TSTP Solution File: LAT092-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT092-1 : 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 : n011.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 06:27:24 EDT 2023
% Result : Unsatisfiable 4.95s 1.03s
% Output : Proof 11.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT092-1 : 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
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 04:31:22 EDT 2023
% 0.13/0.33 % CPUTime :
% 4.95/1.03 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 4.95/1.03
% 4.95/1.03 % SZS status Unsatisfiable
% 4.95/1.03
% 10.10/1.75 % SZS output start Proof
% 10.10/1.75 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.
% 10.10/1.75
% 10.10/1.75 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))).
% 10.10/1.75 Proof:
% 10.10/1.75 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)))
% 10.10/1.75 = { by axiom 1 (single_axiom) R->L }
% 10.10/1.75 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)))
% 10.10/1.75 = { by axiom 1 (single_axiom) }
% 10.10/1.75 join(meet(Y, Z), meet(Z, join(Y, Z)))
% 10.10/1.75
% 10.10/1.75 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.
% 10.10/1.75 Proof:
% 10.10/1.75 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)))
% 10.10/1.76 = { by axiom 1 (single_axiom) R->L }
% 10.10/1.76 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)))
% 10.10/1.76 = { by axiom 1 (single_axiom) R->L }
% 10.10/1.76 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))), 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)))
% 10.10/1.77 = { by axiom 1 (single_axiom) R->L }
% 10.10/1.77 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)))
% 10.10/1.78 = { by axiom 1 (single_axiom) R->L }
% 10.10/1.78 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)))
% 10.10/1.79 = { by axiom 1 (single_axiom) R->L }
% 10.10/1.79 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)))
% 10.10/1.81 = { by axiom 1 (single_axiom) R->L }
% 10.46/1.81 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)))
% 10.46/1.82 = { by axiom 1 (single_axiom) R->L }
% 10.46/1.83 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)))
% 10.46/1.84 = { by axiom 1 (single_axiom) R->L }
% 10.46/1.85 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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% 10.76/1.87 = { by axiom 1 (single_axiom) R->L }
% 10.76/1.87 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), 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Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, 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meet(meet(join(Y, U), join(T, Y)), Y)), 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)))
% 10.76/1.88 = { by axiom 1 (single_axiom) R->L }
% 10.76/1.88 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), 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Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, 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% 10.76/1.89 = { by axiom 1 (single_axiom) R->L }
% 10.76/1.89 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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% 10.76/1.89 = { by axiom 1 (single_axiom) R->L }
% 10.76/1.90 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)), 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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(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)))
% 10.76/1.90 = { by axiom 1 (single_axiom) R->L }
% 10.76/1.91 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)))
% 10.76/1.91 = { by lemma 2 }
% 10.76/1.91 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)))))))
% 10.76/1.91 = { by axiom 1 (single_axiom) }
% 10.76/1.91 Y
% 10.76/1.91
% 10.76/1.91 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.
% 10.76/1.91 Proof:
% 10.76/1.91 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)))
% 10.76/1.92 = { by lemma 3 R->L }
% 10.76/1.92 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)))
% 10.76/1.92 = { by lemma 3 R->L }
% 10.76/1.92 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, 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)))
% 10.76/1.92 = { by lemma 3 R->L }
% 10.76/1.92 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, 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)))
% 10.76/1.92 = { by lemma 3 R->L }
% 10.76/1.92 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, 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)))
% 10.76/1.93 = { by lemma 3 R->L }
% 10.76/1.93 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(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)))
% 10.76/1.93 = { by lemma 3 R->L }
% 10.76/1.93 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(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)))
% 10.76/1.93 = { by lemma 3 R->L }
% 10.76/1.94 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))))), 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)))
% 10.76/1.94 = { by lemma 3 R->L }
% 10.76/1.94 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))))), 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)))
% 10.76/1.94 = { by lemma 3 R->L }
% 10.76/1.95 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(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)))
% 10.76/1.95 = { by lemma 3 R->L }
% 11.30/1.95 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(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)))
% 11.30/1.95 = { by lemma 3 R->L }
% 11.30/1.95 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(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)))
% 11.30/1.95 = { by lemma 3 R->L }
% 11.30/1.95 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)))
% 11.30/1.95 = { by lemma 2 }
% 11.30/1.95 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)))
% 11.30/1.95 = { by lemma 3 }
% 11.30/1.95 Y
% 11.30/1.95
% 11.30/1.95 Lemma 5: join(meet(X, Y), meet(X, join(X, Y))) = X.
