%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL016-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:33:07 PM UTC 2026
% Result : Unsatisfiable 26.55s 3.80s
% Output : Proof 27.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL016-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 27 22:51:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.55/3.80 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 26.55/3.80
% 26.55/3.80 % SZS status Unsatisfiable
% 26.55/3.80
% 27.32/3.86 % SZS output start Proof
% 27.32/3.86 Axiom 1 (composition_identity_6): composition(X, one) = X.
% 27.32/3.86 Axiom 2 (def_zero_13): zero = meet(X, complement(X)).
% 27.32/3.86 Axiom 3 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 27.32/3.86 Axiom 4 (def_top_12): top = join(X, complement(X)).
% 27.32/3.86 Axiom 5 (converse_idempotence_8): converse(converse(X)) = X.
% 27.32/3.86 Axiom 6 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 27.32/3.86 Axiom 7 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 27.32/3.86 Axiom 8 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 27.32/3.86 Axiom 9 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 27.32/3.86 Axiom 10 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 27.32/3.86 Axiom 11 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 27.32/3.86 Axiom 12 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 27.32/3.86 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 27.32/3.86
% 27.32/3.86 Lemma 14: complement(top) = zero.
% 27.32/3.86 Proof:
% 27.32/3.86 complement(top)
% 27.32/3.86 = { by axiom 4 (def_top_12) }
% 27.32/3.86 complement(join(complement(X), complement(complement(X))))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.86 meet(X, complement(X))
% 27.32/3.86 = { by axiom 2 (def_zero_13) R->L }
% 27.32/3.86 zero
% 27.32/3.86
% 27.32/3.86 Lemma 15: join(X, join(Y, complement(X))) = join(Y, top).
% 27.32/3.86 Proof:
% 27.32/3.86 join(X, join(Y, complement(X)))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 join(X, join(complement(X), Y))
% 27.32/3.86 = { by axiom 10 (maddux2_join_associativity_2) }
% 27.32/3.86 join(join(X, complement(X)), Y)
% 27.32/3.86 = { by axiom 4 (def_top_12) R->L }
% 27.32/3.86 join(top, Y)
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.86 join(Y, top)
% 27.32/3.86
% 27.32/3.86 Lemma 16: join(X, join(complement(X), Y)) = join(Y, top).
% 27.32/3.86 Proof:
% 27.32/3.86 join(X, join(complement(X), Y))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 join(X, join(Y, complement(X)))
% 27.32/3.86 = { by lemma 15 }
% 27.32/3.86 join(Y, top)
% 27.32/3.86
% 27.32/3.86 Lemma 17: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 27.32/3.86 Proof:
% 27.32/3.86 converse(composition(converse(X), Y))
% 27.32/3.86 = { by axiom 7 (converse_multiplicativity_10) }
% 27.32/3.86 composition(converse(Y), converse(converse(X)))
% 27.32/3.86 = { by axiom 5 (converse_idempotence_8) }
% 27.32/3.86 composition(converse(Y), X)
% 27.32/3.86
% 27.32/3.86 Lemma 18: composition(converse(one), X) = X.
% 27.32/3.86 Proof:
% 27.32/3.86 composition(converse(one), X)
% 27.32/3.86 = { by lemma 17 R->L }
% 27.32/3.86 converse(composition(converse(X), one))
% 27.32/3.86 = { by axiom 1 (composition_identity_6) }
% 27.32/3.86 converse(converse(X))
% 27.32/3.86 = { by axiom 5 (converse_idempotence_8) }
% 27.32/3.86 X
% 27.32/3.86
% 27.32/3.86 Lemma 19: join(complement(X), complement(X)) = complement(X).
% 27.32/3.86 Proof:
% 27.32/3.86 join(complement(X), complement(X))
% 27.32/3.86 = { by lemma 18 R->L }
% 27.32/3.86 join(complement(X), complement(composition(converse(one), X)))
% 27.32/3.86 = { by axiom 1 (composition_identity_6) R->L }
% 27.32/3.86 join(complement(X), complement(composition(composition(converse(one), one), X)))
% 27.32/3.86 = { by axiom 8 (composition_associativity_5) R->L }
% 27.32/3.86 join(complement(X), complement(composition(converse(one), composition(one, X))))
% 27.32/3.86 = { by lemma 18 }
% 27.32/3.86 join(complement(X), complement(composition(one, X)))
% 27.32/3.86 = { by axiom 5 (converse_idempotence_8) R->L }
% 27.32/3.86 join(complement(X), complement(composition(converse(converse(one)), X)))
% 27.32/3.86 = { by lemma 18 R->L }
% 27.32/3.86 join(complement(X), composition(converse(one), complement(composition(converse(converse(one)), X))))
% 27.32/3.86 = { by axiom 5 (converse_idempotence_8) R->L }
% 27.32/3.86 join(complement(X), composition(converse(converse(converse(one))), complement(composition(converse(converse(one)), X))))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 join(composition(converse(converse(converse(one))), complement(composition(converse(converse(one)), X))), complement(X))
% 27.32/3.86 = { by axiom 13 (converse_cancellativity_11) }
% 27.32/3.86 complement(X)
% 27.32/3.86
% 27.32/3.86 Lemma 20: join(X, join(Y, complement(join(X, Y)))) = top.
