%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL029-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:33:19 PM UTC 2026
% Result : Unsatisfiable 115.55s 15.06s
% Output : Proof 118.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL029-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 22:53:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.55/15.06 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 115.55/15.06
% 115.55/15.06 % SZS status Unsatisfiable
% 115.55/15.06
% 117.73/15.34 % SZS output start Proof
% 117.73/15.34 Axiom 1 (composition_identity_6): composition(X, one) = X.
% 117.73/15.34 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 117.73/15.34 Axiom 3 (def_top_12): top = join(X, complement(X)).
% 117.73/15.34 Axiom 4 (goals_14): join(sk1, one) = one.
% 117.73/15.34 Axiom 5 (goals_15): join(sk2, one) = one.
% 117.73/15.34 Axiom 6 (def_zero_13): zero = meet(X, complement(X)).
% 117.73/15.34 Axiom 7 (converse_idempotence_8): converse(converse(X)) = X.
% 117.73/15.34 Axiom 8 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 117.73/15.34 Axiom 9 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 117.73/15.34 Axiom 10 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 117.73/15.34 Axiom 11 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 117.73/15.34 Axiom 12 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 117.73/15.34 Axiom 13 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 117.73/15.34 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 117.73/15.34 Axiom 15 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 117.73/15.34
% 117.73/15.34 Lemma 16: complement(top) = zero.
% 117.73/15.34 Proof:
% 117.73/15.34 complement(top)
% 117.73/15.34 = { by axiom 3 (def_top_12) }
% 117.73/15.34 complement(join(complement(X), complement(complement(X))))
% 117.73/15.34 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.34 meet(X, complement(X))
% 117.73/15.34 = { by axiom 6 (def_zero_13) R->L }
% 117.73/15.34 zero
% 117.73/15.34
% 117.73/15.34 Lemma 17: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 117.73/15.34 Proof:
% 117.73/15.34 converse(composition(converse(X), Y))
% 117.73/15.34 = { by axiom 9 (converse_multiplicativity_10) }
% 117.73/15.34 composition(converse(Y), converse(converse(X)))
% 117.73/15.34 = { by axiom 7 (converse_idempotence_8) }
% 117.73/15.34 composition(converse(Y), X)
% 117.73/15.34
% 117.73/15.34 Lemma 18: composition(converse(one), X) = X.
% 117.73/15.34 Proof:
% 117.73/15.34 composition(converse(one), X)
% 117.73/15.34 = { by lemma 17 R->L }
% 117.73/15.34 converse(composition(converse(X), one))
% 117.73/15.34 = { by axiom 1 (composition_identity_6) }
% 117.73/15.34 converse(converse(X))
% 117.73/15.34 = { by axiom 7 (converse_idempotence_8) }
% 117.73/15.34 X
% 117.73/15.34
% 117.73/15.34 Lemma 19: converse(one) = one.
% 117.73/15.34 Proof:
% 117.73/15.34 converse(one)
% 117.73/15.34 = { by axiom 1 (composition_identity_6) R->L }
% 117.73/15.34 composition(converse(one), one)
% 117.73/15.34 = { by lemma 18 }
% 117.73/15.35 one
% 117.73/15.35
% 117.73/15.35 Lemma 20: join(X, join(Y, complement(X))) = join(Y, top).
% 117.73/15.35 Proof:
% 117.73/15.35 join(X, join(Y, complement(X)))
% 117.73/15.35 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.35 join(X, join(complement(X), Y))
% 117.73/15.35 = { by axiom 12 (maddux2_join_associativity_2) }
% 117.73/15.35 join(join(X, complement(X)), Y)
% 117.73/15.35 = { by axiom 3 (def_top_12) R->L }
% 117.73/15.35 join(top, Y)
% 117.73/15.35 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.35 join(Y, top)
% 117.73/15.35
% 117.73/15.35 Lemma 21: composition(one, X) = X.
% 117.73/15.35 Proof:
% 117.73/15.35 composition(one, X)
% 117.73/15.35 = { by lemma 18 R->L }
% 117.73/15.35 composition(converse(one), composition(one, X))
% 117.73/15.35 = { by axiom 10 (composition_associativity_5) }
% 117.73/15.35 composition(composition(converse(one), one), X)
% 117.73/15.35 = { by axiom 1 (composition_identity_6) }
% 117.73/15.35 composition(converse(one), X)
% 117.73/15.35 = { by lemma 18 }
% 117.73/15.35 X
% 117.73/15.35
% 117.73/15.35 Lemma 22: join(complement(X), complement(X)) = complement(X).
% 117.73/15.35 Proof:
% 117.73/15.35 join(complement(X), complement(X))
% 117.73/15.35 = { by lemma 18 R->L }
% 117.73/15.35 join(complement(X), composition(converse(one), complement(X)))
% 117.73/15.35 = { by lemma 21 R->L }
% 117.73/15.35 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 117.73/15.35 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.35 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 117.73/15.35 = { by axiom 15 (converse_cancellativity_11) }
% 117.73/15.35 complement(X)
% 117.73/15.35
% 117.73/15.35 Lemma 23: join(top, complement(X)) = top.
% 117.73/15.35 Proof:
% 117.73/15.35 join(top, complement(X))
% 117.73/15.35 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.35 join(complement(X), top)
% 117.73/15.35 = { by lemma 20 R->L }
% 117.73/15.35 join(X, join(complement(X), complement(X)))
% 117.73/15.35 = { by lemma 22 }
% 117.73/15.35 join(X, complement(X))
% 117.73/15.35 = { by axiom 3 (def_top_12) R->L }
% 117.73/15.35 top
% 117.73/15.35
% 117.73/15.35 Lemma 24: join(X, top) = top.