% 11.30/1.95 Proof:
% 11.30/1.95 join(meet(X, Y), meet(X, join(X, Y)))
% 11.30/1.95 = { by lemma 3 R->L }
% 11.30/1.95 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)))
% 11.30/1.95 = { by lemma 3 R->L }
% 11.30/1.95 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)))
% 11.30/1.95 = { by lemma 3 }
% 11.30/1.96 X
% 11.30/1.96
% 11.30/1.96 Lemma 6: 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.
% 11.30/1.96 Proof:
% 11.30/1.96 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))))
% 11.30/1.96 = { by lemma 4 R->L }
% 11.30/1.96 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)))
% 11.30/1.96 = { by lemma 4 }
% 11.30/1.96 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)))
% 11.30/1.96 = { by lemma 4 }
% 11.30/1.96 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)))
% 11.30/1.96 = { by lemma 4 }
% 11.30/1.96 join(meet(Y, V), meet(Y, join(Y, V)))
% 11.30/1.96 = { by lemma 5 }
% 11.51/2.02 Y
% 11.51/2.02
% 11.51/2.02 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.
% 11.51/2.02 Proof:
% 11.51/2.02 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))))
% 11.76/2.05 = { by lemma 3 R->L }
% 11.76/2.05 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))))
% 11.76/2.06 = { by lemma 4 R->L }
% 11.76/2.11 join(meet(join(meet(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))))))), X), meet(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))))))), X))), 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, 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X)), X)))), join(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))))))), X), meet(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, 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% 11.76/2.11 = { by axiom 1 (single_axiom) }
% 11.76/2.14 join(meet(X, U), meet(join(meet(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))))))), X), meet(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))))))), X))), join(join(meet(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)))), T), meet(S, 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, 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join(join(meet(X, Y), meet(Z, X)), X)))))), 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), 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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))))))), U)))
% 11.76/2.15 = { by axiom 1 (single_axiom) }
% 11.76/2.16 join(meet(X, U), meet(X, join(join(meet(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))))))), X), meet(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))))))), X))), 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))))), meet(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)))), join(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))))))), X), meet(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))))))), X))), 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))))))), U)))
% 11.76/2.16 = { by axiom 1 (single_axiom) }
% 11.76/2.16 join(meet(X, U), meet(X, join(X, U)))
% 11.76/2.16 = { by lemma 5 }
% 11.76/2.16 X
% 11.76/2.16
% 11.76/2.16 Lemma 8: join(meet(X, Y), meet(meet(meet(join(X, Z), join(W, X)), X), join(X, Y))) = meet(meet(join(X, Z), join(W, X)), X).
% 11.76/2.16 Proof:
% 11.76/2.16 join(meet(X, Y), meet(meet(meet(join(X, Z), join(W, X)), X), join(X, Y)))
% 11.76/2.16 = { by lemma 7 R->L }
% 11.76/2.16 join(meet(X, Y), meet(meet(meet(join(X, Z), join(W, X)), X), join(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(meet(meet(join(X, Z), join(W, X)), X), join(X, meet(meet(join(X, Z), join(W, X)), X)))), Y)))
% 11.76/2.16 = { by lemma 6 R->L }
% 11.76/2.16 join(meet(X, Y), meet(join(meet(X, join(join(meet(meet(meet(join(X, Z), join(W, X)), X), V), meet(U, 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(X, join(join(meet(meet(meet(join(X, Z), join(W, X)), X), V), meet(U, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(join(X, Z), join(W, X)), X))))), join(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(meet(meet(join(X, Z), join(W, X)), X), join(X, meet(meet(join(X, Z), join(W, X)), X)))), Y)))
% 11.76/2.16 = { by lemma 7 R->L }
% 11.76/2.16 join(meet(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(meet(meet(join(X, Z), join(W, X)), X), join(X, meet(meet(join(X, Z), join(W, X)), X)))), Y), meet(join(meet(X, join(join(meet(meet(meet(join(X, Z), join(W, X)), X), V), meet(U, 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(X, join(join(meet(meet(meet(join(X, Z), join(W, X)), X), V), meet(U, meet(meet(join(X, Z), join(W, X)), X))), meet(meet(join(X, Z), join(W, X)), X))))), join(join(meet(X, meet(meet(join(X, Z), join(W, X)), X)), meet(meet(meet(join(X, Z), join(W, X)), X), join(X, meet(meet(join(X, Z), join(W, X)), X)))), Y)))
% 11.76/2.16 = { by lemma 4 }
% 11.76/2.16 meet(meet(join(X, Z), join(W, X)), X)
% 11.76/2.16
% 11.76/2.16 Lemma 9: meet(meet(join(X, Y), join(Z, X)), X) = X.