% 27.32/3.86 Proof:
% 27.32/3.86 join(X, join(Y, complement(join(X, Y))))
% 27.32/3.86 = { by axiom 10 (maddux2_join_associativity_2) }
% 27.32/3.86 join(join(X, Y), complement(join(X, Y)))
% 27.32/3.86 = { by axiom 4 (def_top_12) R->L }
% 27.32/3.86 top
% 27.32/3.86
% 27.32/3.86 Lemma 21: join(X, top) = top.
% 27.32/3.86 Proof:
% 27.32/3.86 join(X, top)
% 27.32/3.86 = { by axiom 4 (def_top_12) }
% 27.32/3.86 join(X, join(complement(X), complement(complement(X))))
% 27.32/3.86 = { by lemma 16 }
% 27.32/3.86 join(complement(complement(X)), top)
% 27.32/3.86 = { by lemma 15 R->L }
% 27.32/3.86 join(complement(complement(X)), join(complement(complement(X)), complement(complement(complement(X)))))
% 27.32/3.86 = { by lemma 19 R->L }
% 27.32/3.86 join(complement(complement(X)), join(complement(complement(X)), complement(join(complement(complement(X)), complement(complement(X))))))
% 27.32/3.86 = { by lemma 20 }
% 27.32/3.86 top
% 27.32/3.86
% 27.32/3.86 Lemma 22: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 27.32/3.86 Proof:
% 27.32/3.86 join(meet(X, Y), complement(join(complement(X), Y)))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 27.32/3.86 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 27.32/3.86 = { by axiom 12 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 27.32/3.86 X
% 27.32/3.86
% 27.32/3.86 Lemma 23: join(meet(X, Y), join(Z, complement(join(complement(X), Y)))) = join(X, Z).
% 27.32/3.86 Proof:
% 27.32/3.86 join(meet(X, Y), join(Z, complement(join(complement(X), Y))))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 join(meet(X, Y), join(complement(join(complement(X), Y)), Z))
% 27.32/3.86 = { by axiom 10 (maddux2_join_associativity_2) }
% 27.32/3.86 join(join(meet(X, Y), complement(join(complement(X), Y))), Z)
% 27.32/3.86 = { by lemma 22 }
% 27.32/3.86 join(X, Z)
% 27.32/3.86
% 27.32/3.86 Lemma 24: join(zero, meet(X, X)) = X.
% 27.32/3.86 Proof:
% 27.32/3.86 join(zero, meet(X, X))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 27.32/3.86 join(zero, complement(join(complement(X), complement(X))))
% 27.32/3.86 = { by axiom 2 (def_zero_13) }
% 27.32/3.86 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 27.32/3.86 = { by lemma 22 }
% 27.32/3.86 X
% 27.32/3.86
% 27.32/3.86 Lemma 25: join(zero, join(X, meet(Y, Y))) = join(X, Y).
% 27.32/3.86 Proof:
% 27.32/3.86 join(zero, join(X, meet(Y, Y)))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 join(zero, join(meet(Y, Y), X))
% 27.32/3.86 = { by axiom 10 (maddux2_join_associativity_2) }
% 27.32/3.86 join(join(zero, meet(Y, Y)), X)
% 27.32/3.86 = { by lemma 24 }
% 27.32/3.86 join(Y, X)
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.86 join(X, Y)
% 27.32/3.86
% 27.32/3.86 Lemma 26: meet(Y, X) = meet(X, Y).
% 27.32/3.86 Proof:
% 27.32/3.86 meet(Y, X)
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 27.32/3.86 complement(join(complement(Y), complement(X)))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 complement(join(complement(X), complement(Y)))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.86 meet(X, Y)
% 27.32/3.86
% 27.32/3.86 Lemma 27: complement(join(meet(X, Y), complement(Z))) = meet(Z, join(complement(X), complement(Y))).
