53 Proof:
% 9.33/1.53 join(join(meet(X, Y), X), X)
% 9.33/1.53 = { by lemma 9 R->L }
% 9.33/1.53 join(join(meet(X, Y), meet(meet(join(X, Z), join(W, X)), X)), X)
% 9.33/1.53 = { by lemma 11 }
% 9.33/1.53 X
% 9.33/1.53
% 9.33/1.53 Lemma 26: join(X, X) = X.
% 9.33/1.53 Proof:
% 9.33/1.53 join(X, X)
% 9.33/1.53 = { by lemma 25 R->L }
% 9.33/1.53 join(join(join(meet(X, join(X, X)), X), X), X)
% 9.33/1.53 = { by lemma 22 }
% 9.33/1.53 join(join(meet(X, X), X), X)
% 9.33/1.53 = { by lemma 25 }
% 9.33/1.53 X
% 9.33/1.53
% 9.33/1.53 Lemma 27: meet(X, meet(Y, X)) = meet(Y, X).
% 9.33/1.53 Proof:
% 9.33/1.53 meet(X, meet(Y, X))
% 9.33/1.53 = { by lemma 24 R->L }
% 9.33/1.53 meet(meet(X, X), meet(Y, X))
% 9.33/1.53 = { by lemma 26 R->L }
% 9.33/1.53 meet(meet(join(X, X), X), meet(Y, X))
% 9.33/1.53 = { by lemma 26 R->L }
% 9.33/1.53 meet(meet(join(X, X), X), meet(Y, join(X, X)))
% 9.33/1.53 = { by lemma 9 R->L }
% 9.33/1.53 meet(meet(join(X, meet(meet(join(X, Z), join(W, X)), X)), X), meet(Y, join(X, X)))
% 9.33/1.53 = { by lemma 9 R->L }
% 9.33/1.53 meet(meet(join(X, meet(meet(join(X, Z), join(W, X)), X)), X), meet(Y, join(X, meet(meet(join(X, Z), join(W, X)), X))))
% 9.33/1.53 = { by lemma 7 R->L }
% 9.33/1.53 meet(meet(join(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(Y, join(X, meet(meet(join(X, Z), join(W, X)), X))))), meet(Y, join(X, meet(meet(join(X, Z), join(W, X)), X))))
% 9.33/1.53 = { by lemma 12 }
% 9.33/1.53 meet(Y, join(X, meet(meet(join(X, Z), join(W, X)), X)))
% 9.33/1.53 = { by lemma 9 }
% 9.33/1.53 meet(Y, join(X, X))
% 9.33/1.53 = { by lemma 26 }
% 9.33/1.53 meet(Y, X)
% 9.33/1.53
% 9.33/1.53 Lemma 28: join(X, meet(Y, X)) = X.
% 9.33/1.53 Proof:
% 9.33/1.53 join(X, meet(Y, X))
% 9.33/1.53 = { by lemma 26 R->L }
% 9.33/1.53 join(X, meet(Y, join(X, X)))
% 9.33/1.53 = { by lemma 9 R->L }
% 9.33/1.53 join(meet(meet(join(X, Z), join(W, X)), X), meet(Y, join(X, X)))
% 9.33/1.53 = { by lemma 9 R->L }
% 9.33/1.53 join(meet(meet(join(X, Z), join(W, X)), X), meet(Y, join(X, meet(meet(join(X, Z), join(W, X)), X))))
% 9.33/1.53 = { by lemma 27 R->L }
% 9.33/1.53 join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(Y, join(X, meet(meet(join(X, Z), join(W, X)), X))))
% 9.33/1.53 = { by lemma 7 }
% 9.33/1.53 X
% 9.33/1.53
% 9.33/1.53 Lemma 29: meet(meet(X, Y), Y) = meet(X, Y).