% 11.76/2.16 Proof:
% 11.76/2.16 meet(meet(join(X, Y), join(Z, X)), X)
% 11.76/2.16 = { by lemma 8 R->L }
% 11.76/2.16 join(meet(X, W), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, W)))
% 11.76/2.16 = { by lemma 8 R->L }
% 11.76/2.16 join(meet(X, W), meet(join(meet(X, join(join(meet(X, V), meet(U, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, join(join(meet(X, V), meet(U, X)), X)))), join(X, W)))
% 11.76/2.16 = { by lemma 5 R->L }
% 11.76/2.16 join(meet(join(meet(X, X), meet(X, join(X, X))), W), meet(join(meet(X, join(join(meet(X, V), meet(U, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, join(join(meet(X, V), meet(U, X)), X)))), join(X, W)))
% 11.76/2.16 = { by lemma 5 R->L }
% 11.76/2.16 join(meet(join(meet(X, X), meet(X, join(X, X))), W), meet(join(meet(X, join(join(meet(X, V), meet(U, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(X, X), meet(X, join(X, X))), W)))
% 11.76/2.16 = { by lemma 8 R->L }
% 11.76/2.16 join(meet(join(meet(X, X), meet(X, join(X, X))), W), meet(join(meet(X, join(join(meet(X, V), meet(U, X)), X)), meet(join(meet(X, meet(meet(join(X, V), join(U, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, V), join(U, X)), X)))), join(X, join(join(meet(X, V), meet(U, X)), X)))), join(join(meet(X, X), meet(X, join(X, X))), W)))
% 11.76/2.16 = { by axiom 1 (single_axiom) }
% 11.76/2.16 X
% 11.76/2.16
% 11.76/2.16 Lemma 10: join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), Z), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), Z))) = join(meet(Y, X), meet(X, join(Y, X))).
% 11.76/2.16 Proof:
% 11.76/2.16 join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), Z), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), Z)))
% 11.76/2.16 = { by lemma 5 R->L }
% 11.76/2.16 join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), Z), meet(join(meet(X, join(join(meet(join(meet(Y, X), meet(X, join(Y, X))), W), meet(V, join(meet(Y, X), meet(X, join(Y, X))))), join(meet(Y, X), meet(X, join(Y, X))))), meet(X, join(X, join(join(meet(join(meet(Y, X), meet(X, join(Y, X))), W), meet(V, join(meet(Y, X), meet(X, join(Y, X))))), join(meet(Y, X), meet(X, join(Y, X))))))), join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), Z)))
% 11.76/2.16 = { by lemma 2 }
% 11.76/2.16 join(meet(Y, X), meet(X, join(Y, X)))
% 11.76/2.16
% 11.76/2.16 Lemma 11: join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))), meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))))), W), meet(join(meet(Y, X), meet(X, join(Y, X))), join(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))), meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))))), W))) = join(meet(Z, X), meet(X, join(Z, X))).