% 27.32/3.86 Proof:
% 27.32/3.86 complement(join(meet(X, Y), complement(Z)))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 27.32/3.86 complement(join(complement(join(complement(X), complement(Y))), complement(Z)))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.86 meet(join(complement(X), complement(Y)), Z)
% 27.32/3.86 = { by lemma 26 R->L }
% 27.32/3.86 meet(Z, join(complement(X), complement(Y)))
% 27.32/3.86
% 27.32/3.86 Lemma 28: meet(join(X, complement(Y)), join(complement(X), complement(Y))) = complement(Y).
% 27.32/3.86 Proof:
% 27.32/3.86 meet(join(X, complement(Y)), join(complement(X), complement(Y)))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 meet(join(X, complement(Y)), join(complement(Y), complement(X)))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 meet(join(complement(Y), X), join(complement(Y), complement(X)))
% 27.32/3.86 = { by lemma 27 R->L }
% 27.32/3.86 complement(join(meet(Y, X), complement(join(complement(Y), X))))
% 27.32/3.86 = { by lemma 22 }
% 27.32/3.86 complement(Y)
% 27.32/3.86
% 27.32/3.86 Lemma 29: join(meet(X, Y), meet(Y, complement(X))) = Y.
% 27.32/3.86 Proof:
% 27.32/3.86 join(meet(X, Y), meet(Y, complement(X)))
% 27.32/3.86 = { by lemma 26 }
% 27.32/3.86 join(meet(Y, X), meet(Y, complement(X)))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 join(meet(Y, complement(X)), meet(Y, X))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 27.32/3.86 join(meet(Y, complement(X)), complement(join(complement(Y), complement(X))))
% 27.32/3.86 = { by lemma 22 }
% 27.32/3.86 Y
% 27.32/3.86
% 27.32/3.86 Lemma 30: join(zero, complement(X)) = complement(X).
% 27.32/3.86 Proof:
% 27.32/3.86 join(zero, complement(X))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.86 join(complement(X), zero)
% 27.32/3.86 = { by lemma 14 R->L }
% 27.32/3.86 join(complement(X), complement(top))
% 27.32/3.86 = { by lemma 21 R->L }
% 27.32/3.86 join(complement(X), complement(join(meet(complement(complement(X)), complement(complement(X))), top)))
% 27.32/3.86 = { by lemma 16 R->L }
% 27.32/3.86 join(complement(X), complement(join(zero, join(complement(zero), meet(complement(complement(X)), complement(complement(X)))))))
% 27.32/3.86 = { by lemma 25 }
% 27.32/3.86 join(complement(X), complement(join(complement(zero), complement(complement(X)))))
% 27.32/3.86 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.86 join(complement(X), complement(join(complement(complement(X)), complement(zero))))
% 27.32/3.86 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.86 join(complement(X), meet(complement(X), zero))
% 27.32/3.86 = { by lemma 14 R->L }
% 27.32/3.86 join(complement(X), meet(complement(X), complement(top)))
% 27.32/3.86 = { by lemma 28 R->L }
% 27.32/3.86 join(meet(join(X, complement(X)), join(complement(X), complement(X))), meet(complement(X), complement(top)))
% 27.32/3.86 = { by axiom 4 (def_top_12) R->L }
% 27.32/3.86 join(meet(top, join(complement(X), complement(X))), meet(complement(X), complement(top)))
% 27.32/3.86 = { by lemma 19 }
% 27.32/3.86 join(meet(top, complement(X)), meet(complement(X), complement(top)))
% 27.32/3.86 = { by lemma 29 }
% 27.32/3.86 complement(X)
% 27.32/3.86
% 27.32/3.86 Lemma 31: join(X, zero) = X.
% 27.32/3.86 Proof:
% 27.32/3.86 join(X, zero)
% 27.32/3.86 = { by lemma 23 R->L }
% 27.32/3.86 join(meet(X, Y), join(zero, complement(join(complement(X), Y))))
% 27.32/3.87 = { by lemma 30 }
% 27.32/3.87 join(meet(X, Y), complement(join(complement(X), Y)))
% 27.32/3.87 = { by lemma 22 }
% 27.32/3.87 X
% 27.32/3.87
% 27.32/3.87 Lemma 32: complement(complement(X)) = X.
% 27.32/3.87 Proof:
% 27.32/3.87 complement(complement(X))
% 27.32/3.87 = { by lemma 30 R->L }
% 27.32/3.87 join(zero, complement(complement(X)))
% 27.32/3.87 = { by axiom 2 (def_zero_13) }
% 27.32/3.87 join(meet(X, complement(X)), complement(complement(X)))
% 27.32/3.87 = { by lemma 19 R->L }
% 27.32/3.87 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 27.32/3.87 = { by lemma 22 }
% 27.32/3.87 X
% 27.32/3.87
% 27.32/3.87 Lemma 33: complement(join(zero, complement(X))) = meet(X, top).
