TSTP Solution File: LAT094-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT094-1 : 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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:27:25 EDT 2023
% Result : Unsatisfiable 2.89s 0.77s
% Output : Proof 12.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT094-1 : TPTP v8.1.2. Released v2.6.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 05:18:42 EDT 2023
% 0.14/0.34 % CPUTime :
% 2.89/0.77 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.89/0.77
% 2.89/0.77 % SZS status Unsatisfiable
% 2.89/0.77
% 8.14/1.39 % SZS output start Proof
% 8.14/1.39 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.
% 8.14/1.39
% 8.14/1.39 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))).
% 8.14/1.39 Proof:
% 8.14/1.39 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)))
% 8.14/1.39 = { by axiom 1 (single_axiom) R->L }
% 8.14/1.39 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)))
% 8.14/1.39 = { by axiom 1 (single_axiom) }
% 8.14/1.39 join(meet(Y, Z), meet(Z, join(Y, Z)))
% 8.14/1.39
% 8.14/1.39 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.
% 8.14/1.39 Proof:
% 8.14/1.39 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)))
% 8.14/1.40 = { by axiom 1 (single_axiom) R->L }
% 8.14/1.40 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)))
% 8.14/1.40 = { by axiom 1 (single_axiom) R->L }
% 8.14/1.40 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), 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)))
% 8.14/1.41 = { by axiom 1 (single_axiom) R->L }
% 8.14/1.41 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)))
% 8.14/1.42 = { by axiom 1 (single_axiom) R->L }
% 8.14/1.42 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, 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)))
% 8.14/1.43 = { by axiom 1 (single_axiom) R->L }
% 8.14/1.44 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), 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)))
% 8.14/1.45 = { by axiom 1 (single_axiom) R->L }
% 8.14/1.46 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)))
% 8.94/1.47 = { by axiom 1 (single_axiom) R->L }
% 8.94/1.48 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, 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% 8.94/1.49 = { by axiom 1 (single_axiom) R->L }
% 9.17/1.50 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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% 9.17/1.52 = { by axiom 1 (single_axiom) R->L }
% 9.41/1.53 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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% 9.41/1.54 = { by axiom 1 (single_axiom) R->L }
% 9.41/1.55 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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% 9.41/1.55 = { by axiom 1 (single_axiom) R->L }
% 9.41/1.56 join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), Y), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))))), Z), meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(join(meet(join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, 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% 9.41/1.56 = { by axiom 1 (single_axiom) R->L }
% 9.41/1.57 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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Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, 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meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))), W), meet(V, join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))), meet(join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y))))))))), join(meet(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, 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join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), join(meet(X, join(join(meet(Y, U), meet(T, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, U), join(T, Y)), Y)), meet(S, join(Y, meet(meet(join(Y, U), join(T, Y)), Y)))), join(X, join(join(meet(Y, U), meet(T, Y)), Y)))))))), meet(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)))
% 9.41/1.57 = { by axiom 1 (single_axiom) R->L }
% 9.41/1.58 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)))
% 9.41/1.58 = { by lemma 2 }
% 9.41/1.58 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)))))))
% 9.41/1.58 = { by axiom 1 (single_axiom) }
% 9.41/1.58 Y
% 9.41/1.58
% 9.41/1.58 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.
% 9.41/1.58 Proof:
% 9.41/1.58 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)))
% 9.41/1.58 = { by lemma 3 R->L }
% 9.41/1.58 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)))
% 9.41/1.58 = { by lemma 3 R->L }
% 9.41/1.58 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)))
% 9.41/1.59 = { by lemma 3 R->L }
% 9.41/1.59 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)))
% 9.41/1.59 = { by lemma 3 R->L }
% 9.41/1.59 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)))
% 9.41/1.59 = { by lemma 3 R->L }
% 9.41/1.59 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)))
% 9.97/1.60 = { by lemma 3 R->L }
% 9.97/1.60 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)))
% 9.97/1.61 = { by lemma 3 R->L }
% 9.97/1.61 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)))
% 9.97/1.61 = { by lemma 3 R->L }
% 9.97/1.61 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)))
% 9.97/1.62 = { by lemma 3 R->L }
% 9.97/1.62 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)))
% 9.97/1.62 = { by lemma 3 R->L }
% 9.97/1.62 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)))
% 9.97/1.62 = { by lemma 3 R->L }
% 9.97/1.63 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)))
% 9.97/1.63 = { by lemma 3 R->L }
% 9.97/1.63 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)))
% 9.97/1.63 = { by lemma 2 }
% 9.97/1.63 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)))
% 9.97/1.63 = { by lemma 3 }
% 9.97/1.63 Y
% 9.97/1.63
% 9.97/1.63 Lemma 5: join(meet(X, Y), meet(X, join(X, Y))) = X.
% 9.97/1.63 Proof:
% 9.97/1.63 join(meet(X, Y), meet(X, join(X, Y)))
% 9.97/1.63 = { by lemma 3 R->L }
% 9.97/1.63 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)))
% 9.97/1.63 = { by lemma 3 R->L }
% 9.97/1.63 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)))
% 9.97/1.63 = { by lemma 3 }
% 10.62/1.72 X
% 10.62/1.72
% 10.62/1.72 Lemma 6: 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.
