TSTP Solution File: LAT095-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT095-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n008.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 06:27:25 EDT 2023
% Result : Unsatisfiable 10.40s 1.76s
% Output : Proof 20.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT095-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % 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 : n008.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 05:33:02 EDT 2023
% 0.14/0.34 % CPUTime :
% 10.40/1.76 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 10.40/1.76
% 10.40/1.76 % SZS status Unsatisfiable
% 10.40/1.76
% 17.33/2.69 % SZS output start Proof
% 17.33/2.69 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.
% 17.33/2.69
% 17.33/2.69 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))).
% 17.33/2.69 Proof:
% 17.33/2.69 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)))
% 17.33/2.69 = { by axiom 1 (single_axiom) R->L }
% 17.33/2.69 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)))
% 17.33/2.69 = { by axiom 1 (single_axiom) }
% 17.33/2.69 join(meet(Y, Z), meet(Z, join(Y, Z)))
% 17.33/2.69
% 17.33/2.69 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.
% 17.33/2.69 Proof:
% 17.33/2.69 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)))
% 17.33/2.70 = { by axiom 1 (single_axiom) R->L }
% 17.33/2.70 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)))
% 17.33/2.70 = { by axiom 1 (single_axiom) R->L }
% 17.33/2.70 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)))
% 17.33/2.71 = { by axiom 1 (single_axiom) R->L }
% 17.33/2.71 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)))
% 17.33/2.72 = { by axiom 1 (single_axiom) R->L }
% 17.33/2.72 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)))
% 17.33/2.74 = { by axiom 1 (single_axiom) R->L }
% 17.33/2.74 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)))
% 17.87/2.76 = { by axiom 1 (single_axiom) R->L }
% 17.87/2.76 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)))
% 18.08/2.79 = { by axiom 1 (single_axiom) R->L }
% 18.08/2.80 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)))
% 18.08/2.81 = { by axiom 1 (single_axiom) R->L }
% 18.08/2.82 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)))
% 18.55/2.85 = { by axiom 1 (single_axiom) R->L }
% 18.55/2.86 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)))
% 18.55/2.87 = { by axiom 1 (single_axiom) R->L }
% 18.55/2.89 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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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, 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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(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Y))), Z)))
% 18.55/2.89 = { by axiom 1 (single_axiom) R->L }
% 18.55/2.90 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, 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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))), Y))), Z)))
% 18.55/2.90 = { by axiom 1 (single_axiom) R->L }
% 18.55/2.91 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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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)))
% 18.55/2.91 = { by axiom 1 (single_axiom) R->L }
% 18.55/2.92 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)))
% 18.55/2.92 = { by lemma 2 }
% 18.55/2.92 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)))))))
% 18.55/2.92 = { by axiom 1 (single_axiom) }
% 18.55/2.92 Y
% 18.55/2.92
% 18.55/2.92 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.
% 18.55/2.92 Proof:
% 18.55/2.92 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)))
% 18.55/2.92 = { by lemma 3 R->L }
% 18.55/2.92 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)))
% 18.55/2.93 = { by lemma 3 R->L }
% 18.55/2.93 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)))
% 18.55/2.94 = { by lemma 3 R->L }
% 18.55/2.94 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)))
% 18.55/2.94 = { by lemma 3 R->L }
% 18.55/2.94 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)))
% 18.55/2.95 = { by lemma 3 R->L }
% 18.55/2.95 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)))
% 18.55/2.96 = { by lemma 3 R->L }
% 18.55/2.96 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)))
% 18.55/2.96 = { by lemma 3 R->L }
% 18.55/2.97 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)))
% 18.55/2.97 = { by lemma 3 R->L }
% 18.55/2.98 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)))
% 18.55/2.98 = { by lemma 3 R->L }
% 18.55/2.98 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)))
% 18.55/2.98 = { by lemma 3 R->L }
% 18.55/2.98 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)))
% 18.55/2.98 = { by lemma 3 R->L }
% 18.55/2.99 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)))
% 18.55/2.99 = { by lemma 3 R->L }
% 18.55/2.99 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)))
% 18.55/2.99 = { by lemma 2 }
% 18.55/2.99 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)))
% 18.55/2.99 = { by lemma 3 }
% 18.55/2.99 Y
% 18.55/2.99
% 18.55/2.99 Lemma 5: join(meet(X, Y), meet(X, join(X, Y))) = X.
% 18.55/2.99 Proof:
% 18.55/2.99 join(meet(X, Y), meet(X, join(X, Y)))
% 18.55/2.99 = { by lemma 3 R->L }
% 18.55/2.99 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)))
% 18.55/2.99 = { by lemma 3 R->L }
% 18.55/2.99 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)))
% 18.55/2.99 = { by lemma 3 }
% 18.55/3.00 X
% 18.55/3.00
% 18.55/3.00 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.
% 18.55/3.00 Proof:
% 18.55/3.00 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))))
% 18.55/3.00 = { by lemma 4 R->L }
% 18.55/3.00 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)))
% 18.55/3.00 = { by axiom 1 (single_axiom) }
% 18.55/3.01 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)))
% 18.55/3.01 = { by axiom 1 (single_axiom) }
% 18.55/3.01 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)))
% 18.55/3.01 = { by axiom 1 (single_axiom) }
% 18.55/3.01 join(meet(Y, U), meet(Y, join(Y, U)))
% 18.55/3.01 = { by lemma 5 }
% 18.55/3.01 Y
% 18.55/3.01
% 18.55/3.01 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.
% 18.55/3.01 Proof:
% 18.55/3.01 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))))
% 18.55/3.01 = { by lemma 3 R->L }
% 18.55/3.01 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))))
% 18.55/3.01 = { by lemma 6 }
% 18.55/3.01 X
% 18.55/3.01
% 18.55/3.01 Lemma 8: join(meet(X, Y), meet(Y, join(X, Y))) = Y.
% 18.55/3.01 Proof:
% 18.55/3.01 join(meet(X, Y), meet(Y, join(X, Y)))
% 18.55/3.01 = { by lemma 7 R->L }
% 18.55/3.01 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)))))))
% 18.55/3.01 = { by axiom 1 (single_axiom) }
% 18.55/3.01 Y
% 18.55/3.01
% 18.55/3.01 Lemma 9: meet(meet(join(X, Y), join(Z, X)), X) = X.
% 18.55/3.01 Proof:
% 18.55/3.01 meet(meet(join(X, Y), join(Z, X)), X)
% 18.55/3.01 = { by lemma 8 R->L }
% 18.55/3.01 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))))
% 18.55/3.01 = { by lemma 7 }
% 18.55/3.01 X
% 18.55/3.01
% 18.55/3.01 Lemma 10: join(meet(X, X), meet(Y, join(X, X))) = X.