% 27.32/3.87 Proof:
% 27.32/3.87 complement(join(zero, complement(X)))
% 27.32/3.87 = { by lemma 14 R->L }
% 27.32/3.87 complement(join(complement(top), complement(X)))
% 27.32/3.87 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.87 meet(top, X)
% 27.32/3.87 = { by lemma 26 R->L }
% 27.32/3.87 meet(X, top)
% 27.32/3.87
% 27.32/3.87 Lemma 34: meet(X, top) = X.
% 27.32/3.87 Proof:
% 27.32/3.87 meet(X, top)
% 27.32/3.87 = { by lemma 33 R->L }
% 27.32/3.87 complement(join(zero, complement(X)))
% 27.32/3.87 = { by lemma 30 R->L }
% 27.32/3.87 join(zero, complement(join(zero, complement(X))))
% 27.32/3.87 = { by lemma 33 }
% 27.32/3.87 join(zero, meet(X, top))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(meet(X, top), zero)
% 27.32/3.87 = { by lemma 14 R->L }
% 27.32/3.87 join(meet(X, top), complement(top))
% 27.32/3.87 = { by lemma 21 R->L }
% 27.32/3.87 join(meet(X, top), complement(join(complement(X), top)))
% 27.32/3.87 = { by lemma 22 }
% 27.32/3.87 X
% 27.32/3.87
% 27.32/3.87 Lemma 35: meet(top, X) = X.
% 27.32/3.87 Proof:
% 27.32/3.87 meet(top, X)
% 27.32/3.87 = { by lemma 26 }
% 27.32/3.87 meet(X, top)
% 27.32/3.87 = { by lemma 34 }
% 27.32/3.87 X
% 27.32/3.87
% 27.32/3.87 Lemma 36: complement(meet(X, Y)) = join(complement(X), complement(Y)).
% 27.32/3.87 Proof:
% 27.32/3.87 complement(meet(X, Y))
% 27.32/3.87 = { by lemma 26 }
% 27.32/3.87 complement(meet(Y, X))
% 27.32/3.87 = { by lemma 31 R->L }
% 27.32/3.87 complement(join(meet(Y, X), zero))
% 27.32/3.87 = { by lemma 14 R->L }
% 27.32/3.87 complement(join(meet(Y, X), complement(top)))
% 27.32/3.87 = { by lemma 27 }
% 27.32/3.87 meet(top, join(complement(Y), complement(X)))
% 27.32/3.87 = { by lemma 35 }
% 27.32/3.87 join(complement(Y), complement(X))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 join(complement(X), complement(Y))
% 27.32/3.87
% 27.32/3.87 Lemma 37: meet(join(complement(X), Y), join(complement(Y), complement(X))) = complement(X).
% 27.32/3.87 Proof:
% 27.32/3.87 meet(join(complement(X), Y), join(complement(Y), complement(X)))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 meet(join(Y, complement(X)), join(complement(Y), complement(X)))
% 27.32/3.87 = { by lemma 28 }
% 27.32/3.87 complement(X)
% 27.32/3.87
% 27.32/3.87 Lemma 38: join(X, join(X, Y)) = join(X, Y).
% 27.32/3.87 Proof:
% 27.32/3.87 join(X, join(X, Y))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(X, join(Y, X))
% 27.32/3.87 = { by lemma 32 R->L }
% 27.32/3.87 join(X, join(Y, complement(complement(X))))
% 27.32/3.87 = { by axiom 10 (maddux2_join_associativity_2) }
% 27.32/3.87 join(join(X, Y), complement(complement(X)))
% 27.32/3.87 = { by lemma 37 R->L }
% 27.32/3.87 join(join(X, Y), complement(meet(join(complement(X), join(Y, complement(complement(X)))), join(complement(join(Y, complement(complement(X)))), complement(X)))))
% 27.32/3.87 = { by lemma 15 }
% 27.32/3.87 join(join(X, Y), complement(meet(join(Y, top), join(complement(join(Y, complement(complement(X)))), complement(X)))))
% 27.32/3.87 = { by lemma 21 }
% 27.32/3.87 join(join(X, Y), complement(meet(top, join(complement(join(Y, complement(complement(X)))), complement(X)))))
% 27.32/3.87 = { by lemma 35 }
% 27.32/3.87 join(join(X, Y), complement(join(complement(join(Y, complement(complement(X)))), complement(X))))
% 27.32/3.87 = { by lemma 32 }
% 27.32/3.87 join(join(X, Y), complement(join(complement(join(Y, X)), complement(X))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 join(join(X, Y), complement(join(complement(X), complement(join(Y, X)))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 join(join(X, Y), complement(join(complement(X), complement(join(X, Y)))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(join(X, Y), complement(join(complement(join(X, Y)), complement(X))))
% 27.32/3.87 = { by lemma 23 R->L }
% 27.32/3.87 join(meet(join(X, Y), complement(X)), join(complement(join(complement(join(X, Y)), complement(X))), complement(join(complement(join(X, Y)), complement(X)))))
% 27.32/3.87 = { by lemma 19 }
% 27.32/3.87 join(meet(join(X, Y), complement(X)), complement(join(complement(join(X, Y)), complement(X))))
% 27.32/3.87 = { by lemma 22 }
% 27.32/3.87 join(X, Y)
% 27.32/3.87
% 27.32/3.87 Lemma 39: meet(meet(X, complement(Y)), join(Z, X)) = meet(X, complement(Y)).