% 117.73/15.35 Proof:
% 117.73/15.35 join(X, top)
% 117.73/15.35 = { by lemma 23 R->L }
% 117.73/15.35 join(X, join(top, complement(X)))
% 117.73/15.35 = { by lemma 20 }
% 117.73/15.35 join(top, top)
% 117.73/15.35 = { by axiom 3 (def_top_12) }
% 117.73/15.35 join(top, join(zero, complement(zero)))
% 117.73/15.35 = { by axiom 12 (maddux2_join_associativity_2) }
% 117.73/15.35 join(join(top, zero), complement(zero))
% 117.73/15.35 = { by lemma 16 R->L }
% 117.73/15.35 join(join(top, complement(top)), complement(zero))
% 117.73/15.35 = { by axiom 3 (def_top_12) R->L }
% 117.73/15.35 join(top, complement(zero))
% 117.73/15.35 = { by lemma 23 }
% 117.73/15.35 top
% 117.73/15.35
% 117.73/15.35 Lemma 25: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 117.73/15.35 Proof:
% 117.73/15.35 join(meet(X, Y), complement(join(complement(X), Y)))
% 117.73/15.35 = { by axiom 8 (maddux4_definiton_of_meet_4) }
% 117.73/15.35 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 117.73/15.35 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 117.73/15.35 X
% 117.73/15.35
% 117.73/15.35 Lemma 26: join(zero, complement(complement(X))) = X.
% 117.73/15.35 Proof:
% 117.73/15.35 join(zero, complement(complement(X)))
% 117.73/15.35 = { by axiom 6 (def_zero_13) }
% 117.73/15.35 join(meet(X, complement(X)), complement(complement(X)))
% 117.73/15.35 = { by lemma 22 R->L }
% 117.73/15.35 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 117.73/15.35 = { by lemma 25 }
% 117.73/15.35 X
% 117.73/15.35
% 117.73/15.35 Lemma 27: meet(Y, X) = meet(X, Y).
% 117.73/15.35 Proof:
% 117.73/15.35 meet(Y, X)
% 117.73/15.35 = { by axiom 8 (maddux4_definiton_of_meet_4) }
% 117.73/15.35 complement(join(complement(Y), complement(X)))
% 117.73/15.35 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.35 complement(join(complement(X), complement(Y)))
% 117.73/15.35 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.35 meet(X, Y)
% 117.73/15.35
% 117.73/15.35 Lemma 28: complement(join(zero, complement(X))) = meet(X, top).
% 117.73/15.35 Proof:
% 117.73/15.35 complement(join(zero, complement(X)))
% 117.73/15.35 = { by lemma 16 R->L }
% 117.73/15.35 complement(join(complement(top), complement(X)))
% 117.73/15.35 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.35 meet(top, X)
% 117.73/15.35 = { by lemma 27 R->L }
% 117.73/15.35 meet(X, top)
% 117.73/15.35
% 117.73/15.35 Lemma 29: join(zero, meet(X, top)) = X.
% 117.73/15.35 Proof:
% 117.73/15.35 join(zero, meet(X, top))
% 117.73/15.35 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.35 join(meet(X, top), zero)
% 117.73/15.35 = { by lemma 16 R->L }
% 117.73/15.35 join(meet(X, top), complement(top))
% 117.73/15.35 = { by lemma 24 R->L }
% 117.73/15.35 join(meet(X, top), complement(join(complement(X), top)))
% 117.73/15.35 = { by lemma 25 }
% 117.73/15.35 X
% 117.73/15.35
% 117.73/15.35 Lemma 30: join(zero, complement(X)) = complement(X).
% 117.73/15.35 Proof:
% 117.73/15.35 join(zero, complement(X))
% 117.73/15.35 = { by lemma 26 R->L }
% 117.73/15.35 join(zero, complement(join(zero, complement(complement(X)))))
% 117.73/15.35 = { by lemma 28 }
% 117.73/15.35 join(zero, meet(complement(X), top))
% 117.73/15.35 = { by lemma 29 }
% 117.73/15.35 complement(X)
% 117.73/15.35
% 117.73/15.35 Lemma 31: complement(complement(X)) = X.
% 117.73/15.35 Proof:
% 117.73/15.35 complement(complement(X))
% 117.73/15.35 = { by lemma 30 R->L }
% 117.73/15.35 join(zero, complement(complement(X)))
% 117.73/15.35 = { by lemma 26 }
% 117.73/15.35 X
% 117.73/15.35
% 117.73/15.35 Lemma 32: join(zero, X) = X.
% 117.73/15.35 Proof:
% 117.73/15.35 join(zero, X)
% 117.73/15.35 = { by lemma 31 R->L }
% 117.73/15.35 join(zero, complement(complement(X)))
% 117.73/15.35 = { by lemma 26 }
% 117.73/15.35 X
% 117.73/15.35
% 117.73/15.35 Lemma 33: meet(X, top) = X.
% 117.73/15.35 Proof:
% 117.73/15.35 meet(X, top)
% 117.73/15.35 = { by lemma 28 R->L }
% 117.73/15.35 complement(join(zero, complement(X)))
% 117.73/15.35 = { by lemma 30 R->L }
% 117.73/15.35 join(zero, complement(join(zero, complement(X))))
% 117.73/15.35 = { by lemma 28 }
% 117.73/15.35 join(zero, meet(X, top))
% 117.73/15.35 = { by lemma 29 }
% 117.73/15.35 X
% 117.73/15.35
% 117.73/15.35 Lemma 34: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 117.73/15.35 Proof:
% 117.73/15.35 complement(join(X, complement(Y)))
% 117.73/15.35 = { by lemma 31 R->L }
% 117.73/15.35 complement(join(complement(complement(X)), complement(Y)))
% 117.73/15.35 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.35 meet(complement(X), Y)
% 117.73/15.35 = { by lemma 27 R->L }
% 117.73/15.35 meet(Y, complement(X))
% 117.73/15.35
% 117.73/15.35 Lemma 35: complement(join(X, Y)) = meet(complement(X), complement(Y)).