% 18.55/3.01 Proof:
% 18.55/3.01 join(meet(X, X), meet(Y, join(X, X)))
% 18.55/3.01 = { by lemma 9 R->L }
% 18.55/3.01 join(meet(X, X), meet(Y, join(X, meet(meet(join(X, Z), join(W, X)), X))))
% 18.55/3.01 = { by lemma 9 R->L }
% 18.55/3.01 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))))
% 18.55/3.01 = { by lemma 7 }
% 18.55/3.01 X
% 18.55/3.01
% 18.55/3.01 Lemma 11: join(meet(X, join(join(meet(Y, Z), meet(W, Y)), Y)), meet(Y, join(X, join(join(meet(Y, Z), meet(W, Y)), Y)))) = Y.
% 18.55/3.01 Proof:
% 18.55/3.01 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))))
% 18.55/3.01 = { by lemma 4 R->L }
% 18.55/3.01 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)))
% 18.55/3.01 = { by lemma 4 }
% 18.55/3.01 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)))
% 18.55/3.01 = { by lemma 4 }
% 18.55/3.01 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)))
% 18.55/3.02 = { by lemma 4 }
% 18.55/3.02 join(meet(Y, V), meet(Y, join(Y, V)))
% 18.55/3.02 = { by lemma 5 }
% 18.55/3.02 Y
% 18.55/3.02
% 18.55/3.02 Lemma 12: join(join(meet(X, Y), meet(Z, X)), X) = X.
% 18.55/3.02 Proof:
% 18.55/3.02 join(join(meet(X, Y), meet(Z, X)), X)
% 18.55/3.02 = { by lemma 10 R->L }
% 18.55/3.02 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))))
% 18.55/3.02 = { by lemma 11 }
% 18.55/3.02 X
% 18.55/3.02
% 18.55/3.02 Lemma 13: meet(meet(X, join(Y, meet(X, Z))), meet(X, Z)) = meet(X, Z).
% 18.55/3.02 Proof:
% 18.55/3.02 meet(meet(X, join(Y, meet(X, Z))), meet(X, Z))
% 18.55/3.02 = { by lemma 8 R->L }
% 18.55/3.02 meet(meet(X, join(Y, meet(join(meet(W, X), meet(X, join(W, X))), Z))), meet(X, Z))
% 18.55/3.02 = { by lemma 8 R->L }
% 18.55/3.02 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))
% 18.55/3.02 = { by axiom 1 (single_axiom) R->L }
% 18.55/3.02 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))
% 18.55/3.02 = { by lemma 9 }
% 18.55/3.02 meet(join(meet(W, X), meet(X, join(W, X))), Z)
% 18.55/3.02 = { by lemma 8 }
% 18.55/3.02 meet(X, Z)
% 18.55/3.02
% 18.55/3.02 Lemma 14: meet(X, X) = X.
% 18.55/3.02 Proof:
% 18.55/3.02 meet(X, X)
% 18.55/3.02 = { by lemma 9 R->L }
% 18.55/3.02 meet(meet(meet(join(X, Y), join(Z, X)), X), X)
% 18.55/3.02 = { by lemma 9 R->L }
% 18.55/3.02 meet(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), X))
% 18.55/3.02 = { by lemma 9 R->L }
% 18.55/3.02 meet(meet(meet(join(X, Y), join(Z, X)), meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(join(X, Y), join(Z, X)), X))
% 18.55/3.02 = { by lemma 12 R->L }
% 18.55/3.02 meet(meet(meet(join(X, Y), join(Z, X)), join(join(meet(meet(meet(join(X, Y), join(Z, X)), X), W), meet(V, meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X))
% 18.55/3.02 = { by lemma 13 }
% 18.55/3.02 meet(meet(join(X, Y), join(Z, X)), X)
% 18.55/3.02 = { by lemma 9 }
% 18.55/3.02 X
% 18.55/3.02
% 18.55/3.02 Lemma 15: meet(meet(X, join(Y, meet(Z, X))), meet(Z, X)) = meet(Z, X).
% 18.55/3.02 Proof:
% 18.55/3.02 meet(meet(X, join(Y, meet(Z, X))), meet(Z, X))
% 18.55/3.02 = { by lemma 8 R->L }
% 18.55/3.02 meet(meet(join(meet(Z, X), meet(X, join(Z, X))), join(Y, meet(Z, X))), meet(Z, X))
% 18.55/3.02 = { by lemma 9 }
% 18.55/3.02 meet(Z, X)
% 18.55/3.02
% 18.55/3.02 Lemma 16: meet(meet(X, join(Y, X)), X) = X.
% 18.55/3.02 Proof:
% 18.55/3.02 meet(meet(X, join(Y, X)), X)
% 18.55/3.02 = { by lemma 9 R->L }
% 18.55/3.02 meet(meet(X, join(Y, X)), meet(meet(join(X, Z), join(W, X)), X))
% 18.55/3.02 = { by lemma 9 R->L }
% 18.55/3.02 meet(meet(X, join(Y, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(join(X, Z), join(W, X)), X))
% 18.55/3.02 = { by lemma 15 }
% 18.55/3.02 meet(meet(join(X, Z), join(W, X)), X)
% 18.55/3.02 = { by lemma 9 }
% 18.55/3.02 X
% 18.55/3.02
% 18.55/3.02 Lemma 17: join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Z))) = Y.
% 18.55/3.02 Proof:
% 18.55/3.02 join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Z), meet(Y, join(join(meet(X, Y), meet(Y, join(X, Y))), Z)))
% 18.55/3.02 = { by lemma 11 R->L }
% 18.55/3.02 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)))
% 18.55/3.02 = { by lemma 4 }
% 18.55/3.02 Y
% 18.55/3.02
% 18.55/3.02 Lemma 18: join(meet(X, Y), meet(Z, join(meet(X, Y), meet(X, Y)))) = meet(X, Y).
