%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL026+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:33:16 PM UTC 2026
% Result : Theorem 16.47s 2.56s
% Output : Proof 18.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL026+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 22:56:15 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.47/2.56 Command-line arguments: --flatten --complete-subsets
% 16.47/2.56
% 16.47/2.56 % SZS status Theorem
% 16.47/2.56
% 17.18/2.70 % SZS output start Proof
% 17.91/2.70 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 17.91/2.70 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 17.91/2.70 Axiom 3 (goals): join(x0, one) = one.
% 17.91/2.70 Axiom 4 (composition_identity): composition(X, one) = X.
% 17.91/2.70 Axiom 5 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 17.91/2.70 Axiom 6 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 17.91/2.70 Axiom 7 (def_zero): zero = meet(X, complement(X)).
% 17.91/2.70 Axiom 8 (def_top): top = join(X, complement(X)).
% 17.91/2.70 Axiom 9 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 17.91/2.70 Axiom 10 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 17.91/2.70 Axiom 11 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 17.91/2.70 Axiom 12 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 17.91/2.70 Axiom 13 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 17.91/2.70 Axiom 14 (modular_law_1): join(meet(composition(X, Y), Z), meet(composition(X, meet(Y, composition(converse(X), Z))), Z)) = meet(composition(X, meet(Y, composition(converse(X), Z))), Z).
% 17.91/2.70
% 17.91/2.70 Lemma 15: complement(top) = zero.
% 17.91/2.70 Proof:
% 17.91/2.70 complement(top)
% 17.91/2.70 = { by axiom 8 (def_top) }
% 17.91/2.70 complement(join(complement(X), complement(complement(X))))
% 17.91/2.70 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.70 meet(X, complement(X))
% 17.91/2.70 = { by axiom 7 (def_zero) R->L }
% 17.91/2.70 zero
% 17.91/2.70
% 17.91/2.70 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 17.91/2.70 Proof:
% 17.91/2.70 join(X, join(Y, complement(X)))
% 17.91/2.70 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.70 join(X, join(complement(X), Y))
% 17.91/2.70 = { by axiom 9 (maddux2_join_associativity) }
% 17.91/2.70 join(join(X, complement(X)), Y)
% 17.91/2.70 = { by axiom 8 (def_top) R->L }
% 17.91/2.70 join(top, Y)
% 17.91/2.70 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.71 join(Y, top)
% 17.91/2.71
% 17.91/2.71 Lemma 17: composition(X, join(x0, one)) = X.
% 17.91/2.71 Proof:
% 17.91/2.71 composition(X, join(x0, one))
% 17.91/2.71 = { by axiom 3 (goals) }
% 17.91/2.71 composition(X, one)
% 17.91/2.71 = { by axiom 4 (composition_identity) }
% 17.91/2.71 X
% 17.91/2.71
% 17.91/2.71 Lemma 18: composition(converse(join(x0, one)), X) = X.
% 17.91/2.71 Proof:
% 17.91/2.71 composition(converse(join(x0, one)), X)
% 17.91/2.71 = { by axiom 1 (converse_idempotence) R->L }
% 17.91/2.71 composition(converse(join(x0, one)), converse(converse(X)))
% 17.91/2.71 = { by axiom 6 (converse_multiplicativity) R->L }
% 17.91/2.71 converse(composition(converse(X), join(x0, one)))
% 17.91/2.71 = { by lemma 17 }
% 17.91/2.71 converse(converse(X))
% 17.91/2.71 = { by axiom 1 (converse_idempotence) }
% 17.91/2.71 X
% 17.91/2.71
% 17.91/2.71 Lemma 19: converse(join(x0, one)) = join(x0, one).
% 17.91/2.71 Proof:
% 17.91/2.71 converse(join(x0, one))
% 17.91/2.71 = { by lemma 17 R->L }
% 17.91/2.71 composition(converse(join(x0, one)), join(x0, one))
% 17.91/2.71 = { by lemma 18 }
% 17.91/2.71 join(x0, one)
% 17.91/2.71
% 17.91/2.71 Lemma 20: composition(join(x0, one), X) = X.