% 117.73/15.35 Proof:
% 117.73/15.35 complement(join(X, Y))
% 117.73/15.35 = { by lemma 33 R->L }
% 117.73/15.35 complement(join(X, meet(Y, top)))
% 117.73/15.35 = { by lemma 28 R->L }
% 117.73/15.35 complement(join(X, complement(join(zero, complement(Y)))))
% 117.73/15.35 = { by lemma 34 }
% 117.73/15.35 meet(join(zero, complement(Y)), complement(X))
% 117.73/15.35 = { by lemma 30 }
% 117.73/15.35 meet(complement(Y), complement(X))
% 117.73/15.35 = { by lemma 27 R->L }
% 117.73/15.35 meet(complement(X), complement(Y))
% 117.73/15.35
% 117.73/15.35 Lemma 36: complement(join(meet(X, Y), complement(Z))) = meet(Z, join(complement(X), complement(Y))).
% 117.73/15.35 Proof:
% 117.73/15.35 complement(join(meet(X, Y), complement(Z)))
% 117.73/15.35 = { by axiom 8 (maddux4_definiton_of_meet_4) }
% 117.73/15.35 complement(join(complement(join(complement(X), complement(Y))), complement(Z)))
% 117.73/15.35 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.35 meet(join(complement(X), complement(Y)), Z)
% 117.73/15.35 = { by lemma 27 R->L }
% 117.73/15.36 meet(Z, join(complement(X), complement(Y)))
% 117.73/15.36
% 117.73/15.36 Lemma 37: complement(meet(X, Y)) = join(complement(X), complement(Y)).
% 117.73/15.36 Proof:
% 117.73/15.36 complement(meet(X, Y))
% 117.73/15.36 = { by lemma 27 }
% 117.73/15.36 complement(meet(Y, X))
% 117.73/15.36 = { by lemma 25 R->L }
% 117.73/15.36 complement(join(meet(meet(Y, X), top), complement(join(complement(meet(Y, X)), top))))
% 117.73/15.36 = { by lemma 33 }
% 117.73/15.36 complement(join(meet(Y, X), complement(join(complement(meet(Y, X)), top))))
% 117.73/15.36 = { by lemma 24 }
% 117.73/15.36 complement(join(meet(Y, X), complement(top)))
% 117.73/15.36 = { by lemma 36 }
% 117.73/15.36 meet(top, join(complement(Y), complement(X)))
% 117.73/15.36 = { by lemma 27 }
% 117.73/15.36 meet(join(complement(Y), complement(X)), top)
% 117.73/15.36 = { by lemma 33 }
% 117.73/15.36 join(complement(Y), complement(X))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(complement(X), complement(Y))
% 117.73/15.36
% 117.73/15.36 Lemma 38: join(complement(X), join(Y, complement(X))) = join(Y, complement(X)).
% 117.73/15.36 Proof:
% 117.73/15.36 join(complement(X), join(Y, complement(X)))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(complement(X), join(complement(X), Y))
% 117.73/15.36 = { by axiom 12 (maddux2_join_associativity_2) }
% 117.73/15.36 join(join(complement(X), complement(X)), Y)
% 117.73/15.36 = { by lemma 22 }
% 117.73/15.36 join(complement(X), Y)
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(Y, complement(X))
% 117.73/15.36
% 117.73/15.36 Lemma 39: join(X, meet(X, Y)) = X.
% 117.73/15.36 Proof:
% 117.73/15.36 join(X, meet(X, Y))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(meet(X, Y), X)
% 117.73/15.36 = { by lemma 25 R->L }
% 117.73/15.36 join(meet(X, Y), join(meet(X, Y), complement(join(complement(X), Y))))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(meet(X, Y), join(complement(join(complement(X), Y)), meet(X, Y)))
% 117.73/15.36 = { by lemma 33 R->L }
% 117.73/15.36 join(meet(X, Y), join(complement(join(complement(X), Y)), meet(meet(X, Y), top)))
% 117.73/15.36 = { by lemma 28 R->L }
% 117.73/15.36 join(meet(X, Y), join(complement(join(complement(X), Y)), complement(join(zero, complement(meet(X, Y))))))
% 117.73/15.36 = { by lemma 33 R->L }
% 117.73/15.36 join(meet(meet(X, Y), top), join(complement(join(complement(X), Y)), complement(join(zero, complement(meet(X, Y))))))
% 117.73/15.36 = { by lemma 28 R->L }
% 117.73/15.36 join(complement(join(zero, complement(meet(X, Y)))), join(complement(join(complement(X), Y)), complement(join(zero, complement(meet(X, Y))))))
% 117.73/15.36 = { by lemma 38 }
% 117.73/15.36 join(complement(join(complement(X), Y)), complement(join(zero, complement(meet(X, Y)))))
% 117.73/15.36 = { by lemma 28 }
% 117.73/15.36 join(complement(join(complement(X), Y)), meet(meet(X, Y), top))
% 117.73/15.36 = { by lemma 33 }
% 117.73/15.36 join(complement(join(complement(X), Y)), meet(X, Y))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(meet(X, Y), complement(join(complement(X), Y)))
% 117.73/15.36 = { by lemma 25 }
% 117.73/15.36 X
% 117.73/15.36
% 117.73/15.36 Lemma 40: join(X, meet(Y, X)) = X.
% 117.73/15.36 Proof:
% 117.73/15.36 join(X, meet(Y, X))
% 117.73/15.36 = { by lemma 27 }
% 117.73/15.36 join(X, meet(X, Y))
% 117.73/15.36 = { by lemma 39 }
% 117.73/15.36 X
% 117.73/15.36
% 117.73/15.36 Lemma 41: join(X, composition(Y, X)) = composition(join(Y, one), X).
% 117.73/15.36 Proof:
% 117.73/15.36 join(X, composition(Y, X))
% 117.73/15.36 = { by lemma 21 R->L }
% 117.73/15.36 join(composition(one, X), composition(Y, X))
% 117.73/15.36 = { by axiom 13 (composition_distributivity_7) R->L }
% 117.73/15.36 composition(join(one, Y), X)
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 composition(join(Y, one), X)
% 117.73/15.36
% 117.73/15.36 Lemma 42: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 117.73/15.36 Proof:
% 117.73/15.36 join(Z, join(X, Y))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(join(X, Y), Z)
% 117.73/15.36 = { by axiom 12 (maddux2_join_associativity_2) R->L }
% 117.73/15.36 join(X, join(Y, Z))
% 117.73/15.36
% 117.73/15.36 Lemma 43: meet(X, join(X, Y)) = X.