% 18.55/3.02 Proof:
% 18.55/3.02 join(meet(X, Y), meet(Z, join(meet(X, Y), meet(X, Y))))
% 18.55/3.02 = { by lemma 9 R->L }
% 18.55/3.02 join(meet(X, Y), meet(Z, join(meet(X, Y), meet(meet(join(meet(X, Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 14 R->L }
% 18.55/3.02 join(meet(meet(X, Y), meet(X, Y)), meet(Z, join(meet(X, Y), meet(meet(join(meet(X, Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 13 R->L }
% 18.55/3.02 join(meet(meet(X, Y), meet(meet(X, join(W, meet(X, Y))), meet(X, Y))), meet(Z, join(meet(X, Y), meet(meet(join(meet(X, Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 17 R->L }
% 18.55/3.02 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(X, Y))), meet(X, Y))), meet(Z, join(meet(X, Y), meet(meet(join(meet(X, Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 17 R->L }
% 18.55/3.02 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(X, Y))), meet(Z, join(meet(X, Y), meet(meet(join(meet(X, Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 17 R->L }
% 18.55/3.02 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(Z, join(meet(X, Y), meet(meet(join(meet(X, Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 17 R->L }
% 18.55/3.02 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(Z, join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(join(meet(X, Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 17 R->L }
% 18.55/3.02 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(Z, join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(X, join(X, Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.02 = { by lemma 17 R->L }
% 18.55/3.03 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(Z, join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(X, join(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), join(W, meet(X, Y))), meet(X, Y)))))
% 18.55/3.03 = { by lemma 17 R->L }
% 18.55/3.03 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(Z, join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(X, join(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(X, Y)))))
% 18.55/3.03 = { by lemma 17 R->L }
% 18.55/3.03 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(X, join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(Z, join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(X, join(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y)))))
% 18.55/3.03 = { by lemma 3 R->L }
% 18.55/3.03 join(meet(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(X, join(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(Z, join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(meet(join(meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y), meet(X, join(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), join(W, meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y))), meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y)))))
% 18.55/3.03 = { by lemma 7 }
% 18.55/3.03 meet(join(meet(join(meet(V, X), meet(X, join(V, X))), X), meet(X, join(join(meet(V, X), meet(X, join(V, X))), X))), Y)
% 18.55/3.03 = { by lemma 17 }
% 18.55/3.03 meet(X, Y)
% 18.55/3.03
% 18.55/3.03 Lemma 19: join(meet(X, meet(Y, join(X, X))), X) = X.
% 18.55/3.03 Proof:
% 18.55/3.03 join(meet(X, meet(Y, join(X, X))), X)
% 18.55/3.03 = { by lemma 9 R->L }
% 18.55/3.03 join(meet(X, meet(Y, join(meet(meet(join(X, Z), join(W, X)), X), X))), X)
% 18.55/3.03 = { by lemma 9 R->L }
% 18.55/3.03 join(meet(X, meet(Y, join(meet(meet(join(X, Z), join(W, X)), X), meet(meet(join(X, Z), join(W, X)), X)))), X)
% 18.55/3.03 = { by lemma 9 R->L }
% 18.55/3.03 join(meet(X, meet(Y, join(meet(meet(join(X, Z), join(W, X)), X), meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(join(X, Z), join(W, X)), X))
% 18.55/3.03 = { by lemma 9 R->L }
% 18.55/3.03 join(meet(meet(meet(join(X, Z), join(W, X)), X), meet(Y, join(meet(meet(join(X, Z), join(W, X)), X), meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(join(X, Z), join(W, X)), X))
% 18.55/3.03 = { by lemma 14 R->L }
% 18.55/3.03 join(meet(meet(meet(join(X, Z), join(W, X)), X), meet(Y, join(meet(meet(join(X, Z), join(W, X)), X), meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(meet(join(X, Z), join(W, X)), X), meet(meet(join(X, Z), join(W, X)), X)))
% 18.55/3.03 = { by lemma 18 R->L }
% 18.55/3.03 join(meet(meet(meet(join(X, Z), join(W, X)), X), meet(Y, join(meet(meet(join(X, Z), join(W, X)), X), meet(meet(join(X, Z), join(W, X)), X)))), meet(meet(meet(join(X, Z), join(W, X)), X), join(meet(meet(join(X, Z), join(W, X)), X), meet(Y, join(meet(meet(join(X, Z), join(W, X)), X), meet(meet(join(X, Z), join(W, X)), X))))))
% 18.55/3.03 = { by lemma 5 }
% 18.55/3.03 meet(meet(join(X, Z), join(W, X)), X)
% 18.55/3.03 = { by lemma 9 }
% 18.55/3.03 X
% 18.55/3.03
% 18.55/3.03 Lemma 20: join(X, X) = X.
% 18.55/3.03 Proof:
% 18.55/3.03 join(X, X)
% 18.55/3.03 = { by lemma 14 R->L }
% 18.55/3.03 join(X, meet(X, X))
% 18.55/3.03 = { by lemma 12 R->L }
% 18.55/3.03 join(join(join(meet(X, Y), meet(Z, X)), X), meet(X, X))
% 18.55/3.03 = { by lemma 12 R->L }
% 18.55/3.03 join(join(join(meet(X, Y), meet(Z, X)), X), meet(X, join(join(meet(X, Y), meet(Z, X)), X)))
% 18.55/3.03 = { by lemma 16 R->L }
% 18.55/3.03 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(join(meet(X, Y), meet(Z, X)), X)))
% 18.55/3.03 = { by lemma 19 R->L }
% 18.55/3.03 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), meet(meet(join(join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X)), W), join(V, join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X)))), join(join(join(meet(X, Y), meet(Z, X)), X), join(join(meet(X, Y), meet(Z, X)), X)))), join(join(meet(X, Y), meet(Z, X)), X))))
% 18.55/3.03 = { by lemma 9 }
% 18.55/3.03 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))))
% 18.55/3.03 = { by lemma 11 }
% 18.55/3.03 X
% 18.55/3.03
% 18.55/3.03 Lemma 21: join(X, meet(Y, X)) = X.
% 18.55/3.03 Proof:
% 18.55/3.03 join(X, meet(Y, X))
% 18.55/3.03 = { by lemma 16 R->L }
% 18.55/3.03 join(X, meet(Y, meet(meet(X, join(Z, X)), X)))
% 18.55/3.03 = { by lemma 20 R->L }
% 18.55/3.03 join(X, meet(Y, join(meet(meet(X, join(Z, X)), X), meet(meet(X, join(Z, X)), X))))
% 18.55/3.03 = { by lemma 16 R->L }
% 18.55/3.03 join(meet(meet(X, join(Z, X)), X), meet(Y, join(meet(meet(X, join(Z, X)), X), meet(meet(X, join(Z, X)), X))))
% 18.55/3.03 = { by lemma 18 }
% 18.55/3.03 meet(meet(X, join(Z, X)), X)
% 18.55/3.03 = { by lemma 16 }
% 18.55/3.03 X
% 18.55/3.03
% 18.55/3.03 Lemma 22: meet(X, meet(Y, X)) = meet(Y, X).