% 10.62/1.72 Proof:
% 10.62/1.72 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))))
% 10.62/1.77 = { by lemma 3 R->L }
% 10.62/1.77 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))))
% 11.43/1.79 = { by lemma 4 R->L }
% 11.79/1.85 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, 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% 11.79/1.85 = { by axiom 1 (single_axiom) }
% 11.79/1.89 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), 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% 11.79/1.89 = { by axiom 1 (single_axiom) }
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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)))
% 11.79/1.90 = { by axiom 1 (single_axiom) }
% 11.79/1.90 join(meet(X, U), meet(X, join(X, U)))
% 11.79/1.90 = { by lemma 5 }
% 11.79/1.90 X
% 11.79/1.90
% 11.79/1.90 Lemma 7: join(meet(X, Y), meet(Y, join(X, Y))) = Y.
% 11.79/1.90 Proof:
% 11.79/1.90 join(meet(X, Y), meet(Y, join(X, Y)))
% 11.79/1.90 = { by lemma 6 R->L }
% 11.79/1.90 join(meet(join(meet(X, Y), meet(Y, join(X, Y))), meet(meet(join(join(meet(X, Y), meet(Y, join(X, Y))), Z), join(W, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y))))), meet(join(meet(X, join(join(meet(Y, V), meet(U, Y)), Y)), meet(join(meet(Y, meet(meet(join(Y, V), join(U, Y)), Y)), meet(T, join(Y, meet(meet(join(Y, V), join(U, Y)), Y)))), join(X, join(join(meet(Y, V), meet(U, Y)), Y)))), join(join(meet(X, Y), meet(Y, join(X, Y))), meet(meet(join(join(meet(X, Y), meet(Y, join(X, Y))), Z), join(W, join(meet(X, Y), meet(Y, join(X, Y))))), join(meet(X, Y), meet(Y, join(X, Y)))))))
% 11.79/1.90 = { by axiom 1 (single_axiom) }
% 11.79/1.90 Y
% 11.79/1.90
% 11.79/1.90 Lemma 8: meet(meet(join(X, Y), join(Z, X)), X) = X.
% 11.79/1.90 Proof:
% 11.79/1.90 meet(meet(join(X, Y), join(Z, X)), X)
% 11.79/1.90 = { by lemma 7 R->L }
% 11.79/1.90 join(meet(X, meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(meet(join(X, Y), join(Z, X)), X), join(X, meet(meet(join(X, Y), join(Z, X)), X))))
% 11.79/1.90 = { by lemma 6 }
% 11.79/1.90 X
% 11.79/1.90
% 11.79/1.90 Lemma 9: join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X)) = X.
% 11.79/1.90 Proof:
% 11.79/1.90 join(meet(X, meet(X, join(meet(join(X, Y), join(Z, X)), X))), meet(X, X))
% 11.79/1.90 = { by lemma 8 R->L }
% 11.79/1.90 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))
% 11.79/1.90 = { by lemma 8 R->L }
% 11.79/1.90 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))
% 11.79/1.90 = { by lemma 7 R->L }
% 11.79/1.90 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)))))
% 11.79/1.90 = { by lemma 5 }
% 11.79/1.90 meet(meet(join(X, Y), join(Z, X)), X)
% 11.79/1.90 = { by lemma 8 }
% 11.79/1.91 X
% 11.79/1.91
% 11.79/1.91 Goal 1 (prove_wal_axioms_3): join(a, a) = a.
% 11.79/1.91 Proof:
% 11.79/1.91 join(a, a)
% 11.79/1.91 = { by lemma 6 R->L }
% 11.79/1.91 join(meet(join(a, a), meet(meet(join(join(a, a), X), join(Y, join(a, a))), join(a, a))), meet(a, join(join(a, a), meet(meet(join(join(a, a), X), join(Y, join(a, a))), join(a, a)))))
% 11.79/1.91 = { by lemma 8 }
% 11.79/1.91 join(meet(join(a, a), join(a, a)), meet(a, join(join(a, a), meet(meet(join(join(a, a), X), join(Y, join(a, a))), join(a, a)))))
% 11.79/1.91 = { by lemma 8 }
% 11.79/1.91 join(meet(join(a, a), join(a, a)), meet(a, join(join(a, a), join(a, a))))
% 11.79/1.91 = { by lemma 9 R->L }
% 11.79/1.91 join(meet(join(a, a), join(a, a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))
% 11.79/1.91 = { by lemma 9 R->L }
% 11.79/1.91 join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))
% 11.79/1.91 = { by lemma 4 R->L }
% 11.79/1.91 join(meet(join(meet(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))), meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), join(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))))), V), meet(join(meet(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(join(meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), U), meet(T, join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))), meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), join(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(join(meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), U), meet(T, join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))))), join(join(meet(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))), meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), join(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))))), V)))
% 11.79/1.91 = { by lemma 4 }
% 12.48/1.91 join(meet(a, V), meet(join(meet(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(join(meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), U), meet(T, join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))), meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), join(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(join(meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), U), meet(T, join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))))))), join(join(meet(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))), meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), join(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))))), V)))
% 12.48/1.91 = { by lemma 4 }
% 12.48/1.92 join(meet(a, V), meet(a, join(join(meet(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))), meet(join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)))), join(join(meet(join(a, a), a), meet(a, join(join(a, a), a))), join(meet(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a)), meet(a, join(join(a, a), join(join(meet(a, meet(a, join(meet(join(a, Z), join(W, a)), a))), meet(a, a)), a))))))), V)))
% 12.48/1.92 = { by lemma 4 }
% 12.48/1.92 join(meet(a, V), meet(a, join(a, V)))
% 12.48/1.92 = { by lemma 5 }
% 12.48/1.92 a
% 12.48/1.92 % SZS output end Proof
% 12.48/1.92
% 12.48/1.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------