% 117.73/15.36 Proof:
% 117.73/15.36 meet(X, join(X, Y))
% 117.73/15.36 = { by lemma 33 R->L }
% 117.73/15.36 meet(X, join(X, meet(Y, top)))
% 117.73/15.36 = { by lemma 28 R->L }
% 117.73/15.36 meet(X, join(X, complement(join(zero, complement(Y)))))
% 117.73/15.36 = { by lemma 31 R->L }
% 117.73/15.36 meet(X, join(complement(complement(X)), complement(join(zero, complement(Y)))))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 meet(X, join(complement(join(zero, complement(Y))), complement(complement(X))))
% 117.73/15.36 = { by axiom 8 (maddux4_definiton_of_meet_4) }
% 117.73/15.36 complement(join(complement(X), complement(join(complement(join(zero, complement(Y))), complement(complement(X))))))
% 117.73/15.36 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.36 complement(join(complement(X), meet(join(zero, complement(Y)), complement(X))))
% 117.73/15.36 = { by lemma 27 R->L }
% 117.73/15.36 complement(join(complement(X), meet(complement(X), join(zero, complement(Y)))))
% 117.73/15.36 = { by lemma 39 }
% 117.73/15.36 complement(complement(X))
% 117.73/15.36 = { by lemma 31 }
% 117.73/15.36 X
% 117.73/15.36
% 117.73/15.36 Lemma 44: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 117.73/15.36 Proof:
% 117.73/15.36 converse(join(X, converse(Y)))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 converse(join(converse(Y), X))
% 117.73/15.36 = { by axiom 11 (converse_additivity_9) }
% 117.73/15.36 join(converse(converse(Y)), converse(X))
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) }
% 117.73/15.36 join(Y, converse(X))
% 117.73/15.36
% 117.73/15.36 Lemma 45: converse(composition(X, converse(Y))) = composition(Y, converse(X)).
% 117.73/15.36 Proof:
% 117.73/15.36 converse(composition(X, converse(Y)))
% 117.73/15.36 = { by axiom 9 (converse_multiplicativity_10) }
% 117.73/15.36 composition(converse(converse(Y)), converse(X))
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) }
% 117.73/15.36 composition(Y, converse(X))
% 117.73/15.36
% 117.73/15.36 Lemma 46: join(X, join(Y, composition(X, sk2))) = join(X, Y).
% 117.73/15.36 Proof:
% 117.73/15.36 join(X, join(Y, composition(X, sk2)))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(X, join(composition(X, sk2), Y))
% 117.73/15.36 = { by axiom 12 (maddux2_join_associativity_2) }
% 117.73/15.36 join(join(X, composition(X, sk2)), Y)
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) R->L }
% 117.73/15.36 join(join(X, composition(X, converse(converse(sk2)))), Y)
% 117.73/15.36 = { by lemma 45 R->L }
% 117.73/15.36 join(join(X, converse(composition(converse(sk2), converse(X)))), Y)
% 117.73/15.36 = { by lemma 44 R->L }
% 117.73/15.36 join(converse(join(composition(converse(sk2), converse(X)), converse(X))), Y)
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(converse(join(converse(X), composition(converse(sk2), converse(X)))), Y)
% 117.73/15.36 = { by lemma 41 }
% 117.73/15.36 join(converse(composition(join(converse(sk2), one), converse(X))), Y)
% 117.73/15.36 = { by lemma 45 }
% 117.73/15.36 join(composition(X, converse(join(converse(sk2), one))), Y)
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(composition(X, converse(join(one, converse(sk2)))), Y)
% 117.73/15.36 = { by axiom 11 (converse_additivity_9) }
% 117.73/15.36 join(composition(X, join(converse(one), converse(converse(sk2)))), Y)
% 117.73/15.36 = { by lemma 19 }
% 117.73/15.36 join(composition(X, join(one, converse(converse(sk2)))), Y)
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) }
% 117.73/15.36 join(composition(X, join(one, sk2)), Y)
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(composition(X, join(sk2, one)), Y)
% 117.73/15.36 = { by axiom 5 (goals_15) }
% 117.73/15.36 join(composition(X, one), Y)
% 117.73/15.36 = { by axiom 1 (composition_identity_6) }
% 117.73/15.36 join(X, Y)
% 117.73/15.36
% 117.73/15.36 Lemma 47: join(composition(join(Z, one), X), Y) = join(X, join(Y, composition(Z, X))).
% 117.73/15.36 Proof:
% 117.73/15.36 join(composition(join(Z, one), X), Y)
% 117.73/15.36 = { by lemma 41 R->L }
% 117.73/15.36 join(join(X, composition(Z, X)), Y)
% 117.73/15.36 = { by axiom 12 (maddux2_join_associativity_2) R->L }
% 117.73/15.36 join(X, join(composition(Z, X), Y))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(X, join(Y, composition(Z, X)))
% 117.73/15.36
% 117.73/15.36 Lemma 48: join(X, join(Y, composition(sk1, X))) = join(X, Y).
% 117.73/15.36 Proof:
% 117.73/15.36 join(X, join(Y, composition(sk1, X)))
% 117.73/15.36 = { by lemma 47 R->L }
% 117.73/15.36 join(composition(join(sk1, one), X), Y)
% 117.73/15.36 = { by axiom 4 (goals_14) }
% 117.73/15.36 join(composition(one, X), Y)
% 117.73/15.36 = { by lemma 21 }
% 117.73/15.36 join(X, Y)
% 117.73/15.36
% 117.73/15.36 Lemma 49: join(X, composition(sk1, join(X, Y))) = join(X, composition(sk1, Y)).