% 18.55/3.03 Proof:
% 18.55/3.03 meet(X, meet(Y, X))
% 18.55/3.03 = { by lemma 14 R->L }
% 18.55/3.03 meet(meet(X, X), meet(Y, X))
% 18.55/3.03 = { by lemma 21 R->L }
% 18.55/3.03 meet(meet(X, join(X, meet(Y, X))), meet(Y, X))
% 18.55/3.03 = { by lemma 15 }
% 18.55/3.03 meet(Y, X)
% 18.55/3.03
% 18.55/3.03 Lemma 23: join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), Y)) = meet(X, Y).
% 18.55/3.03 Proof:
% 18.55/3.03 join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), Y))
% 18.55/3.03 = { by lemma 8 R->L }
% 18.55/3.03 join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), join(meet(X, Y), meet(Y, join(X, Y)))))
% 18.55/3.03 = { by lemma 5 }
% 18.55/3.03 meet(X, Y)
% 18.55/3.03
% 18.55/3.03 Lemma 24: join(meet(meet(X, Y), meet(Y, join(X, Y))), Y) = meet(Y, join(X, Y)).
% 18.55/3.03 Proof:
% 18.55/3.03 join(meet(meet(X, Y), meet(Y, join(X, Y))), Y)
% 18.55/3.03 = { by lemma 16 R->L }
% 18.55/3.03 join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(Y, join(X, Y)), Y))
% 18.55/3.03 = { by lemma 8 R->L }
% 18.55/3.03 join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(Y, join(X, Y)), join(meet(X, Y), meet(Y, join(X, Y)))))
% 18.55/3.03 = { by lemma 8 }
% 18.55/3.03 meet(Y, join(X, Y))
% 18.55/3.03
% 18.55/3.03 Lemma 25: meet(meet(meet(X, Y), Y), meet(X, Y)) = meet(X, Y).
% 18.55/3.03 Proof:
% 18.55/3.03 meet(meet(meet(X, Y), Y), meet(X, Y))
% 18.55/3.03 = { by lemma 22 R->L }
% 18.55/3.03 meet(meet(Y, meet(meet(X, Y), Y)), meet(X, Y))
% 18.55/3.03 = { by lemma 21 R->L }
% 18.55/3.03 meet(meet(Y, meet(meet(X, Y), join(Y, meet(X, Y)))), meet(X, Y))
% 18.55/3.03 = { by lemma 9 R->L }
% 18.55/3.03 meet(meet(Y, meet(meet(X, Y), join(meet(meet(join(Y, Z), join(W, Y)), Y), meet(X, Y)))), meet(X, Y))
% 18.55/3.03 = { by lemma 22 R->L }
% 18.55/3.03 meet(meet(Y, meet(meet(X, Y), join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(X, Y)))), meet(X, Y))
% 18.55/3.03 = { by lemma 21 R->L }
% 18.55/3.03 meet(meet(Y, meet(meet(X, Y), join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))))), meet(X, Y))
% 18.55/3.03 = { by lemma 21 R->L }
% 18.55/3.03 meet(meet(Y, meet(meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))), join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))))), meet(X, Y))
% 18.55/3.03 = { by lemma 24 R->L }
% 18.55/3.03 meet(meet(Y, join(meet(meet(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), meet(meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))), join(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))))), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))))), meet(X, Y))
% 18.55/3.03 = { by lemma 7 }
% 18.55/3.03 meet(meet(Y, join(meet(meet(meet(Y, meet(meet(join(Y, Z), join(W, Y)), Y)), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), meet(meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))), Y)), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))))), meet(X, Y))
% 18.55/3.04 = { by lemma 22 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(meet(meet(join(Y, Z), join(W, Y)), Y), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), meet(meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))), Y)), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))))), meet(X, Y))
% 18.55/3.04 = { by lemma 9 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(meet(meet(join(Y, Z), join(W, Y)), Y), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), meet(meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y))), Y)), meet(X, join(Y, Y)))), meet(X, Y))
% 18.55/3.04 = { by lemma 9 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(meet(meet(join(Y, Z), join(W, Y)), Y), meet(X, join(Y, meet(meet(join(Y, Z), join(W, Y)), Y)))), meet(meet(X, join(Y, Y)), Y)), meet(X, join(Y, Y)))), meet(X, Y))
% 18.55/3.04 = { by lemma 9 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(meet(meet(join(Y, Z), join(W, Y)), Y), meet(X, join(Y, Y))), meet(meet(X, join(Y, Y)), Y)), meet(X, join(Y, Y)))), meet(X, Y))
% 18.55/3.04 = { by lemma 9 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(Y, meet(X, join(Y, Y))), meet(meet(X, join(Y, Y)), Y)), meet(X, join(Y, Y)))), meet(X, Y))
% 18.55/3.04 = { by lemma 20 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(Y, meet(X, join(Y, Y))), meet(meet(X, join(Y, Y)), Y)), meet(X, Y))), meet(X, Y))
% 18.55/3.04 = { by lemma 20 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(Y, meet(X, join(Y, Y))), meet(meet(X, Y), Y)), meet(X, Y))), meet(X, Y))
% 18.55/3.04 = { by lemma 20 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(Y, meet(X, Y)), meet(meet(X, Y), Y)), meet(X, Y))), meet(X, Y))
% 18.55/3.04 = { by lemma 22 }
% 18.55/3.04 meet(meet(Y, join(meet(meet(X, Y), meet(meet(X, Y), Y)), meet(X, Y))), meet(X, Y))
% 18.55/3.04 = { by lemma 15 }
% 18.55/3.04 meet(X, Y)
% 18.55/3.04
% 18.55/3.04 Lemma 26: join(meet(X, Y), Y) = Y.