% 9.33/1.53 Proof:
% 9.33/1.53 meet(meet(X, Y), Y)
% 9.33/1.53 = { by lemma 26 R->L }
% 9.33/1.53 join(meet(meet(X, Y), Y), meet(meet(X, Y), Y))
% 9.33/1.53 = { by lemma 24 R->L }
% 9.33/1.53 join(meet(meet(X, Y), meet(Y, Y)), meet(meet(X, Y), Y))
% 9.33/1.53 = { by lemma 27 R->L }
% 9.33/1.53 join(meet(meet(Y, meet(X, Y)), meet(Y, Y)), meet(meet(X, Y), Y))
% 9.33/1.53 = { by lemma 27 R->L }
% 9.33/1.53 join(meet(meet(Y, meet(X, Y)), meet(Y, Y)), meet(meet(Y, meet(X, Y)), Y))
% 9.33/1.53 = { by lemma 28 R->L }
% 9.33/1.53 join(meet(meet(Y, meet(X, Y)), meet(Y, join(Y, meet(X, Y)))), meet(meet(Y, meet(X, Y)), Y))
% 9.33/1.53 = { by lemma 21 }
% 9.33/1.53 meet(Y, meet(X, Y))
% 9.33/1.53 = { by lemma 27 }
% 9.33/1.53 meet(X, Y)
% 9.33/1.53
% 9.33/1.53 Lemma 30: meet(X, join(Y, X)) = X.
% 9.33/1.53 Proof:
% 9.33/1.53 meet(X, join(Y, X))
% 9.33/1.53 = { by lemma 5 R->L }
% 9.33/1.53 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(meet(X, join(Y, X)), X)))
% 9.33/1.53 = { by lemma 28 R->L }
% 9.33/1.53 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(X, join(meet(X, join(Y, X)), X)))))
% 9.33/1.53 = { by lemma 9 R->L }
% 9.33/1.53 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(meet(join(X, Z), join(W, X)), X), join(meet(X, join(Y, X)), X)))))
% 9.33/1.53 = { by lemma 9 R->L }
% 9.33/1.54 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(meet(join(X, Z), join(W, X)), X), join(meet(X, join(Y, meet(meet(join(X, Z), join(W, X)), X))), X)))))
% 9.33/1.54 = { by lemma 9 R->L }
% 9.33/1.54 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(meet(join(X, Z), join(W, X)), X), join(meet(X, join(Y, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(join(X, Z), join(W, X)), X))))))
% 9.33/1.54 = { by lemma 27 R->L }
% 9.33/1.54 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(X, join(Y, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(join(X, Z), join(W, X)), X))))))
% 9.33/1.54 = { by lemma 27 R->L }
% 9.33/1.54 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(X, join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(join(X, Z), join(W, X)), X))))))
% 9.33/1.54 = { by lemma 27 R->L }
% 9.33/1.54 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(X, join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))
% 9.33/1.54 = { by lemma 7 R->L }
% 9.33/1.54 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))
% 9.33/1.54 = { by lemma 5 R->L }
% 9.33/1.54 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))))))
% 9.33/1.55 = { by lemma 9 R->L }
% 9.33/1.55 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))))
% 9.33/1.55 = { by lemma 29 R->L }
% 9.33/1.55 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))))
% 9.33/1.55 = { by lemma 9 R->L }
% 9.33/1.55 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), U), join(T, meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))))), join(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))), meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))))
% 9.33/1.56 = { by lemma 8 }
% 9.33/1.56 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), U), join(T, meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))), meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))))
% 9.33/1.56 = { by lemma 15 }
% 9.61/1.56 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))), meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))))
% 9.61/1.57 = { by lemma 13 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))), meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))))
% 9.61/1.57 = { by lemma 9 R->L }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))), meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))))
% 9.61/1.57 = { by lemma 8 R->L }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), join(meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))), meet(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), join(meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))))))))))
% 9.61/1.57 = { by lemma 5 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))))))
% 9.61/1.57 = { by lemma 9 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), join(meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))))
% 9.61/1.57 = { by lemma 26 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(V, join(X, meet(meet(join(X, Z), join(W, X)), X)))), join(Y, meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X)))), meet(X, meet(meet(join(X, Z), join(W, X)), X))))))
% 9.61/1.57 = { by lemma 13 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(X, meet(meet(join(X, Z), join(W, X)), X)))))
% 9.61/1.57 = { by lemma 27 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), meet(meet(join(X, Z), join(W, X)), X))))
% 9.61/1.57 = { by lemma 9 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), X)))
% 9.61/1.57 = { by lemma 25 }
% 9.61/1.57 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), X))
% 9.61/1.57 = { by lemma 26 }
% 9.61/1.57 meet(meet(X, join(Y, X)), X)
% 9.61/1.57 = { by lemma 13 }
% 9.61/1.57 X
% 9.61/1.57
% 9.61/1.57 Lemma 31: join(join(X, Y), Y) = join(X, Y).