% 117.73/15.36 Proof:
% 117.73/15.36 join(X, composition(sk1, join(X, Y)))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(X, composition(sk1, join(Y, X)))
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) R->L }
% 117.73/15.36 join(X, composition(sk1, join(Y, converse(converse(X)))))
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) R->L }
% 117.73/15.36 join(X, composition(converse(converse(sk1)), join(Y, converse(converse(X)))))
% 117.73/15.36 = { by lemma 44 R->L }
% 117.73/15.36 join(X, composition(converse(converse(sk1)), converse(join(converse(X), converse(Y)))))
% 117.73/15.36 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 117.73/15.36 join(X, converse(composition(join(converse(X), converse(Y)), converse(sk1))))
% 117.73/15.36 = { by axiom 13 (composition_distributivity_7) }
% 117.73/15.36 join(X, converse(join(composition(converse(X), converse(sk1)), composition(converse(Y), converse(sk1)))))
% 117.73/15.36 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 117.73/15.36 join(X, converse(join(converse(composition(sk1, X)), composition(converse(Y), converse(sk1)))))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.36 join(X, converse(join(composition(converse(Y), converse(sk1)), converse(composition(sk1, X)))))
% 117.73/15.36 = { by axiom 11 (converse_additivity_9) }
% 117.73/15.36 join(X, join(converse(composition(converse(Y), converse(sk1))), converse(converse(composition(sk1, X)))))
% 117.73/15.36 = { by lemma 17 }
% 117.73/15.36 join(X, join(composition(converse(converse(sk1)), Y), converse(converse(composition(sk1, X)))))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(X, join(converse(converse(composition(sk1, X))), composition(converse(converse(sk1)), Y)))
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) }
% 117.73/15.36 join(X, join(composition(sk1, X), composition(converse(converse(sk1)), Y)))
% 117.73/15.36 = { by axiom 7 (converse_idempotence_8) }
% 117.73/15.36 join(X, join(composition(sk1, X), composition(sk1, Y)))
% 117.73/15.36 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.36 join(X, join(composition(sk1, Y), composition(sk1, X)))
% 117.73/15.36 = { by lemma 48 }
% 117.73/15.36 join(X, composition(sk1, Y))
% 117.73/15.36
% 117.73/15.37 Lemma 50: join(complement(X), join(Y, complement(Z))) = join(Y, complement(meet(X, Z))).
% 117.73/15.37 Proof:
% 117.73/15.37 join(complement(X), join(Y, complement(Z)))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(complement(X), join(complement(Z), Y))
% 117.73/15.37 = { by axiom 12 (maddux2_join_associativity_2) }
% 117.73/15.37 join(join(complement(X), complement(Z)), Y)
% 117.73/15.37 = { by lemma 37 R->L }
% 117.73/15.37 join(complement(meet(X, Z)), Y)
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.37 join(Y, complement(meet(X, Z)))
% 117.73/15.37
% 117.73/15.37 Lemma 51: join(composition(X, Y), composition(Z, Y)) = composition(join(Z, X), Y).
% 117.73/15.37 Proof:
% 117.73/15.37 join(composition(X, Y), composition(Z, Y))
% 117.73/15.37 = { by axiom 13 (composition_distributivity_7) R->L }
% 117.73/15.37 composition(join(X, Z), Y)
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.37 composition(join(Z, X), Y)
% 117.73/15.37
% 117.73/15.37 Lemma 52: join(complement(meet(X, Y)), complement(Y)) = complement(meet(X, Y)).
% 117.73/15.37 Proof:
% 117.73/15.37 join(complement(meet(X, Y)), complement(Y))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(complement(Y), complement(meet(X, Y)))
% 117.73/15.37 = { by lemma 37 }
% 117.73/15.37 join(complement(Y), join(complement(X), complement(Y)))
% 117.73/15.37 = { by lemma 38 }
% 117.73/15.37 join(complement(X), complement(Y))
% 117.73/15.37 = { by lemma 37 R->L }
% 117.73/15.37 complement(meet(X, Y))
% 117.73/15.37
% 117.73/15.37 Lemma 53: join(meet(X, Y), meet(X, complement(Y))) = X.
% 117.73/15.37 Proof:
% 117.73/15.37 join(meet(X, Y), meet(X, complement(Y)))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(meet(X, complement(Y)), meet(X, Y))
% 117.73/15.37 = { by axiom 8 (maddux4_definiton_of_meet_4) }
% 117.73/15.37 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 117.73/15.37 = { by lemma 25 }
% 117.73/15.37 X
% 117.73/15.37
% 117.73/15.37 Lemma 54: join(meet(X, Y), meet(Y, complement(X))) = Y.
% 117.73/15.37 Proof:
% 117.73/15.37 join(meet(X, Y), meet(Y, complement(X)))
% 117.73/15.37 = { by lemma 27 }
% 117.73/15.37 join(meet(Y, X), meet(Y, complement(X)))
% 117.73/15.37 = { by lemma 53 }
% 117.73/15.37 Y
% 117.73/15.37
% 117.73/15.37 Lemma 55: join(join(meet(composition(X, Y), Z), composition(meet(X, W), Y)), composition(X, Y)) = composition(X, Y).
% 117.73/15.37 Proof:
% 117.73/15.37 join(join(meet(composition(X, Y), Z), composition(meet(X, W), Y)), composition(X, Y))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(composition(X, Y), join(meet(composition(X, Y), Z), composition(meet(X, W), Y)))
% 117.73/15.37 = { by lemma 42 }
% 117.73/15.37 join(meet(composition(X, Y), Z), join(composition(meet(X, W), Y), composition(X, Y)))
% 117.73/15.37 = { by lemma 51 }
% 117.73/15.37 join(meet(composition(X, Y), Z), composition(join(X, meet(X, W)), Y))
% 117.73/15.37 = { by lemma 39 }
% 117.73/15.37 join(meet(composition(X, Y), Z), composition(X, Y))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(composition(X, Y), meet(composition(X, Y), Z))
% 117.73/15.37 = { by lemma 39 }
% 117.73/15.37 composition(X, Y)
% 117.73/15.37
% 117.73/15.37 Lemma 56: complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))) = complement(meet(composition(X, Y), composition(Z, Y))).