% 27.32/3.87 Proof:
% 27.32/3.87 meet(meet(X, complement(Y)), join(Z, X))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(X, Z))
% 27.32/3.87 = { by lemma 22 R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(meet(X, complement(Y)), complement(join(complement(X), complement(Y)))), Z))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(meet(X, complement(Y)), complement(join(complement(Y), complement(X)))), Z))
% 27.32/3.87 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(meet(X, complement(Y)), meet(Y, X)), Z))
% 27.32/3.87 = { by lemma 26 R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(meet(X, complement(Y)), meet(X, Y)), Z))
% 27.32/3.87 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(meet(X, complement(Y)), join(meet(X, Y), Z)))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 meet(meet(X, complement(Y)), join(meet(X, complement(Y)), join(Z, meet(X, Y))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(Z, meet(X, Y)), meet(X, complement(Y))))
% 27.32/3.87 = { by lemma 31 R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(Z, meet(X, Y)), join(meet(X, complement(Y)), zero)))
% 27.32/3.87 = { by lemma 14 R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(Z, meet(X, Y)), join(meet(X, complement(Y)), complement(top))))
% 27.32/3.87 = { by lemma 21 R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(Z, meet(X, Y)), join(meet(X, complement(Y)), complement(join(join(Z, meet(X, Y)), top)))))
% 27.32/3.87 = { by lemma 32 R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(Z, meet(X, Y)), join(complement(complement(meet(X, complement(Y)))), complement(join(join(Z, meet(X, Y)), top)))))
% 27.32/3.87 = { by axiom 10 (maddux2_join_associativity_2) }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))), complement(join(join(Z, meet(X, Y)), top))))
% 27.32/3.87 = { by lemma 15 R->L }
% 27.32/3.87 meet(meet(X, complement(Y)), join(join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))), complement(join(complement(meet(X, complement(Y))), join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y)))))))))
% 27.32/3.87 = { by lemma 31 R->L }
% 27.32/3.87 join(meet(meet(X, complement(Y)), join(join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))), complement(join(complement(meet(X, complement(Y))), join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))))))), zero)
% 27.32/3.87 = { by lemma 14 R->L }
% 27.32/3.87 join(meet(meet(X, complement(Y)), join(join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))), complement(join(complement(meet(X, complement(Y))), join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))))))), complement(top))
% 27.32/3.87 = { by lemma 20 R->L }
% 27.32/3.87 join(meet(meet(X, complement(Y)), join(join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))), complement(join(complement(meet(X, complement(Y))), join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))))))), complement(join(complement(meet(X, complement(Y))), join(join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y))))), complement(join(complement(meet(X, complement(Y))), join(join(Z, meet(X, Y)), complement(complement(meet(X, complement(Y)))))))))))
% 27.32/3.87 = { by lemma 22 }
% 27.32/3.87 meet(X, complement(Y))
% 27.32/3.87
% 27.32/3.87 Lemma 40: join(meet(X, complement(Y)), Y) = join(X, Y).