% 9.61/1.57 Proof:
% 9.61/1.57 join(join(X, Y), Y)
% 9.61/1.57 = { by lemma 30 R->L }
% 9.61/1.57 join(join(X, Y), meet(Y, join(X, Y)))
% 9.61/1.57 = { by lemma 28 }
% 9.61/1.57 join(X, Y)
% 9.61/1.57
% 9.61/1.57 Lemma 32: meet(X, join(X, Y)) = X.
% 9.61/1.57 Proof:
% 9.61/1.57 meet(X, join(X, Y))
% 9.61/1.57 = { by lemma 26 R->L }
% 9.61/1.57 join(meet(X, join(X, Y)), meet(X, join(X, Y)))
% 9.61/1.57 = { by lemma 6 R->L }
% 9.61/1.57 join(meet(X, join(X, Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(X, Y)))
% 9.61/1.57 = { by lemma 8 R->L }
% 9.61/1.57 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(X, Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(X, Y)))
% 9.61/1.58 = { by lemma 8 R->L }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(X, Y)))
% 9.61/1.58 = { by lemma 8 R->L }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)))
% 9.61/1.58 = { by lemma 11 R->L }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(join(join(meet(Z, X), meet(X, join(Z, X))), Y), join(meet(Z, X), meet(X, join(Z, X)))), meet(meet(join(join(join(meet(Z, X), meet(X, join(Z, X))), Y), T), join(S, join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))))
% 9.61/1.58 = { by lemma 29 R->L }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(meet(join(join(meet(Z, X), meet(X, join(Z, X))), Y), join(meet(Z, X), meet(X, join(Z, X)))), join(meet(Z, X), meet(X, join(Z, X)))), meet(meet(join(join(join(meet(Z, X), meet(X, join(Z, X))), Y), T), join(S, join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))))
% 9.61/1.58 = { by lemma 11 R->L }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(meet(join(join(meet(Z, X), meet(X, join(Z, X))), Y), join(join(meet(join(meet(Z, X), meet(X, join(Z, X))), X2), meet(Y2, join(meet(Z, X), meet(X, join(Z, X))))), join(meet(Z, X), meet(X, join(Z, X))))), join(meet(Z, X), meet(X, join(Z, X)))), meet(meet(join(join(join(meet(Z, X), meet(X, join(Z, X))), Y), T), join(S, join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))))
% 9.61/1.58 = { by lemma 9 }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(join(meet(Z, X), meet(X, join(Z, X))), meet(meet(join(join(join(meet(Z, X), meet(X, join(Z, X))), Y), T), join(S, join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))))
% 9.61/1.58 = { by lemma 9 }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), join(join(meet(Z, X), meet(X, join(Z, X))), Y))))
% 9.61/1.58 = { by lemma 31 }
% 9.61/1.58 join(meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y)), meet(join(meet(Z, join(join(meet(X, W), meet(V, X)), X)), meet(join(meet(X, meet(meet(join(X, W), join(V, X)), X)), meet(U, join(X, meet(meet(join(X, W), join(V, X)), X)))), join(Z, join(join(meet(X, W), meet(V, X)), X)))), join(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(Z, X), meet(X, join(Z, X))), Y))))
% 9.61/1.58 = { by axiom 1 (single_axiom) }
% 9.61/1.58 X
% 9.61/1.58
% 9.61/1.58 Lemma 33: meet(meet(X, Y), meet(Y, X)) = meet(Y, X).