% 18.55/3.04 Proof:
% 18.55/3.04 join(meet(X, Y), Y)
% 18.55/3.04 = { by lemma 14 R->L }
% 18.55/3.04 join(meet(X, Y), meet(Y, Y))
% 18.55/3.04 = { by lemma 21 R->L }
% 18.55/3.04 join(meet(X, Y), meet(Y, join(Y, meet(X, Y))))
% 18.55/3.04 = { by lemma 6 R->L }
% 18.55/3.04 join(meet(X, Y), meet(join(meet(Z, 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(Z, join(join(meet(Y, W), meet(V, Y)), Y)))), join(Y, meet(X, Y))))
% 18.55/3.04 = { by lemma 8 R->L }
% 18.55/3.04 join(meet(X, join(meet(Z, Y), meet(Y, join(Z, Y)))), meet(join(meet(Z, 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(Z, join(join(meet(Y, W), meet(V, Y)), Y)))), join(Y, meet(X, Y))))
% 18.55/3.04 = { by lemma 8 R->L }
% 18.55/3.04 join(meet(X, join(meet(Z, Y), meet(Y, join(Z, Y)))), meet(join(meet(Z, 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(Z, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), meet(X, Y))))
% 18.55/3.04 = { by lemma 8 R->L }
% 18.55/3.04 join(meet(X, join(meet(Z, Y), meet(Y, join(Z, Y)))), meet(join(meet(Z, 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(Z, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), meet(X, join(meet(Z, Y), meet(Y, join(Z, Y)))))))
% 18.55/3.04 = { by lemma 22 R->L }
% 18.55/3.04 join(meet(join(meet(Z, Y), meet(Y, join(Z, Y))), meet(X, join(meet(Z, Y), meet(Y, join(Z, Y))))), meet(join(meet(Z, 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(Z, join(join(meet(Y, W), meet(V, Y)), Y)))), join(join(meet(Z, Y), meet(Y, join(Z, Y))), meet(X, join(meet(Z, Y), meet(Y, join(Z, Y)))))))
% 18.55/3.04 = { by axiom 1 (single_axiom) }
% 18.55/3.04 Y
% 18.55/3.04
% 18.55/3.04 Lemma 27: join(meet(meet(X, Y), meet(X, join(X, Y))), meet(meet(X, Y), X)) = meet(X, Y).
% 18.55/3.04 Proof:
% 18.55/3.04 join(meet(meet(X, Y), meet(X, join(X, Y))), meet(meet(X, Y), X))
% 18.55/3.04 = { by lemma 5 R->L }
% 18.55/3.04 join(meet(meet(X, Y), meet(X, join(X, Y))), meet(meet(X, Y), join(meet(X, Y), meet(X, join(X, Y)))))
% 18.55/3.04 = { by lemma 5 }
% 18.55/3.04 meet(X, Y)
% 18.55/3.04
% 18.55/3.04 Lemma 28: meet(meet(X, Y), Y) = meet(X, Y).
% 18.55/3.04 Proof:
% 18.55/3.04 meet(meet(X, Y), Y)
% 18.55/3.04 = { by lemma 9 R->L }
% 18.55/3.04 meet(meet(join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), Y))), join(meet(meet(X, Y), meet(Y, join(X, Y))), meet(meet(X, Y), Y))), meet(meet(X, Y), Y))
% 18.55/3.04 = { by lemma 23 }
% 18.55/3.04 meet(meet(join(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), Y))), meet(X, Y)), meet(meet(X, Y), Y))
% 18.55/3.04 = { by lemma 5 }
% 18.55/3.04 meet(meet(meet(X, Y), meet(X, Y)), meet(meet(X, Y), Y))
% 18.55/3.04 = { by lemma 14 }
% 18.55/3.04 meet(meet(X, Y), meet(meet(X, Y), Y))
% 18.55/3.04 = { by lemma 20 R->L }
% 18.55/3.04 join(meet(meet(X, Y), meet(meet(X, Y), Y)), meet(meet(X, Y), meet(meet(X, Y), Y)))
% 18.55/3.04 = { by lemma 14 R->L }
% 18.55/3.04 join(meet(meet(X, Y), meet(meet(meet(X, Y), Y), meet(meet(X, Y), Y))), meet(meet(X, Y), meet(meet(X, Y), Y)))
% 18.55/3.04 = { by lemma 25 R->L }
% 18.55/3.04 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(X, Y), Y))), meet(meet(X, Y), meet(meet(X, Y), Y)))
% 18.55/3.04 = { by lemma 25 R->L }
% 18.55/3.04 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(X, Y), Y))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.04 = { by lemma 26 R->L }
% 18.55/3.04 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(X, Y), Y)))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.04 = { by lemma 22 R->L }
% 18.55/3.04 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(X, Y), join(meet(Y, meet(X, Y)), Y)))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.04 = { by lemma 22 R->L }
% 18.55/3.04 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(Y, meet(X, Y)), join(meet(Y, meet(X, Y)), Y)))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.04 = { by lemma 20 R->L }
% 18.55/3.04 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(Y, meet(X, Y)), join(meet(Y, meet(X, join(Y, Y))), Y)))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.05 = { by lemma 20 R->L }
% 18.55/3.05 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.06 = { by lemma 17 R->L }
% 18.55/3.06 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.06 = { by lemma 17 R->L }
% 18.55/3.07 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.08 = { by lemma 3 }
% 18.55/3.08 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.09 = { by lemma 17 }
% 18.55/3.09 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 18.55/3.10 = { by lemma 17 }
% 19.22/3.10 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.11 = { by lemma 17 }
% 19.22/3.11 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.11 = { by lemma 17 }
% 19.22/3.12 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.12 = { by lemma 17 }
% 19.22/3.12 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.12 = { by lemma 17 }
% 19.22/3.13 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.13 = { by lemma 17 }
% 19.22/3.13 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.13 = { by lemma 17 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(join(meet(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(join(meet(Z, meet(Y, meet(X, join(Y, Y)))), meet(meet(Y, meet(X, join(Y, Y))), join(Z, meet(Y, meet(X, join(Y, Y)))))), meet(Y, meet(X, join(Y, Y)))))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 17 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 5 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), meet(meet(join(join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))), W), join(V, join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 7 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y))), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 19 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(Y, meet(X, join(Y, Y))), Y)), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 14 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, join(Y, Y))))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 20 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, join(Y, Y))), Y)), meet(Y, meet(X, Y)))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 20 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(meet(Y, meet(X, join(Y, Y))), join(meet(Y, meet(X, Y)), Y)), meet(Y, meet(X, Y)))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 20 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, join(Y, Y))), Y), meet(meet(meet(Y, meet(X, Y)), join(meet(Y, meet(X, Y)), Y)), meet(Y, meet(X, Y)))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 20 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, Y)), Y), meet(meet(meet(Y, meet(X, Y)), join(meet(Y, meet(X, Y)), Y)), meet(Y, meet(X, Y)))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 22 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, Y)), Y), meet(meet(meet(Y, meet(X, Y)), join(meet(Y, meet(X, Y)), Y)), meet(X, Y))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 22 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, Y)), Y), meet(meet(meet(Y, meet(X, Y)), join(meet(X, Y), Y)), meet(X, Y))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 22 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(Y, meet(X, Y)), Y), meet(meet(meet(X, Y), join(meet(X, Y), Y)), meet(X, Y))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 22 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(X, Y), Y), meet(meet(meet(X, Y), join(meet(X, Y), Y)), meet(X, Y))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 26 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(X, Y), Y), meet(meet(meet(X, Y), Y), meet(X, Y))))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 25 }
% 19.22/3.14 join(meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(meet(X, Y), Y), join(meet(meet(X, Y), Y), meet(X, Y)))), meet(meet(meet(meet(X, Y), Y), meet(X, Y)), meet(meet(X, Y), Y)))
% 19.22/3.14 = { by lemma 27 }
% 19.22/3.14 meet(meet(meet(X, Y), Y), meet(X, Y))
% 19.22/3.14 = { by lemma 25 }
% 19.22/3.14 meet(X, Y)
% 19.22/3.14
% 19.22/3.14 Lemma 29: join(join(meet(X, Y), X), X) = X.