% 27.32/3.87 Proof:
% 27.32/3.87 join(meet(X, complement(Y)), Y)
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(Y, meet(X, complement(Y)))
% 27.32/3.87 = { by lemma 39 R->L }
% 27.32/3.87 join(Y, meet(meet(X, complement(Y)), join(Y, X)))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(Y, meet(meet(X, complement(Y)), join(X, Y)))
% 27.32/3.87 = { by lemma 32 R->L }
% 27.32/3.87 join(complement(complement(Y)), meet(meet(X, complement(Y)), join(X, Y)))
% 27.32/3.87 = { by lemma 32 R->L }
% 27.32/3.87 join(complement(complement(Y)), meet(meet(X, complement(Y)), join(X, complement(complement(Y)))))
% 27.32/3.87 = { by lemma 26 R->L }
% 27.32/3.87 join(complement(complement(Y)), meet(meet(complement(Y), X), join(X, complement(complement(Y)))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(complement(complement(Y)), meet(meet(complement(Y), X), join(complement(complement(Y)), X)))
% 27.32/3.87 = { by lemma 26 }
% 27.32/3.87 join(complement(complement(Y)), meet(join(complement(complement(Y)), X), meet(complement(Y), X)))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(meet(join(complement(complement(Y)), X), meet(complement(Y), X)), complement(complement(Y)))
% 27.32/3.87 = { by lemma 22 R->L }
% 27.32/3.87 join(meet(join(complement(complement(Y)), X), meet(complement(Y), X)), complement(join(meet(complement(Y), X), complement(join(complement(complement(Y)), X)))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(meet(join(complement(complement(Y)), X), meet(complement(Y), X)), complement(join(complement(join(complement(complement(Y)), X)), meet(complement(Y), X))))
% 27.32/3.87 = { by lemma 22 }
% 27.32/3.87 join(complement(complement(Y)), X)
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 join(X, complement(complement(Y)))
% 27.32/3.87 = { by lemma 32 }
% 27.32/3.87 join(X, Y)
% 27.32/3.87
% 27.32/3.87 Lemma 41: join(composition(X, Y), composition(X, Z)) = composition(X, join(Z, Y)).
% 27.32/3.87 Proof:
% 27.32/3.87 join(composition(X, Y), composition(X, Z))
% 27.32/3.87 = { by axiom 5 (converse_idempotence_8) R->L }
% 27.32/3.87 join(composition(X, Y), composition(converse(converse(X)), Z))
% 27.32/3.87 = { by axiom 5 (converse_idempotence_8) R->L }
% 27.32/3.87 join(converse(converse(composition(X, Y))), composition(converse(converse(X)), Z))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(composition(converse(converse(X)), Z), converse(converse(composition(X, Y))))
% 27.32/3.87 = { by lemma 17 R->L }
% 27.32/3.87 join(converse(composition(converse(Z), converse(X))), converse(converse(composition(X, Y))))
% 27.32/3.87 = { by axiom 9 (converse_additivity_9) R->L }
% 27.32/3.87 converse(join(composition(converse(Z), converse(X)), converse(composition(X, Y))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 converse(join(converse(composition(X, Y)), composition(converse(Z), converse(X))))
% 27.32/3.87 = { by axiom 7 (converse_multiplicativity_10) }
% 27.32/3.87 converse(join(composition(converse(Y), converse(X)), composition(converse(Z), converse(X))))
% 27.32/3.87 = { by axiom 11 (composition_distributivity_7) R->L }
% 27.32/3.87 converse(composition(join(converse(Y), converse(Z)), converse(X)))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 converse(composition(join(converse(Z), converse(Y)), converse(X)))
% 27.32/3.87 = { by axiom 7 (converse_multiplicativity_10) }
% 27.32/3.87 composition(converse(converse(X)), converse(join(converse(Z), converse(Y))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 composition(converse(converse(X)), converse(join(converse(Y), converse(Z))))
% 27.32/3.87 = { by axiom 9 (converse_additivity_9) }
% 27.32/3.87 composition(converse(converse(X)), join(converse(converse(Y)), converse(converse(Z))))
% 27.32/3.87 = { by axiom 5 (converse_idempotence_8) }
% 27.32/3.87 composition(converse(converse(X)), join(Y, converse(converse(Z))))
% 27.32/3.87 = { by axiom 5 (converse_idempotence_8) }
% 27.32/3.87 composition(X, join(Y, converse(converse(Z))))
% 27.32/3.87 = { by axiom 5 (converse_idempotence_8) }
% 27.32/3.87 composition(X, join(Y, Z))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 composition(X, join(Z, Y))
% 27.32/3.87
% 27.32/3.87 Lemma 42: meet(join(X, Y), join(X, complement(Y))) = X.