% 17.91/2.71 Proof:
% 17.91/2.71 composition(join(x0, one), X)
% 17.91/2.71 = { by lemma 19 R->L }
% 17.91/2.71 composition(converse(join(x0, one)), X)
% 17.91/2.71 = { by lemma 18 }
% 17.91/2.71 X
% 17.91/2.71
% 17.91/2.71 Lemma 21: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 17.91/2.71 Proof:
% 17.91/2.71 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 17.91/2.71 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.71 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 17.91/2.71 = { by axiom 12 (converse_cancellativity) }
% 17.91/2.71 complement(X)
% 17.91/2.71
% 17.91/2.71 Lemma 22: join(complement(X), complement(X)) = complement(X).
% 17.91/2.71 Proof:
% 17.91/2.71 join(complement(X), complement(X))
% 17.91/2.71 = { by lemma 18 R->L }
% 17.91/2.71 join(complement(X), composition(converse(join(x0, one)), complement(X)))
% 17.91/2.71 = { by lemma 20 R->L }
% 17.91/2.71 join(complement(X), composition(converse(join(x0, one)), complement(composition(join(x0, one), X))))
% 17.91/2.71 = { by lemma 21 }
% 17.91/2.71 complement(X)
% 17.91/2.71
% 17.91/2.71 Lemma 23: join(top, complement(X)) = top.
% 17.91/2.71 Proof:
% 17.91/2.71 join(top, complement(X))
% 17.91/2.71 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.71 join(complement(X), top)
% 17.91/2.71 = { by lemma 16 R->L }
% 17.91/2.71 join(X, join(complement(X), complement(X)))
% 17.91/2.71 = { by lemma 22 }
% 17.91/2.71 join(X, complement(X))
% 17.91/2.71 = { by axiom 8 (def_top) R->L }
% 17.91/2.71 top
% 17.91/2.71
% 17.91/2.71 Lemma 24: join(Y, top) = join(X, top).
% 17.91/2.71 Proof:
% 17.91/2.71 join(Y, top)
% 17.91/2.71 = { by lemma 23 R->L }
% 17.91/2.71 join(Y, join(top, complement(Y)))
% 17.91/2.71 = { by lemma 16 }
% 17.91/2.71 join(top, top)
% 17.91/2.71 = { by lemma 16 R->L }
% 17.91/2.71 join(X, join(top, complement(X)))
% 17.91/2.71 = { by lemma 23 }
% 17.91/2.71 join(X, top)
% 17.91/2.71
% 17.91/2.71 Lemma 25: join(X, top) = top.
% 17.91/2.71 Proof:
% 17.91/2.71 join(X, top)
% 17.91/2.71 = { by lemma 24 }
% 17.91/2.71 join(zero, top)
% 17.91/2.71 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.71 join(top, zero)
% 17.91/2.71 = { by lemma 15 R->L }
% 17.91/2.71 join(top, complement(top))
% 17.91/2.71 = { by axiom 8 (def_top) R->L }
% 17.91/2.71 top
% 17.91/2.71
% 17.91/2.71 Lemma 26: join(X, join(complement(X), Y)) = top.
% 17.91/2.71 Proof:
% 17.91/2.71 join(X, join(complement(X), Y))
% 17.91/2.71 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.71 join(X, join(Y, complement(X)))
% 17.91/2.71 = { by lemma 16 }
% 17.91/2.71 join(Y, top)
% 17.91/2.71 = { by lemma 24 R->L }
% 17.91/2.71 join(Z, top)
% 17.91/2.71 = { by lemma 25 }
% 17.91/2.71 top
% 17.91/2.71
% 17.91/2.71 Lemma 27: join(X, converse(top)) = top.
% 17.91/2.71 Proof:
% 17.91/2.71 join(X, converse(top))
% 17.91/2.71 = { by axiom 8 (def_top) }
% 17.91/2.71 join(X, converse(join(converse(complement(X)), complement(converse(complement(X))))))
% 17.91/2.71 = { by axiom 5 (converse_additivity) }
% 17.91/2.71 join(X, join(converse(converse(complement(X))), converse(complement(converse(complement(X))))))
% 17.91/2.71 = { by axiom 1 (converse_idempotence) }
% 17.91/2.71 join(X, join(complement(X), converse(complement(converse(complement(X))))))
% 17.91/2.71 = { by lemma 26 }
% 17.91/2.71 top
% 17.91/2.71
% 17.91/2.71 Lemma 28: converse(top) = top.