% 19.22/3.14 Proof:
% 19.22/3.14 join(join(meet(X, Y), X), X)
% 19.22/3.14 = { by lemma 9 R->L }
% 19.22/3.14 join(join(meet(X, Y), meet(meet(join(X, Z), join(W, X)), X)), X)
% 19.22/3.14 = { by lemma 12 }
% 19.22/3.15 X
% 19.22/3.15
% 19.22/3.15 Lemma 30: meet(X, join(Y, X)) = X.
% 19.22/3.15 Proof:
% 19.22/3.15 meet(X, join(Y, X))
% 19.22/3.15 = { by lemma 5 R->L }
% 19.22/3.15 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(meet(X, join(Y, X)), X)))
% 19.22/3.15 = { by lemma 21 R->L }
% 19.22/3.15 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)))))
% 19.22/3.15 = { by lemma 9 R->L }
% 19.22/3.15 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)))))
% 19.22/3.15 = { by lemma 9 R->L }
% 19.22/3.15 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)))))
% 19.22/3.15 = { by lemma 9 R->L }
% 19.22/3.15 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))))))
% 19.22/3.15 = { by lemma 22 R->L }
% 19.22/3.15 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))))))
% 19.22/3.15 = { by lemma 22 R->L }
% 19.22/3.15 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))))))
% 20.38/3.15 = { by lemma 22 R->L }
% 20.38/3.15 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)))))))
% 20.38/3.15 = { by lemma 7 R->L }
% 20.38/3.15 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)))))))
% 20.38/3.16 = { by lemma 5 R->L }
% 20.38/3.16 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))))))))
% 20.38/3.16 = { by lemma 9 R->L }
% 20.38/3.16 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)))))))))
% 20.38/3.16 = { by lemma 28 R->L }
% 20.38/3.16 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)))))))))
% 20.38/3.17 = { by lemma 13 R->L }
% 20.38/3.17 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(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(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(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)))))))))
% 20.38/3.17 = { by lemma 16 R->L }
% 20.38/3.17 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(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(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(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(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)))))))))
% 20.38/3.18 = { by lemma 12 R->L }
% 20.38/3.18 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(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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(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(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)))))))))
% 20.38/3.18 = { by lemma 12 R->L }
% 20.38/3.19 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(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), 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)))))))))
% 20.38/3.19 = { by lemma 12 R->L }
% 20.38/3.19 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(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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(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)))))))))
% 20.38/3.20 = { by lemma 12 R->L }
% 20.38/3.20 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(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))))))))
% 20.38/3.20 = { by lemma 11 R->L }
% 20.38/3.21 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(X, meet(meet(join(X, Z), join(W, X)), X)), join(meet(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))))))))
% 20.38/3.21 = { by lemma 24 }
% 20.38/3.21 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(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))))))))
% 20.38/3.21 = { by lemma 12 }
% 20.38/3.22 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(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(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))))))))
% 20.38/3.22 = { by lemma 12 }
% 20.38/3.22 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(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(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)))), join(join(meet(meet(X, meet(meet(join(X, Z), join(W, X)), X)), U), meet(T, 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)))))))))
% 20.38/3.22 = { by lemma 12 }
% 20.38/3.22 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(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(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)))))))))
% 20.38/3.22 = { by lemma 8 }
% 20.38/3.23 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(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)))), 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)))))))))
% 20.38/3.23 = { by lemma 16 }
% 20.85/3.23 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(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)))))))))
% 20.85/3.23 = { by lemma 14 }
% 20.85/3.23 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)))))))))
% 20.85/3.23 = { by lemma 9 R->L }
% 20.85/3.23 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)))))))))
% 20.85/3.23 = { by lemma 23 }
% 20.85/3.23 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))))))))
% 20.85/3.23 = { by lemma 9 }
% 20.85/3.23 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)))))))
% 20.85/3.23 = { by lemma 20 }
% 20.85/3.23 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))))))
% 20.85/3.23 = { by lemma 16 }
% 20.85/3.23 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)))))
% 20.85/3.23 = { by lemma 22 }
% 20.85/3.23 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))))
% 20.85/3.23 = { by lemma 9 }
% 20.85/3.23 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), join(join(meet(X, join(Y, X)), X), X)))
% 20.85/3.23 = { by lemma 29 }
% 20.85/3.23 join(meet(meet(X, join(Y, X)), X), meet(meet(X, join(Y, X)), X))
% 20.85/3.23 = { by lemma 20 }
% 20.85/3.23 meet(meet(X, join(Y, X)), X)
% 20.85/3.23 = { by lemma 16 }
% 20.85/3.23 X
% 20.85/3.23
% 20.85/3.23 Lemma 31: meet(join(X, Y), Y) = Y.
% 20.85/3.23 Proof:
% 20.85/3.23 meet(join(X, Y), Y)
% 20.85/3.23 = { by lemma 28 R->L }
% 20.85/3.23 meet(meet(join(X, Y), Y), Y)
% 20.85/3.23 = { by lemma 30 R->L }
% 20.85/3.23 meet(meet(join(X, Y), Y), meet(Y, join(X, Y)))
% 20.85/3.23 = { by lemma 8 R->L }
% 20.85/3.23 meet(meet(join(X, Y), join(meet(X, Y), meet(Y, join(X, Y)))), meet(Y, join(X, Y)))
% 20.85/3.23 = { by lemma 15 }
% 20.85/3.23 meet(Y, join(X, Y))
% 20.85/3.24 = { by lemma 30 }
% 20.85/3.24 Y
% 20.85/3.24
% 20.85/3.24 Lemma 32: join(X, meet(join(Y, X), join(join(Y, X), X))) = join(Y, X).