% 117.73/15.37 Proof:
% 117.73/15.37 complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)))
% 117.73/15.37 = { by lemma 43 R->L }
% 117.73/15.37 complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), join(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), composition(X, Y))))
% 117.73/15.37 = { by lemma 55 }
% 117.73/15.37 complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), composition(X, Y)))
% 117.73/15.37 = { by lemma 37 }
% 117.73/15.37 join(complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))), complement(composition(X, Y)))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(complement(composition(X, Y)), complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by lemma 43 R->L }
% 117.73/15.37 join(complement(composition(X, Y)), complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), join(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), composition(Z, Y)))))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(complement(composition(X, Y)), complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), join(composition(Z, Y), join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))))
% 117.73/15.37 = { by lemma 42 }
% 117.73/15.37 join(complement(composition(X, Y)), complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), join(meet(composition(X, Y), composition(Z, Y)), join(composition(meet(X, Z), Y), composition(Z, Y))))))
% 117.73/15.37 = { by lemma 51 }
% 117.73/15.37 join(complement(composition(X, Y)), complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), join(meet(composition(X, Y), composition(Z, Y)), composition(join(Z, meet(X, Z)), Y)))))
% 117.73/15.37 = { by lemma 40 }
% 117.73/15.37 join(complement(composition(X, Y)), complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), join(meet(composition(X, Y), composition(Z, Y)), composition(Z, Y)))))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(complement(composition(X, Y)), complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), join(composition(Z, Y), meet(composition(X, Y), composition(Z, Y))))))
% 117.73/15.37 = { by lemma 40 }
% 117.73/15.37 join(complement(composition(X, Y)), complement(meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), composition(Z, Y))))
% 117.73/15.37 = { by lemma 37 }
% 117.73/15.37 join(complement(composition(X, Y)), join(complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))), complement(composition(Z, Y))))
% 117.73/15.37 = { by lemma 50 }
% 117.73/15.37 join(complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))), complement(meet(composition(X, Y), composition(Z, Y))))
% 117.73/15.37 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by lemma 27 }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(meet(composition(Z, Y), composition(X, Y)), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by axiom 8 (maddux4_definiton_of_meet_4) }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(complement(join(complement(composition(Z, Y)), complement(composition(X, Y)))), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by lemma 22 R->L }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(join(complement(join(complement(composition(Z, Y)), complement(composition(X, Y)))), complement(join(complement(composition(Z, Y)), complement(composition(X, Y))))), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(join(meet(composition(Z, Y), composition(X, Y)), complement(join(complement(composition(Z, Y)), complement(composition(X, Y))))), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(join(meet(composition(Z, Y), composition(X, Y)), meet(composition(Z, Y), composition(X, Y))), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by lemma 27 R->L }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(join(meet(composition(Z, Y), composition(X, Y)), meet(composition(X, Y), composition(Z, Y))), composition(meet(X, Z), Y))))
% 117.73/15.37 = { by lemma 27 R->L }
% 117.73/15.37 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(join(meet(composition(X, Y), composition(Z, Y)), meet(composition(X, Y), composition(Z, Y))), composition(meet(X, Z), Y))))
% 117.73/15.38 = { by axiom 12 (maddux2_join_associativity_2) R->L }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(meet(composition(X, Y), composition(Z, Y)), join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)))))
% 117.73/15.38 = { by lemma 33 R->L }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(meet(composition(X, Y), composition(Z, Y)), meet(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)), top))))
% 117.73/15.38 = { by lemma 28 R->L }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(meet(composition(X, Y), composition(Z, Y)), complement(join(zero, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))))))
% 117.73/15.38 = { by lemma 31 R->L }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(complement(complement(meet(composition(X, Y), composition(Z, Y)))), complement(join(zero, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))))))
% 117.73/15.38 = { by lemma 52 R->L }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(complement(join(complement(meet(composition(X, Y), composition(Z, Y))), complement(composition(Z, Y)))), complement(join(zero, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))))))
% 117.73/15.38 = { by axiom 8 (maddux4_definiton_of_meet_4) R->L }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), complement(join(meet(meet(composition(X, Y), composition(Z, Y)), composition(Z, Y)), complement(join(zero, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))))))
% 117.73/15.38 = { by lemma 36 }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), meet(join(zero, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)))), join(complement(meet(composition(X, Y), composition(Z, Y))), complement(composition(Z, Y)))))
% 117.73/15.38 = { by lemma 52 }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), meet(join(zero, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)))), complement(meet(composition(X, Y), composition(Z, Y)))))
% 117.73/15.38 = { by lemma 30 }
% 117.73/15.38 join(complement(meet(composition(X, Y), composition(Z, Y))), meet(complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))), complement(meet(composition(X, Y), composition(Z, Y)))))
% 117.73/15.38 = { by lemma 40 }
% 117.73/15.38 complement(meet(composition(X, Y), composition(Z, Y)))
% 117.73/15.38
% 117.73/15.38 Lemma 57: join(W, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y)))) = join(complement(composition(X, Y)), join(complement(composition(Z, Y)), W)).
% 117.73/15.38 Proof:
% 117.73/15.38 join(W, complement(join(meet(composition(X, Y), composition(Z, Y)), composition(meet(X, Z), Y))))
% 117.73/15.38 = { by lemma 56 }
% 117.73/15.38 join(W, complement(meet(composition(X, Y), composition(Z, Y))))
% 117.73/15.38 = { by lemma 50 R->L }
% 117.73/15.38 join(complement(composition(X, Y)), join(W, complement(composition(Z, Y))))
% 117.73/15.38 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.38 join(complement(composition(X, Y)), join(complement(composition(Z, Y)), W))
% 117.73/15.38
% 117.73/15.38 Goal 1 (goals_16): tuple(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), join(composition(meet(sk1, sk2), sk3), meet(composition(sk1, sk3), composition(sk2, sk3)))) = tuple(composition(meet(sk1, sk2), sk3), meet(composition(sk1, sk3), composition(sk2, sk3))).