% 17.91/2.71 Proof:
% 17.91/2.71 converse(top)
% 17.91/2.71 = { by lemma 27 R->L }
% 17.91/2.71 converse(join(X, converse(top)))
% 17.91/2.71 = { by axiom 5 (converse_additivity) }
% 17.91/2.71 join(converse(X), converse(converse(top)))
% 17.91/2.71 = { by axiom 1 (converse_idempotence) }
% 17.91/2.71 join(converse(X), top)
% 17.91/2.71 = { by lemma 25 }
% 17.91/2.71 top
% 17.91/2.71
% 17.91/2.71 Lemma 29: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 17.91/2.71 Proof:
% 17.91/2.71 join(meet(X, Y), complement(join(complement(X), Y)))
% 17.91/2.71 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.71 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 17.91/2.71 = { by axiom 13 (maddux3_a_kind_of_de_Morgan) R->L }
% 17.91/2.71 X
% 17.91/2.71
% 17.91/2.71 Lemma 30: join(zero, meet(X, X)) = X.
% 17.91/2.71 Proof:
% 17.91/2.71 join(zero, meet(X, X))
% 17.91/2.71 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.71 join(zero, complement(join(complement(X), complement(X))))
% 17.91/2.71 = { by axiom 7 (def_zero) }
% 17.91/2.71 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 17.91/2.71 = { by lemma 29 }
% 17.91/2.71 X
% 17.91/2.71
% 17.91/2.71 Lemma 31: join(zero, join(X, complement(complement(Y)))) = join(X, Y).
% 17.91/2.71 Proof:
% 17.91/2.71 join(zero, join(X, complement(complement(Y))))
% 17.91/2.71 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.71 join(zero, join(complement(complement(Y)), X))
% 17.91/2.71 = { by lemma 22 R->L }
% 17.91/2.71 join(zero, join(complement(join(complement(Y), complement(Y))), X))
% 17.91/2.71 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.71 join(zero, join(meet(Y, Y), X))
% 17.91/2.71 = { by axiom 9 (maddux2_join_associativity) }
% 17.91/2.71 join(join(zero, meet(Y, Y)), X)
% 17.91/2.71 = { by lemma 30 }
% 17.91/2.71 join(Y, X)
% 17.91/2.71 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.71 join(X, Y)
% 17.91/2.71
% 17.91/2.71 Lemma 32: join(zero, complement(complement(X))) = X.
% 17.91/2.71 Proof:
% 17.91/2.71 join(zero, complement(complement(X)))
% 17.91/2.71 = { by axiom 7 (def_zero) }
% 17.91/2.71 join(meet(X, complement(X)), complement(complement(X)))
% 17.91/2.71 = { by lemma 22 R->L }
% 17.91/2.71 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 17.91/2.71 = { by lemma 29 }
% 17.91/2.71 X
% 17.91/2.71
% 17.91/2.71 Lemma 33: meet(Y, X) = meet(X, Y).
% 17.91/2.71 Proof:
% 17.91/2.71 meet(Y, X)
% 17.91/2.71 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.71 complement(join(complement(Y), complement(X)))
% 17.91/2.71 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.71 complement(join(complement(X), complement(Y)))
% 17.91/2.71 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.71 meet(X, Y)
% 17.91/2.71
% 17.91/2.71 Lemma 34: complement(join(zero, complement(X))) = meet(X, top).