% 20.85/3.24 Proof:
% 20.85/3.24 join(X, meet(join(Y, X), join(join(Y, X), X)))
% 20.85/3.24 = { by lemma 31 R->L }
% 20.85/3.24 join(meet(join(Y, X), X), meet(join(Y, X), join(join(Y, X), X)))
% 20.85/3.24 = { by lemma 5 }
% 20.85/3.24 join(Y, X)
% 20.85/3.24
% 20.85/3.24 Lemma 33: join(meet(X, Y), X) = X.
% 20.85/3.24 Proof:
% 20.85/3.24 join(meet(X, Y), X)
% 20.85/3.24 = { by lemma 32 R->L }
% 20.85/3.24 join(X, meet(join(meet(X, Y), X), join(join(meet(X, Y), X), X)))
% 20.85/3.24 = { by lemma 29 }
% 20.85/3.24 join(X, meet(join(meet(X, Y), X), X))
% 20.85/3.24 = { by lemma 21 }
% 20.85/3.24 X
% 20.85/3.24
% 20.85/3.24 Lemma 34: meet(meet(join(X, Y), X), X) = X.
% 20.85/3.24 Proof:
% 20.85/3.24 meet(meet(join(X, Y), X), X)
% 20.85/3.24 = { by lemma 29 R->L }
% 20.85/3.24 meet(meet(join(X, Y), join(join(meet(X, Z), X), X)), X)
% 20.85/3.24 = { by lemma 9 }
% 20.85/3.24 X
% 20.85/3.24
% 20.85/3.24 Lemma 35: join(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))) = X.
% 20.85/3.24 Proof:
% 20.85/3.24 join(X, meet(X, join(meet(join(X, Y), join(Z, X)), X)))
% 20.85/3.24 = { by lemma 9 R->L }
% 20.85/3.24 join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))
% 20.85/3.24 = { by lemma 8 }
% 20.85/3.24 X
% 20.85/3.24
% 20.85/3.24 Lemma 36: meet(X, join(X, Y)) = X.
% 20.85/3.24 Proof:
% 20.85/3.24 meet(X, join(X, Y))
% 20.85/3.24 = { by lemma 20 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(X, Y)))
% 20.85/3.24 = { by lemma 33 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(meet(join(X, Y), X), join(X, Y))))
% 20.85/3.24 = { by lemma 5 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), X))), join(X, Y))))
% 20.85/3.24 = { by lemma 34 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), X)))), join(X, Y))))
% 20.85/3.24 = { by lemma 21 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(X, meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 34 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), X), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 9 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), meet(meet(join(X, Y), join(meet(Z, X), X)), X)), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 27 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), join(meet(meet(meet(join(X, Y), join(meet(Z, X), X)), X), meet(meet(join(X, Y), join(meet(Z, X), X)), join(meet(join(X, Y), join(meet(Z, X), X)), X))), meet(meet(meet(join(X, Y), join(meet(Z, X), X)), X), meet(join(X, Y), join(meet(Z, X), X))))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 9 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), join(meet(X, meet(meet(join(X, Y), join(meet(Z, X), X)), join(meet(join(X, Y), join(meet(Z, X), X)), X))), meet(meet(meet(join(X, Y), join(meet(Z, X), X)), X), meet(join(X, Y), join(meet(Z, X), X))))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 9 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), join(meet(X, meet(meet(join(X, Y), join(meet(Z, X), X)), join(meet(join(X, Y), join(meet(Z, X), X)), X))), meet(X, meet(join(X, Y), join(meet(Z, X), X))))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 26 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), join(meet(X, meet(meet(join(X, Y), X), join(meet(join(X, Y), join(meet(Z, X), X)), X))), meet(X, meet(join(X, Y), join(meet(Z, X), X))))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 26 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), join(meet(X, meet(meet(join(X, Y), X), join(meet(join(X, Y), join(meet(Z, X), X)), X))), meet(X, meet(join(X, Y), X)))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 26 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), join(meet(X, meet(meet(join(X, Y), X), join(meet(join(X, Y), X), X))), meet(X, meet(join(X, Y), X)))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 22 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(meet(join(X, Y), X), join(meet(X, meet(meet(join(X, Y), X), join(meet(join(X, Y), X), X))), meet(join(X, Y), X))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 35 R->L }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(join(meet(join(X, Y), X), meet(meet(join(X, Y), X), join(meet(join(meet(join(X, Y), X), W), join(V, meet(join(X, Y), X))), meet(join(X, Y), X)))), join(meet(X, meet(meet(join(X, Y), X), join(meet(join(X, Y), X), X))), meet(join(X, Y), X))), meet(join(X, Y), X)))))), join(X, Y))))
% 20.85/3.24 = { by lemma 35 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), meet(join(X, Y), X))), join(X, Y))))
% 20.85/3.24 = { by lemma 34 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(X, meet(meet(join(X, Y), X), meet(join(X, Y), X))), join(X, Y))))
% 20.85/3.24 = { by lemma 14 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(join(X, meet(join(X, Y), X)), join(X, Y))))
% 20.85/3.24 = { by lemma 21 }
% 20.85/3.24 join(meet(X, join(X, Y)), meet(X, join(X, join(X, Y))))
% 20.85/3.24 = { by lemma 5 }
% 20.85/3.24 X
% 20.85/3.24
% 20.85/3.24 Lemma 37: meet(meet(X, Y), X) = meet(X, Y).
% 20.85/3.24 Proof:
% 20.85/3.24 meet(meet(X, Y), X)
% 20.85/3.24 = { by lemma 20 R->L }
% 20.85/3.24 join(meet(meet(X, Y), X), meet(meet(X, Y), X))
% 20.85/3.24 = { by lemma 33 R->L }
% 20.85/3.24 join(meet(meet(X, Y), X), meet(meet(X, Y), join(meet(X, Y), X)))
% 20.85/3.24 = { by lemma 5 }
% 20.85/3.24 meet(X, Y)
% 20.85/3.24
% 20.85/3.24 Lemma 38: meet(meet(join(meet(X, Y), Z), Y), meet(X, Y)) = meet(X, Y).