% 27.32/3.87 Proof:
% 27.32/3.87 meet(join(X, Y), join(X, complement(Y)))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 meet(join(X, Y), join(complement(Y), X))
% 27.32/3.87 = { by lemma 34 R->L }
% 27.32/3.87 meet(join(X, Y), join(complement(Y), meet(X, top)))
% 27.32/3.87 = { by lemma 33 R->L }
% 27.32/3.87 meet(join(X, Y), join(complement(Y), complement(join(zero, complement(X)))))
% 27.32/3.87 = { by lemma 34 R->L }
% 27.32/3.87 meet(join(meet(X, top), Y), join(complement(Y), complement(join(zero, complement(X)))))
% 27.32/3.87 = { by lemma 33 R->L }
% 27.32/3.87 meet(join(complement(join(zero, complement(X))), Y), join(complement(Y), complement(join(zero, complement(X)))))
% 27.32/3.87 = { by lemma 37 }
% 27.32/3.87 complement(join(zero, complement(X)))
% 27.32/3.87 = { by lemma 33 }
% 27.32/3.87 meet(X, top)
% 27.32/3.87 = { by lemma 34 }
% 27.32/3.87 X
% 27.32/3.87
% 27.32/3.87 Lemma 43: join(meet(X, Y), complement(join(X, complement(Y)))) = Y.
% 27.32/3.87 Proof:
% 27.32/3.87 join(meet(X, Y), complement(join(X, complement(Y))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.87 join(meet(X, Y), complement(join(complement(Y), X)))
% 27.32/3.87 = { by lemma 26 }
% 27.32/3.87 join(meet(Y, X), complement(join(complement(Y), X)))
% 27.32/3.87 = { by lemma 22 }
% 27.32/3.87 Y
% 27.32/3.87
% 27.32/3.87 Lemma 44: meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))) = meet(composition(X, Y), complement(composition(X, Z))).
% 27.32/3.87 Proof:
% 27.32/3.87 meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))
% 27.32/3.87 = { by lemma 42 R->L }
% 27.32/3.87 meet(join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(complement(composition(X, Z)), complement(composition(X, meet(Y, complement(Z)))))), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), complement(meet(complement(composition(X, Z)), complement(composition(X, meet(Y, complement(Z))))))))
% 27.32/3.87 = { by lemma 29 }
% 27.32/3.87 meet(complement(composition(X, Z)), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), complement(meet(complement(composition(X, Z)), complement(composition(X, meet(Y, complement(Z))))))))
% 27.32/3.87 = { by lemma 36 }
% 27.32/3.87 meet(complement(composition(X, Z)), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), join(complement(complement(composition(X, Z))), complement(complement(composition(X, meet(Y, complement(Z))))))))
% 27.32/3.87 = { by lemma 32 }
% 27.32/3.87 meet(complement(composition(X, Z)), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), join(composition(X, Z), complement(complement(composition(X, meet(Y, complement(Z))))))))
% 27.32/3.87 = { by lemma 32 }
% 27.32/3.87 meet(complement(composition(X, Z)), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), join(composition(X, Z), composition(X, meet(Y, complement(Z))))))
% 27.32/3.87 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.87 meet(complement(composition(X, Z)), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), join(composition(X, meet(Y, complement(Z))), composition(X, Z))))
% 27.32/3.87 = { by lemma 40 R->L }
% 27.32/3.87 meet(complement(composition(X, Z)), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), composition(X, Z))))
% 27.32/3.87 = { by lemma 38 }
% 27.32/3.87 meet(complement(composition(X, Z)), join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), composition(X, Z)))
% 27.32/3.87 = { by lemma 40 }
% 27.32/3.87 meet(complement(composition(X, Z)), join(composition(X, meet(Y, complement(Z))), composition(X, Z)))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(composition(X, Z), composition(X, meet(Y, complement(Z)))))
% 27.32/3.88 = { by lemma 41 }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(Y, complement(Z)), Z)))
% 27.32/3.88 = { by lemma 32 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(Y, complement(Z)), complement(complement(Z)))))
% 27.32/3.88 = { by lemma 39 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(complement(Z)))))
% 27.32/3.88 = { by lemma 43 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(meet(Y, complement(Z)), complement(join(Y, complement(complement(Z)))))))))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(complement(join(Y, complement(complement(Z)))), meet(Y, complement(Z)))))))
% 27.32/3.88 = { by lemma 32 }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(complement(join(Y, Z)), meet(Y, complement(Z)))))))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(meet(Y, complement(Z)), complement(join(Y, Z)))))))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(meet(Y, complement(Z)), complement(join(Z, Y)))))))
% 27.32/3.88 = { by lemma 43 }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(Z, Y)))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), composition(X, join(Y, Z)))
% 27.32/3.88 = { by lemma 41 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(composition(X, Z), composition(X, Y)))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.88 meet(complement(composition(X, Z)), join(composition(X, Y), composition(X, Z)))
% 27.32/3.88 = { by lemma 40 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(meet(composition(X, Y), complement(composition(X, Z))), composition(X, Z)))
% 27.32/3.88 = { by lemma 38 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(meet(composition(X, Y), complement(composition(X, Z))), join(meet(composition(X, Y), complement(composition(X, Z))), composition(X, Z))))