% 17.91/2.72 Proof:
% 17.91/2.72 complement(join(zero, complement(X)))
% 17.91/2.72 = { by lemma 15 R->L }
% 17.91/2.72 complement(join(complement(top), complement(X)))
% 17.91/2.72 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.72 meet(top, X)
% 17.91/2.72 = { by lemma 33 R->L }
% 17.91/2.72 meet(X, top)
% 17.91/2.72
% 17.91/2.72 Lemma 35: join(zero, meet(X, top)) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 join(zero, meet(X, top))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 join(meet(X, top), zero)
% 17.91/2.72 = { by lemma 15 R->L }
% 17.91/2.72 join(meet(X, top), complement(top))
% 17.91/2.72 = { by lemma 28 R->L }
% 17.91/2.72 join(meet(X, converse(top)), complement(top))
% 17.91/2.72 = { by lemma 27 R->L }
% 17.91/2.72 join(meet(X, converse(top)), complement(join(complement(X), converse(top))))
% 17.91/2.72 = { by lemma 29 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 36: join(zero, meet(top, X)) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 join(zero, meet(top, X))
% 17.91/2.72 = { by lemma 33 }
% 17.91/2.72 join(zero, meet(X, top))
% 17.91/2.72 = { by lemma 35 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 37: join(zero, complement(X)) = complement(X).
% 17.91/2.72 Proof:
% 17.91/2.72 join(zero, complement(X))
% 17.91/2.72 = { by lemma 32 R->L }
% 17.91/2.72 join(zero, complement(join(zero, complement(complement(X)))))
% 17.91/2.72 = { by lemma 34 }
% 17.91/2.72 join(zero, meet(complement(X), top))
% 17.91/2.72 = { by lemma 33 R->L }
% 17.91/2.72 join(zero, meet(top, complement(X)))
% 17.91/2.72 = { by lemma 36 }
% 17.91/2.72 complement(X)
% 17.91/2.72
% 17.91/2.72 Lemma 38: join(X, zero) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 join(X, zero)
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 join(zero, X)
% 17.91/2.72 = { by lemma 31 R->L }
% 17.91/2.72 join(zero, join(zero, complement(complement(X))))
% 17.91/2.72 = { by lemma 37 }
% 17.91/2.72 join(zero, complement(complement(X)))
% 17.91/2.72 = { by lemma 32 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 39: join(zero, X) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 join(zero, X)
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 join(X, zero)
% 17.91/2.72 = { by lemma 38 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 40: complement(complement(X)) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 complement(complement(X))
% 17.91/2.72 = { by lemma 37 R->L }
% 17.91/2.72 join(zero, complement(complement(X)))
% 17.91/2.72 = { by lemma 32 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 41: meet(X, top) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 meet(X, top)
% 17.91/2.72 = { by lemma 34 R->L }
% 17.91/2.72 complement(join(zero, complement(X)))
% 17.91/2.72 = { by lemma 37 R->L }
% 17.91/2.72 join(zero, complement(join(zero, complement(X))))
% 17.91/2.72 = { by lemma 34 }
% 17.91/2.72 join(zero, meet(X, top))
% 17.91/2.72 = { by lemma 35 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 42: join(meet(X, Y), meet(X, complement(Y))) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 join(meet(X, Y), meet(X, complement(Y)))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 join(meet(X, complement(Y)), meet(X, Y))
% 17.91/2.72 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.72 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 17.91/2.72 = { by lemma 29 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 43: meet(X, zero) = zero.
% 17.91/2.72 Proof:
% 17.91/2.72 meet(X, zero)
% 17.91/2.72 = { by lemma 33 }
% 17.91/2.72 meet(zero, X)
% 17.91/2.72 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.72 complement(join(complement(zero), complement(X)))
% 17.91/2.72 = { by lemma 36 R->L }
% 17.91/2.72 complement(join(join(zero, meet(top, complement(zero))), complement(X)))
% 17.91/2.72 = { by lemma 15 R->L }
% 17.91/2.72 complement(join(join(zero, meet(top, complement(complement(top)))), complement(X)))
% 17.91/2.72 = { by axiom 7 (def_zero) }
% 17.91/2.72 complement(join(join(meet(top, complement(top)), meet(top, complement(complement(top)))), complement(X)))
% 17.91/2.72 = { by lemma 42 }
% 17.91/2.72 complement(join(top, complement(X)))
% 17.91/2.72 = { by lemma 23 }
% 17.91/2.72 complement(top)
% 17.91/2.72 = { by lemma 15 }
% 17.91/2.72 zero
% 17.91/2.72
% 17.91/2.72 Lemma 44: meet(zero, X) = zero.