% 20.85/3.24 Proof:
% 20.85/3.24 meet(meet(join(meet(X, Y), Z), Y), meet(X, Y))
% 20.85/3.24 = { by lemma 21 R->L }
% 20.85/3.24 meet(meet(join(meet(X, join(Y, meet(meet(join(Y, W), join(V, Y)), Y))), Z), Y), meet(X, Y))
% 20.85/3.24 = { by lemma 21 R->L }
% 20.85/3.24 meet(meet(join(meet(X, join(Y, meet(meet(join(Y, W), join(V, Y)), Y))), Z), Y), meet(X, join(Y, meet(meet(join(Y, W), join(V, Y)), Y))))
% 20.85/3.24 = { by lemma 7 R->L }
% 20.85/3.24 meet(meet(join(meet(X, join(Y, meet(meet(join(Y, W), join(V, Y)), Y))), Z), join(meet(Y, meet(meet(join(Y, W), join(V, Y)), Y)), meet(X, join(Y, meet(meet(join(Y, W), join(V, Y)), Y))))), meet(X, join(Y, meet(meet(join(Y, W), join(V, Y)), Y))))
% 20.85/3.24 = { by lemma 9 }
% 20.85/3.24 meet(X, join(Y, meet(meet(join(Y, W), join(V, Y)), Y)))
% 20.85/3.24 = { by lemma 21 }
% 20.85/3.24 meet(X, Y)
% 20.85/3.24
% 20.85/3.24 Lemma 39: meet(meet(join(X, Y), join(Y, Z)), Y) = Y.
% 20.85/3.24 Proof:
% 20.85/3.24 meet(meet(join(X, Y), join(Y, Z)), Y)
% 20.85/3.24 = { by lemma 32 R->L }
% 20.85/3.24 meet(meet(join(Y, meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), Y)
% 20.85/3.24 = { by lemma 28 R->L }
% 20.85/3.24 meet(meet(meet(join(Y, meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), Y), Y)
% 20.85/3.24 = { by lemma 36 R->L }
% 20.85/3.24 meet(meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), Y), Y)
% 20.85/3.24 = { by lemma 36 R->L }
% 20.85/3.24 meet(meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), Y), meet(Y, join(Y, Z)))
% 20.85/3.25 = { by lemma 5 R->L }
% 20.85/3.25 meet(meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), join(meet(Y, Z), meet(Y, join(Y, Z)))), meet(Y, join(Y, Z)))
% 20.85/3.25 = { by lemma 38 R->L }
% 20.85/3.25 meet(meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), join(meet(Y, Z), meet(Y, join(Y, Z)))), meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), meet(Y, join(Y, Z))))
% 20.85/3.25 = { by lemma 38 R->L }
% 20.85/3.25 meet(meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), join(meet(Y, Z), meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), meet(Y, join(Y, Z))))), meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), meet(Y, join(Y, Z))))
% 20.85/3.25 = { by lemma 13 }
% 20.85/3.25 meet(meet(join(meet(Y, join(Y, Z)), meet(join(X, Y), join(join(X, Y), Y))), join(Y, Z)), meet(Y, join(Y, Z)))
% 20.85/3.25 = { by lemma 38 }
% 20.85/3.25 meet(Y, join(Y, Z))
% 20.85/3.25 = { by lemma 36 }
% 20.85/3.25 Y
% 20.85/3.25
% 20.85/3.25 Goal 1 (prove_wal_axioms_4): join(b, a) = join(a, b).
% 20.85/3.25 Proof:
% 20.85/3.25 join(b, a)
% 20.85/3.25 = { by lemma 12 R->L }
% 20.85/3.25 join(join(meet(join(b, a), a), meet(b, join(b, a))), join(b, a))
% 20.85/3.25 = { by lemma 31 }
% 20.85/3.25 join(join(a, meet(b, join(b, a))), join(b, a))
% 20.85/3.25 = { by lemma 36 }
% 20.85/3.25 join(join(a, b), join(b, a))
% 20.85/3.25 = { by lemma 21 R->L }
% 20.85/3.25 join(join(a, b), join(join(b, a), meet(meet(join(b, a), join(a, b)), join(b, a))))
% 20.85/3.25 = { by lemma 37 }
% 20.85/3.25 join(join(a, b), join(join(b, a), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 39 R->L }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(join(b, a), join(a, b)), a)), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 37 R->L }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 9 R->L }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(join(meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))), meet(meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))), join(meet(join(meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))), X), join(Y, meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))))), meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b)))))), join(meet(meet(meet(join(b, a), join(a, b)), a), meet(meet(join(b, a), join(a, b)), join(meet(join(b, a), join(a, b)), a))), meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))))), meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 27 }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(join(meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))), meet(meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))), join(meet(join(meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))), X), join(Y, meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))))), meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b)))))), meet(meet(join(b, a), join(a, b)), a)), meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 35 }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))), meet(meet(join(b, a), join(a, b)), a)), meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 39 }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(meet(a, meet(join(b, a), join(a, b))), meet(meet(join(b, a), join(a, b)), a)), meet(meet(meet(join(b, a), join(a, b)), a), meet(join(b, a), join(a, b))))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 39 }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(meet(a, meet(join(b, a), join(a, b))), meet(meet(join(b, a), join(a, b)), a)), meet(a, meet(join(b, a), join(a, b))))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 39 }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(meet(a, meet(join(b, a), join(a, b))), a), meet(a, meet(join(b, a), join(a, b))))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 37 }
% 20.85/3.25 join(join(a, b), join(join(b, meet(meet(a, meet(join(b, a), join(a, b))), a)), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 37 }
% 20.85/3.25 join(join(a, b), join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))))
% 20.85/3.25 = { by lemma 10 R->L }
% 20.85/3.25 join(join(a, b), join(meet(join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))), join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b)))), meet(meet(join(b, a), join(a, b)), join(join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))), join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b)))))))
% 20.85/3.25 = { by lemma 9 R->L }
% 20.85/3.25 join(join(a, b), join(meet(join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))), join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b)))), meet(meet(join(b, a), join(a, b)), join(join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))), join(join(meet(meet(join(b, a), join(a, b)), b), meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b)))))))
% 20.85/3.25 = { by lemma 9 R->L }
% 20.85/3.25 join(join(a, b), join(meet(join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))), join(join(meet(meet(join(b, a), join(a, b)), b), meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b)))), meet(meet(join(b, a), join(a, b)), join(join(join(b, meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b))), join(join(meet(meet(join(b, a), join(a, b)), b), meet(a, meet(join(b, a), join(a, b)))), meet(join(b, a), join(a, b)))))))
% 20.85/3.25 = { by lemma 11 }
% 20.85/3.25 join(join(a, b), meet(join(b, a), join(a, b)))
% 20.85/3.25 = { by lemma 21 }
% 20.85/3.25 join(a, b)
% 20.85/3.25 % SZS output end Proof
% 20.85/3.25
% 20.85/3.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------