% 117.73/15.38 Proof:
% 117.73/15.38 tuple(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), join(composition(meet(sk1, sk2), sk3), meet(composition(sk1, sk3), composition(sk2, sk3))))
% 117.73/15.38 = { by axiom 2 (maddux1_join_commutativity_1) }
% 117.73/15.38 tuple(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.38 = { by lemma 53 R->L }
% 117.73/15.38 tuple(join(meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(composition(meet(sk1, sk2), sk3))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.38 = { by lemma 27 }
% 117.73/15.38 tuple(join(meet(complement(composition(meet(sk1, sk2), sk3)), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.38 = { by lemma 31 R->L }
% 117.73/15.38 tuple(join(meet(complement(composition(meet(sk1, sk2), sk3)), complement(complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.38 = { by lemma 35 R->L }
% 117.73/15.38 tuple(join(complement(join(composition(meet(sk1, sk2), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 53 R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(meet(meet(sk1, sk2), complement(composition(sk1, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 31 R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(meet(complement(complement(meet(sk1, sk2))), complement(composition(sk1, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 35 R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(complement(meet(sk1, sk2)), composition(sk1, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 46 R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(complement(meet(sk1, sk2)), join(composition(sk1, sk2), composition(complement(meet(sk1, sk2)), sk2)))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by axiom 13 (composition_distributivity_7) R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(complement(meet(sk1, sk2)), composition(join(sk1, complement(meet(sk1, sk2))), sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 39 R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(complement(meet(sk1, sk2)), composition(join(join(sk1, meet(sk1, sk2)), complement(meet(sk1, sk2))), sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by axiom 12 (maddux2_join_associativity_2) R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(complement(meet(sk1, sk2)), composition(join(sk1, join(meet(sk1, sk2), complement(meet(sk1, sk2)))), sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by axiom 3 (def_top_12) R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(complement(meet(sk1, sk2)), composition(join(sk1, top), sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 24 }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(complement(meet(sk1, sk2)), composition(top, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(composition(top, sk2), complement(meet(sk1, sk2)))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 24 R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(composition(join(one, top), sk2), complement(meet(sk1, sk2)))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(composition(join(top, one), sk2), complement(meet(sk1, sk2)))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 47 }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(sk2, join(complement(meet(sk1, sk2)), composition(top, sk2)))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by axiom 12 (maddux2_join_associativity_2) }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(join(sk2, complement(meet(sk1, sk2))), composition(top, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 37 }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(join(sk2, join(complement(sk1), complement(sk2))), composition(top, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 20 }
% 117.73/15.39 tuple(join(complement(join(composition(join(complement(join(join(complement(sk1), top), composition(top, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.39 = { by lemma 24 }
% 117.73/15.40 tuple(join(complement(join(composition(join(complement(join(top, composition(top, sk2))), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 117.73/15.40 tuple(join(complement(join(composition(join(complement(join(composition(top, sk2), top)), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 24 }
% 117.73/15.40 tuple(join(complement(join(composition(join(complement(top), meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 16 }
% 117.73/15.40 tuple(join(complement(join(composition(join(zero, meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 32 }
% 117.73/15.40 tuple(join(complement(join(composition(meet(meet(sk1, sk2), complement(complement(composition(sk1, sk2)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 34 R->L }
% 117.73/15.40 tuple(join(complement(join(composition(complement(join(complement(composition(sk1, sk2)), complement(meet(sk1, sk2)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 50 R->L }
% 117.73/15.40 tuple(join(complement(join(composition(complement(join(complement(sk1), join(complement(composition(sk1, sk2)), complement(sk2)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 35 }
% 117.73/15.40 tuple(join(complement(join(composition(meet(complement(complement(sk1)), complement(join(complement(composition(sk1, sk2)), complement(sk2)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 31 }
% 117.73/15.40 tuple(join(complement(join(composition(meet(sk1, complement(join(complement(composition(sk1, sk2)), complement(sk2)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 34 }
% 117.73/15.40 tuple(join(complement(join(composition(meet(sk1, meet(sk2, complement(complement(composition(sk1, sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 31 }
% 117.73/15.40 tuple(join(complement(join(composition(meet(sk1, meet(sk2, composition(sk1, sk2))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 27 }
% 117.73/15.40 tuple(join(complement(join(composition(meet(sk1, meet(composition(sk1, sk2), sk2)), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 31 R->L }
% 117.73/15.40 tuple(join(complement(join(composition(meet(sk1, meet(composition(sk1, sk2), complement(complement(sk2)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 117.73/15.40 = { by lemma 32 R->L }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(zero, meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 16 R->L }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(complement(top), meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 24 R->L }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(complement(join(sk2, top)), meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by axiom 3 (def_top_12) }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(complement(join(sk2, join(composition(sk1, sk2), complement(composition(sk1, sk2))))), meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(complement(join(sk2, join(complement(composition(sk1, sk2)), composition(sk1, sk2)))), meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 48 }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(complement(join(sk2, complement(composition(sk1, sk2)))), meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 35 }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(meet(complement(sk2), complement(complement(composition(sk1, sk2)))), meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 31 }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, join(meet(complement(sk2), composition(sk1, sk2)), meet(composition(sk1, sk2), complement(complement(sk2))))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 54 }
% 118.51/15.41 tuple(join(complement(join(composition(meet(sk1, composition(sk1, sk2)), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 27 }
% 118.51/15.41 tuple(join(complement(join(composition(meet(composition(sk1, sk2), sk1), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 31 R->L }