% 11.76/2.16 Proof:
% 11.76/2.16 join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))), meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))))), W), meet(join(meet(Y, X), meet(X, join(Y, X))), join(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))), meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))))), W)))
% 11.76/2.16 = { by lemma 10 R->L }
% 11.76/2.16 join(meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))), meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))))), W), meet(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(join(meet(Z, X), meet(X, join(Z, X))), V), meet(U, join(meet(Z, X), meet(X, join(Z, X))))), join(meet(Z, X), meet(X, join(Z, X))))), meet(X, join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(join(meet(join(meet(Z, X), meet(X, join(Z, X))), V), meet(U, join(meet(Z, X), meet(X, join(Z, X))))), join(meet(Z, X), meet(X, join(Z, X))))))), join(join(meet(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))), meet(join(meet(Z, X), meet(X, join(Z, X))), join(join(meet(X, join(meet(Y, X), meet(X, join(Y, X)))), meet(join(meet(Y, X), meet(X, join(Y, X))), join(X, join(meet(Y, X), meet(X, join(Y, X)))))), join(meet(Z, X), meet(X, join(Z, X)))))), W)))
% 11.76/2.16 = { by lemma 2 }
% 11.76/2.16 join(meet(Z, X), meet(X, join(Z, X)))
% 11.76/2.16
% 11.76/2.16 Lemma 12: join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)) = X.
% 11.76/2.16 Proof:
% 11.76/2.16 join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X))
% 11.76/2.16 = { by lemma 9 R->L }
% 11.76/2.16 join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), X))
% 11.76/2.17 = { by lemma 9 R->L }
% 11.76/2.17 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), X))
% 11.76/2.17 = { by lemma 5 R->L }
% 11.76/2.17 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(X, X), meet(X, join(X, X)))))
% 11.76/2.17 = { by lemma 2 R->L }
% 11.76/2.17 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))))), W), meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(join(meet(join(meet(X, X), meet(X, join(X, X))), V), meet(U, join(meet(X, X), meet(X, join(X, X))))), join(meet(X, X), meet(X, join(X, X))))), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(join(meet(join(meet(X, X), meet(X, join(X, X))), V), meet(U, join(meet(X, X), meet(X, join(X, X))))), join(meet(X, X), meet(X, join(X, X))))))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))))), W)))))
% 11.76/2.17 = { by lemma 10 }
% 11.76/2.17 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))))), W)))))
% 11.76/2.18 = { by lemma 5 }
% 11.76/2.18 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W)))))
% 11.76/2.18 = { by lemma 5 }
% 11.76/2.18 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W)))))
% 11.76/2.18 = { by lemma 5 }
% 11.76/2.18 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W)))))
% 11.76/2.18 = { by lemma 5 }
% 11.76/2.18 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(join(meet(X, X), meet(X, join(X, X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W)))))
% 11.76/2.18 = { by lemma 5 }
% 11.76/2.19 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(X, X), meet(X, join(X, X)))), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W)))))
% 11.76/2.19 = { by lemma 5 }
% 11.76/2.19 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W)))))
% 11.76/2.19 = { by lemma 10 }
% 11.76/2.19 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X), meet(X, join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), X))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), W)))))
% 11.76/2.19 = { by lemma 10 }
% 11.76/2.19 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), W)))))
% 11.76/2.19 = { by lemma 11 R->L }
% 11.76/2.19 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), W)))))
% 11.76/2.19 = { by lemma 11 R->L }
% 11.76/2.20 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), W), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(join(meet(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))), meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), join(X, join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))), W)))))
% 11.76/2.20 = { by lemma 3 }
% 11.76/2.20 join(meet(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(meet(meet(join(X, Y), join(Z, X)), X), join(meet(meet(join(X, Y), join(Z, X)), X), meet(X, join(meet(join(X, Y), join(Z, X)), X)))))
% 11.76/2.20 = { by lemma 5 }
% 11.76/2.20 meet(meet(join(X, Y), join(Z, X)), X)
% 11.76/2.20 = { by lemma 9 }
% 11.76/2.20 X
% 11.76/2.20
% 11.76/2.20 Lemma 13: join(meet(X, X), meet(X, X)) = X.