% 9.61/1.58 Proof:
% 9.61/1.58 meet(meet(X, Y), meet(Y, X))
% 9.61/1.58 = { by lemma 11 R->L }
% 9.61/1.58 meet(meet(X, Y), meet(Y, join(join(meet(X, Z), meet(W, X)), X)))
% 9.61/1.58 = { by lemma 10 R->L }
% 9.61/1.58 meet(meet(join(meet(Y, join(join(meet(X, Z), meet(W, X)), X)), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), Y), meet(Y, join(join(meet(X, Z), meet(W, X)), X)))
% 9.61/1.58 = { by lemma 8 R->L }
% 9.61/1.58 meet(meet(join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), Y), meet(Y, join(join(meet(X, Z), meet(W, X)), X)))
% 9.61/1.58 = { by lemma 8 R->L }
% 9.61/1.58 meet(meet(join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), Y), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))
% 9.61/1.58 = { by axiom 1 (single_axiom) R->L }
% 9.61/1.58 meet(meet(join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))
% 9.61/1.58 = { by lemma 29 R->L }
% 9.61/1.59 meet(meet(meet(join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))
% 9.61/1.59 = { by lemma 32 R->L }
% 9.61/1.59 meet(meet(meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))
% 9.61/1.59 = { by lemma 32 R->L }
% 9.61/1.59 meet(meet(meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))))
% 9.61/1.59 = { by lemma 25 R->L }
% 9.61/1.60 meet(meet(join(join(meet(meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))))
% 9.61/1.60 = { by lemma 28 R->L }
% 9.61/1.60 meet(meet(join(join(meet(meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))))
% 9.61/1.60 = { by lemma 9 }
% 9.61/1.60 meet(meet(join(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))))
% 9.61/1.60 = { by lemma 31 }
% 9.61/1.61 meet(meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(join(meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))), meet(X, join(Y, join(join(meet(X, Z), meet(W, X)), X)))), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))), meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))), meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))))))
% 9.61/1.61 = { by lemma 16 }
% 9.61/1.61 meet(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), join(meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)), meet(join(meet(V, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(V, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X)))))
% 9.61/1.61 = { by lemma 32 }
% 9.61/1.61 meet(join(meet(V, Y), meet(Y, join(V, Y))), join(join(meet(X, Z), meet(W, X)), X))
% 9.61/1.61 = { by lemma 8 }
% 9.61/1.61 meet(Y, join(join(meet(X, Z), meet(W, X)), X))
% 9.61/1.61 = { by lemma 11 }
% 9.61/1.61 meet(Y, X)
% 9.61/1.61
% 9.61/1.61 Lemma 34: join(join(meet(X, Y), meet(Z, Y)), Y) = Y.
% 9.61/1.61 Proof:
% 9.61/1.61 join(join(meet(X, Y), meet(Z, Y)), Y)
% 9.61/1.61 = { by lemma 27 R->L }
% 9.61/1.61 join(join(meet(Y, meet(X, Y)), meet(Z, Y)), Y)
% 9.61/1.61 = { by lemma 11 }
% 9.61/1.61 Y
% 9.61/1.61
% 9.61/1.61 Lemma 35: join(join(X, Y), join(Y, X)) = join(Y, X).
% 9.61/1.61 Proof:
% 9.61/1.61 join(join(X, Y), join(Y, X))
% 9.61/1.61 = { by lemma 32 R->L }
% 9.61/1.61 join(join(X, meet(Y, join(Y, X))), join(Y, X))
% 9.61/1.61 = { by lemma 30 R->L }
% 9.61/1.61 join(join(meet(X, join(Y, X)), meet(Y, join(Y, X))), join(Y, X))
% 9.61/1.61 = { by lemma 34 }
% 9.61/1.61 join(Y, X)
% 9.61/1.61
% 9.61/1.61 Goal 1 (prove_wal_axioms): tuple(join(join(meet(a, b), meet(c, b)), b), join(a, a), join(b, a), meet(meet(join(a, b), join(c, b)), b), meet(a, a), meet(b, a)) = tuple(b, a, join(a, b), b, a, meet(a, b)).