% 17.91/2.72 Proof:
% 17.91/2.72 meet(zero, X)
% 17.91/2.72 = { by lemma 33 }
% 17.91/2.72 meet(X, zero)
% 17.91/2.72 = { by lemma 43 }
% 17.91/2.72 zero
% 17.91/2.72
% 17.91/2.72 Lemma 45: composition(join(join(x0, one), Y), X) = join(X, composition(Y, X)).
% 17.91/2.72 Proof:
% 17.91/2.72 composition(join(join(x0, one), Y), X)
% 17.91/2.72 = { by lemma 19 R->L }
% 17.91/2.72 composition(join(converse(join(x0, one)), Y), X)
% 17.91/2.72 = { by axiom 11 (composition_distributivity) }
% 17.91/2.72 join(composition(converse(join(x0, one)), X), composition(Y, X))
% 17.91/2.72 = { by lemma 18 }
% 17.91/2.72 join(X, composition(Y, X))
% 17.91/2.72
% 17.91/2.72 Lemma 46: composition(top, zero) = zero.
% 17.91/2.72 Proof:
% 17.91/2.72 composition(top, zero)
% 17.91/2.72 = { by lemma 28 R->L }
% 17.91/2.72 composition(converse(top), zero)
% 17.91/2.72 = { by lemma 39 R->L }
% 17.91/2.72 join(zero, composition(converse(top), zero))
% 17.91/2.72 = { by lemma 15 R->L }
% 17.91/2.72 join(complement(top), composition(converse(top), zero))
% 17.91/2.72 = { by lemma 15 R->L }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(top)))
% 17.91/2.72 = { by lemma 25 R->L }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(join(composition(top, top), top))))
% 17.91/2.72 = { by lemma 39 R->L }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(join(zero, join(composition(top, top), top)))))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(join(zero, join(top, composition(top, top))))))
% 17.91/2.72 = { by lemma 28 R->L }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(join(zero, join(top, composition(converse(top), top))))))
% 17.91/2.72 = { by lemma 45 R->L }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(join(zero, composition(join(join(x0, one), converse(top)), top)))))
% 17.91/2.72 = { by lemma 27 }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(join(zero, composition(top, top)))))
% 17.91/2.72 = { by lemma 39 }
% 17.91/2.72 join(complement(top), composition(converse(top), complement(composition(top, top))))
% 17.91/2.72 = { by lemma 21 }
% 17.91/2.72 complement(top)
% 17.91/2.72 = { by lemma 15 }
% 17.91/2.72 zero
% 17.91/2.72
% 17.91/2.72 Lemma 47: composition(X, zero) = zero.
% 17.91/2.72 Proof:
% 17.91/2.72 composition(X, zero)
% 17.91/2.72 = { by lemma 39 R->L }
% 17.91/2.72 join(zero, composition(X, zero))
% 17.91/2.72 = { by lemma 46 R->L }
% 17.91/2.72 join(composition(top, zero), composition(X, zero))
% 17.91/2.72 = { by axiom 11 (composition_distributivity) R->L }
% 17.91/2.72 composition(join(top, X), zero)
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 composition(join(X, top), zero)
% 17.91/2.72 = { by lemma 24 R->L }
% 17.91/2.72 composition(join(Y, top), zero)
% 17.91/2.72 = { by lemma 25 }
% 17.91/2.72 composition(top, zero)
% 17.91/2.72 = { by lemma 46 }
% 17.91/2.72 zero
% 17.91/2.72
% 17.91/2.72 Lemma 48: join(X, complement(complement(X))) = X.