% 118.51/15.41 tuple(join(complement(join(composition(meet(composition(sk1, sk2), complement(complement(sk1))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 32 R->L }
% 118.51/15.41 tuple(join(complement(join(composition(join(zero, meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 16 R->L }
% 118.51/15.41 tuple(join(complement(join(composition(join(complement(top), meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.41 = { by lemma 24 R->L }
% 118.51/15.42 tuple(join(complement(join(composition(join(complement(join(sk1, top)), meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by axiom 3 (def_top_12) }
% 118.51/15.42 tuple(join(complement(join(composition(join(complement(join(sk1, join(composition(sk1, sk2), complement(composition(sk1, sk2))))), meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 118.51/15.42 tuple(join(complement(join(composition(join(complement(join(sk1, join(complement(composition(sk1, sk2)), composition(sk1, sk2)))), meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 46 }
% 118.51/15.42 tuple(join(complement(join(composition(join(complement(join(sk1, complement(composition(sk1, sk2)))), meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 35 }
% 118.51/15.42 tuple(join(complement(join(composition(join(meet(complement(sk1), complement(complement(composition(sk1, sk2)))), meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 31 }
% 118.51/15.42 tuple(join(complement(join(composition(join(meet(complement(sk1), composition(sk1, sk2)), meet(composition(sk1, sk2), complement(complement(sk1)))), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 54 }
% 118.51/15.42 tuple(join(complement(join(composition(composition(sk1, sk2), sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by axiom 10 (composition_associativity_5) R->L }
% 118.51/15.42 tuple(join(complement(join(composition(sk1, composition(sk2, sk3)), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 31 R->L }
% 118.51/15.42 tuple(join(complement(join(composition(sk1, complement(complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 57 }
% 118.51/15.42 tuple(join(complement(join(complement(composition(sk1, sk3)), join(complement(composition(sk2, sk3)), composition(sk1, complement(complement(composition(sk2, sk3))))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 49 R->L }
% 118.51/15.42 tuple(join(complement(join(complement(composition(sk1, sk3)), join(complement(composition(sk2, sk3)), composition(sk1, join(complement(composition(sk2, sk3)), complement(complement(composition(sk2, sk3)))))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by axiom 3 (def_top_12) R->L }
% 118.51/15.42 tuple(join(complement(join(complement(composition(sk1, sk3)), join(complement(composition(sk2, sk3)), composition(sk1, top)))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 57 R->L }
% 118.51/15.42 tuple(join(complement(join(composition(sk1, top), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by lemma 24 R->L }
% 118.51/15.42 tuple(join(complement(join(composition(sk1, join(sk3, top)), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by axiom 3 (def_top_12) }
% 118.51/15.42 tuple(join(complement(join(composition(sk1, join(sk3, join(composition(sk2, sk3), complement(composition(sk2, sk3))))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by axiom 12 (maddux2_join_associativity_2) }
% 118.51/15.42 tuple(join(complement(join(composition(sk1, join(join(sk3, composition(sk2, sk3)), complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.42 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 118.51/15.42 tuple(join(complement(join(composition(sk1, join(join(composition(sk2, sk3), sk3), complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 18 R->L }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, join(join(composition(sk2, sk3), composition(converse(one), sk3)), complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 51 }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, join(composition(join(converse(one), sk2), sk3), complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 19 }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, join(composition(join(one, sk2), sk3), complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by axiom 2 (maddux1_join_commutativity_1) }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, join(composition(join(sk2, one), sk3), complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by axiom 5 (goals_15) }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, join(composition(one, sk3), complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 21 }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, join(sk3, complement(composition(sk2, sk3)))), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 57 }
% 118.51/15.43 tuple(join(complement(join(complement(composition(sk1, sk3)), join(complement(composition(sk2, sk3)), composition(sk1, join(sk3, complement(composition(sk2, sk3))))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 118.51/15.43 tuple(join(complement(join(complement(composition(sk1, sk3)), join(complement(composition(sk2, sk3)), composition(sk1, join(complement(composition(sk2, sk3)), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 49 }
% 118.51/15.43 tuple(join(complement(join(complement(composition(sk1, sk3)), join(complement(composition(sk2, sk3)), composition(sk1, sk3)))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 57 R->L }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 55 R->L }
% 118.51/15.43 tuple(join(complement(join(join(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), composition(sk1, sk3)), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by axiom 12 (maddux2_join_associativity_2) R->L }
% 118.51/15.43 tuple(join(complement(join(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), join(composition(sk1, sk3), complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))))), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 20 }
% 118.51/15.43 tuple(join(complement(join(composition(sk1, sk3), top)), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 24 }
% 118.51/15.43 tuple(join(complement(top), meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 16 }
% 118.51/15.43 tuple(join(zero, meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3))))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 32 }
% 118.51/15.43 tuple(meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), complement(complement(composition(meet(sk1, sk2), sk3)))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 31 }
% 118.51/15.43 tuple(meet(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)), composition(meet(sk1, sk2), sk3)), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 27 }
% 118.51/15.43 tuple(meet(composition(meet(sk1, sk2), sk3), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 118.51/15.43 tuple(meet(composition(meet(sk1, sk2), sk3), join(composition(meet(sk1, sk2), sk3), meet(composition(sk1, sk3), composition(sk2, sk3)))), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 43 }
% 118.51/15.43 tuple(composition(meet(sk1, sk2), sk3), join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))
% 118.51/15.43 = { by lemma 31 R->L }
% 118.51/15.43 tuple(composition(meet(sk1, sk2), sk3), complement(complement(join(meet(composition(sk1, sk3), composition(sk2, sk3)), composition(meet(sk1, sk2), sk3)))))
% 118.51/15.43 = { by lemma 56 }
% 118.51/15.43 tuple(composition(meet(sk1, sk2), sk3), complement(complement(meet(composition(sk1, sk3), composition(sk2, sk3)))))
% 118.51/15.43 = { by lemma 31 }
% 118.51/15.43 tuple(composition(meet(sk1, sk2), sk3), meet(composition(sk1, sk3), composition(sk2, sk3)))
% 118.51/15.43 % SZS output end Proof
% 118.51/15.43
% 118.51/15.43 RESULT: Unsatisfiable (the axioms are contradictory).
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