% 9.61/1.61 Proof:
% 9.61/1.61 tuple(join(join(meet(a, b), meet(c, b)), b), join(a, a), join(b, a), meet(meet(join(a, b), join(c, b)), b), meet(a, a), meet(b, a))
% 9.61/1.61 = { by lemma 24 }
% 9.61/1.61 tuple(join(join(meet(a, b), meet(c, b)), b), join(a, a), join(b, a), meet(meet(join(a, b), join(c, b)), b), a, meet(b, a))
% 9.61/1.61 = { by lemma 26 }
% 9.61/1.61 tuple(join(join(meet(a, b), meet(c, b)), b), a, join(b, a), meet(meet(join(a, b), join(c, b)), b), a, meet(b, a))
% 9.61/1.61 = { by lemma 34 }
% 9.61/1.61 tuple(b, a, join(b, a), meet(meet(join(a, b), join(c, b)), b), a, meet(b, a))
% 9.61/1.61 = { by lemma 30 R->L }
% 9.61/1.61 tuple(b, a, join(b, a), meet(meet(join(a, b), join(c, b)), meet(b, join(a, b))), a, meet(b, a))
% 9.61/1.61 = { by lemma 30 R->L }
% 9.61/1.61 tuple(b, a, join(b, a), meet(meet(join(a, b), join(c, meet(b, join(a, b)))), meet(b, join(a, b))), a, meet(b, a))
% 9.61/1.61 = { by lemma 12 }
% 9.61/1.61 tuple(b, a, join(b, a), meet(b, join(a, b)), a, meet(b, a))
% 9.61/1.61 = { by lemma 30 }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, meet(b, a))
% 9.61/1.61 = { by lemma 33 R->L }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, meet(meet(a, b), meet(b, a)))
% 9.61/1.61 = { by lemma 5 R->L }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, join(meet(meet(meet(a, b), meet(b, a)), meet(a, b)), meet(meet(meet(a, b), meet(b, a)), join(meet(meet(a, b), meet(b, a)), meet(a, b)))))
% 9.61/1.61 = { by lemma 31 R->L }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, join(meet(meet(meet(a, b), meet(b, a)), meet(a, b)), meet(meet(meet(a, b), meet(b, a)), join(join(meet(meet(a, b), meet(b, a)), meet(a, b)), meet(a, b)))))
% 9.61/1.61 = { by lemma 25 }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, join(meet(meet(meet(a, b), meet(b, a)), meet(a, b)), meet(meet(meet(a, b), meet(b, a)), meet(a, b))))
% 9.61/1.61 = { by lemma 26 }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, meet(meet(meet(a, b), meet(b, a)), meet(a, b)))
% 9.61/1.61 = { by lemma 33 }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, meet(meet(b, a), meet(a, b)))
% 9.61/1.61 = { by lemma 33 }
% 9.61/1.61 tuple(b, a, join(b, a), b, a, meet(a, b))
% 9.61/1.61 = { by lemma 35 R->L }
% 9.61/1.61 tuple(b, a, join(join(a, b), join(b, a)), b, a, meet(a, b))
% 9.61/1.61 = { by lemma 28 R->L }
% 9.61/1.61 tuple(b, a, join(join(join(a, b), join(b, a)), meet(join(a, b), join(join(a, b), join(b, a)))), b, a, meet(a, b))
% 9.61/1.61 = { by lemma 32 }
% 9.61/1.61 tuple(b, a, join(join(join(a, b), join(b, a)), join(a, b)), b, a, meet(a, b))
% 9.61/1.61 = { by lemma 35 }
% 9.61/1.61 tuple(b, a, join(join(b, a), join(a, b)), b, a, meet(a, b))
% 9.61/1.61 = { by lemma 35 }
% 9.61/1.61 tuple(b, a, join(a, b), b, a, meet(a, b))
% 9.61/1.61 % SZS output end Proof
% 9.61/1.61
% 9.61/1.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------