% 11.76/2.20 Proof:
% 11.76/2.20 join(meet(X, X), meet(X, X))
% 11.76/2.20 = { by lemma 6 R->L }
% 11.76/2.20 join(meet(X, X), meet(X, join(meet(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X)), meet(X, join(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X))))))
% 11.76/2.20 = { by lemma 9 R->L }
% 11.76/2.20 join(meet(X, X), meet(X, join(meet(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X)), meet(X, join(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), meet(meet(join(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), W), join(V, join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X))), join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X)))))))
% 11.76/2.20 = { by lemma 9 R->L }
% 11.76/2.20 join(meet(X, X), meet(X, join(meet(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), meet(meet(join(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), W), join(V, join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X))), join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X))), meet(X, join(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), meet(meet(join(join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X), W), join(V, join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X))), join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X)))))))
% 11.76/2.20 = { by lemma 7 }
% 11.76/2.20 join(meet(X, X), meet(X, join(join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)), X)))
% 11.76/2.20 = { by lemma 12 }
% 11.76/2.20 join(meet(X, X), meet(X, join(X, X)))
% 11.76/2.20 = { by lemma 5 }
% 11.76/2.20 X
% 11.76/2.20
% 11.76/2.20 Lemma 14: meet(meet(X, join(Y, meet(X, Z))), meet(X, Z)) = meet(X, Z).
% 11.76/2.20 Proof:
% 11.76/2.20 meet(meet(X, join(Y, meet(X, Z))), meet(X, Z))
% 11.76/2.20 = { by lemma 5 R->L }
% 11.76/2.20 meet(meet(join(meet(X, Z), meet(X, join(X, Z))), join(Y, meet(X, Z))), meet(X, Z))
% 11.76/2.20 = { by lemma 9 }
% 11.76/2.20 meet(X, Z)
% 11.76/2.20
% 11.76/2.20 Goal 1 (prove_wal_axioms_1): meet(a, a) = a.
% 11.76/2.20 Proof:
% 11.76/2.20 meet(a, a)
% 11.76/2.20 = { by lemma 7 R->L }
% 11.76/2.20 join(meet(meet(a, a), meet(meet(join(meet(a, a), meet(a, join(a, a))), join(X, meet(a, a))), meet(a, a))), meet(a, join(meet(a, a), meet(meet(join(meet(a, a), meet(a, join(a, a))), join(X, meet(a, a))), meet(a, a)))))
% 11.76/2.20 = { by lemma 5 }
% 11.76/2.20 join(meet(meet(a, a), meet(meet(a, join(X, meet(a, a))), meet(a, a))), meet(a, join(meet(a, a), meet(meet(join(meet(a, a), meet(a, join(a, a))), join(X, meet(a, a))), meet(a, a)))))
% 11.76/2.20 = { by lemma 14 }
% 11.76/2.20 join(meet(meet(a, a), meet(a, a)), meet(a, join(meet(a, a), meet(meet(join(meet(a, a), meet(a, join(a, a))), join(X, meet(a, a))), meet(a, a)))))
% 11.76/2.20 = { by lemma 12 R->L }
% 11.76/2.20 join(meet(meet(a, join(meet(a, meet(a, join(meet(join(a, Y), join(Z, a)), a))), meet(a, a))), meet(a, a)), meet(a, join(meet(a, a), meet(meet(join(meet(a, a), meet(a, join(a, a))), join(X, meet(a, a))), meet(a, a)))))
% 11.76/2.20 = { by lemma 14 }
% 11.76/2.20 join(meet(a, a), meet(a, join(meet(a, a), meet(meet(join(meet(a, a), meet(a, join(a, a))), join(X, meet(a, a))), meet(a, a)))))
% 11.76/2.20 = { by lemma 9 }
% 11.76/2.20 join(meet(a, a), meet(a, join(meet(a, a), meet(a, a))))
% 11.76/2.20 = { by lemma 13 }
% 11.76/2.20 join(meet(a, a), meet(a, a))
% 11.76/2.20 = { by lemma 13 }
% 11.76/2.20 a
% 11.76/2.20 % SZS output end Proof
% 11.76/2.20
% 11.76/2.20 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------