% 27.32/3.88 = { by lemma 40 }
% 27.32/3.88 meet(complement(composition(X, Z)), join(meet(composition(X, Y), complement(composition(X, Z))), join(composition(X, Y), composition(X, Z))))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(meet(composition(X, Y), complement(composition(X, Z))), join(composition(X, Z), composition(X, Y))))
% 27.32/3.88 = { by lemma 32 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(meet(composition(X, Y), complement(composition(X, Z))), join(composition(X, Z), complement(complement(composition(X, Y))))))
% 27.32/3.88 = { by lemma 32 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(meet(composition(X, Y), complement(composition(X, Z))), join(complement(complement(composition(X, Z))), complement(complement(composition(X, Y))))))
% 27.32/3.88 = { by lemma 36 R->L }
% 27.32/3.88 meet(complement(composition(X, Z)), join(meet(composition(X, Y), complement(composition(X, Z))), complement(meet(complement(composition(X, Z)), complement(composition(X, Y))))))
% 27.32/3.88 = { by lemma 29 R->L }
% 27.32/3.88 meet(join(meet(composition(X, Y), complement(composition(X, Z))), meet(complement(composition(X, Z)), complement(composition(X, Y)))), join(meet(composition(X, Y), complement(composition(X, Z))), complement(meet(complement(composition(X, Z)), complement(composition(X, Y))))))
% 27.32/3.88 = { by lemma 42 }
% 27.32/3.88 meet(composition(X, Y), complement(composition(X, Z)))
% 27.32/3.88
% 27.32/3.88 Lemma 45: join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, Y), complement(composition(X, Z)))) = meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))).
% 27.32/3.88 Proof:
% 27.32/3.88 join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, Y), complement(composition(X, Z))))
% 27.32/3.88 = { by lemma 44 R->L }
% 27.32/3.88 join(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))
% 27.32/3.88 = { by lemma 32 R->L }
% 27.32/3.88 join(complement(complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))
% 27.32/3.88 = { by lemma 19 R->L }
% 27.32/3.88 join(complement(join(complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))
% 27.32/3.88 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.88 join(meet(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))
% 27.32/3.88 = { by lemma 25 R->L }
% 27.32/3.88 join(zero, join(meet(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), meet(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))))
% 27.32/3.88 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 27.32/3.88 join(zero, join(meet(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), complement(join(complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))))))
% 27.32/3.88 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 27.32/3.88 join(zero, join(complement(join(complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))))), complement(join(complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))))))))
% 27.32/3.88 = { by lemma 19 }
% 27.32/3.88 join(zero, complement(join(complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))), complement(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))))))
% 27.32/3.88 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 27.32/3.88 join(zero, meet(meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z))), meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))))
% 27.32/3.88 = { by lemma 24 }
% 27.32/3.88 meet(composition(X, meet(Y, complement(Z))), complement(composition(X, Z)))
% 27.32/3.88
% 27.32/3.88 Goal 1 (goals_14): tuple(join(meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))), meet(composition(sk1, sk2), complement(composition(sk1, sk3)))), join(meet(composition(sk1, sk2), complement(composition(sk1, sk3))), meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))))) = tuple(meet(composition(sk1, sk2), complement(composition(sk1, sk3))), meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3)))).
% 27.32/3.88 Proof:
% 27.32/3.88 tuple(join(meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))), meet(composition(sk1, sk2), complement(composition(sk1, sk3)))), join(meet(composition(sk1, sk2), complement(composition(sk1, sk3))), meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3)))))
% 27.32/3.88 = { by axiom 3 (maddux1_join_commutativity_1) }
% 27.32/3.88 tuple(join(meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))), meet(composition(sk1, sk2), complement(composition(sk1, sk3)))), join(meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))), meet(composition(sk1, sk2), complement(composition(sk1, sk3)))))
% 27.32/3.88 = { by lemma 45 }
% 27.32/3.88 tuple(join(meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))), meet(composition(sk1, sk2), complement(composition(sk1, sk3)))), meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))))
% 27.32/3.88 = { by lemma 45 }
% 27.32/3.88 tuple(meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))), meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))))
% 27.32/3.88 = { by lemma 44 }
% 27.32/3.88 tuple(meet(composition(sk1, sk2), complement(composition(sk1, sk3))), meet(composition(sk1, meet(sk2, complement(sk3))), complement(composition(sk1, sk3))))
% 27.32/3.88 % SZS output end Proof
% 27.32/3.88
% 27.32/3.88 RESULT: Unsatisfiable (the axioms are contradictory).
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