% 17.91/2.72 Proof:
% 17.91/2.72 join(X, complement(complement(X)))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 join(complement(complement(X)), X)
% 17.91/2.72 = { by lemma 31 R->L }
% 17.91/2.72 join(zero, join(complement(complement(X)), complement(complement(X))))
% 17.91/2.72 = { by lemma 22 }
% 17.91/2.72 join(zero, complement(complement(X)))
% 17.91/2.72 = { by lemma 32 }
% 17.91/2.72 X
% 17.91/2.72
% 17.91/2.72 Lemma 49: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 17.91/2.72 Proof:
% 17.91/2.72 join(Y, join(X, Z))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 join(join(X, Z), Y)
% 17.91/2.72 = { by axiom 9 (maddux2_join_associativity) R->L }
% 17.91/2.72 join(X, join(Z, Y))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.72 join(X, join(Y, Z))
% 17.91/2.72
% 17.91/2.72 Lemma 50: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 17.91/2.72 Proof:
% 17.91/2.72 meet(X, join(complement(Y), complement(Z)))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 meet(X, join(complement(Z), complement(Y)))
% 17.91/2.72 = { by lemma 33 }
% 17.91/2.72 meet(join(complement(Z), complement(Y)), X)
% 17.91/2.72 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.72 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 17.91/2.72 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.72 complement(join(meet(Z, Y), complement(X)))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.72 complement(join(complement(X), meet(Z, Y)))
% 17.91/2.72 = { by lemma 33 R->L }
% 17.91/2.72 complement(join(complement(X), meet(Y, Z)))
% 17.91/2.72
% 17.91/2.72 Lemma 51: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 17.91/2.72 Proof:
% 17.91/2.72 complement(join(X, complement(Y)))
% 17.91/2.72 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.72 complement(join(complement(Y), X))
% 17.91/2.72 = { by lemma 41 R->L }
% 17.91/2.72 complement(join(complement(Y), meet(X, top)))
% 17.91/2.72 = { by lemma 33 R->L }
% 17.91/2.72 complement(join(complement(Y), meet(top, X)))
% 17.91/2.72 = { by lemma 50 R->L }
% 17.91/2.72 meet(Y, join(complement(top), complement(X)))
% 17.91/2.72 = { by lemma 15 }
% 17.91/2.73 meet(Y, join(zero, complement(X)))
% 17.91/2.73 = { by lemma 37 }
% 17.91/2.73 meet(Y, complement(X))
% 17.91/2.73
% 17.91/2.73 Lemma 52: complement(join(complement(X), Y)) = meet(X, complement(Y)).
% 17.91/2.73 Proof:
% 17.91/2.73 complement(join(complement(X), Y))
% 17.91/2.73 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.73 complement(join(Y, complement(X)))
% 17.91/2.73 = { by lemma 51 }
% 17.91/2.73 meet(X, complement(Y))
% 17.91/2.73
% 17.91/2.73 Lemma 53: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 17.91/2.73 Proof:
% 17.91/2.73 complement(meet(X, complement(Y)))
% 17.91/2.73 = { by lemma 39 R->L }
% 17.91/2.73 complement(join(zero, meet(X, complement(Y))))
% 17.91/2.73 = { by lemma 51 R->L }
% 17.91/2.73 complement(join(zero, complement(join(Y, complement(X)))))
% 17.91/2.73 = { by lemma 34 }
% 17.91/2.73 meet(join(Y, complement(X)), top)
% 17.91/2.73 = { by lemma 41 }
% 17.91/2.73 join(Y, complement(X))
% 17.91/2.73
% 17.91/2.73 Lemma 54: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 17.91/2.73 Proof:
% 17.91/2.73 complement(meet(complement(X), Y))
% 17.91/2.73 = { by lemma 33 }
% 17.91/2.73 complement(meet(Y, complement(X)))
% 17.91/2.73 = { by lemma 53 }
% 17.91/2.73 join(X, complement(Y))
% 17.91/2.73
% 17.91/2.73 Lemma 55: meet(complement(X), complement(Y)) = complement(join(X, Y)).
% 17.91/2.73 Proof:
% 17.91/2.73 meet(complement(X), complement(Y))
% 17.91/2.73 = { by lemma 33 }
% 17.91/2.73 meet(complement(Y), complement(X))
% 17.91/2.73 = { by lemma 37 R->L }
% 17.91/2.73 meet(join(zero, complement(Y)), complement(X))
% 17.91/2.73 = { by lemma 51 R->L }
% 17.91/2.73 complement(join(X, complement(join(zero, complement(Y)))))
% 17.91/2.73 = { by lemma 34 }
% 17.91/2.73 complement(join(X, meet(Y, top)))
% 17.91/2.73 = { by lemma 41 }
% 17.91/2.73 complement(join(X, Y))
% 17.91/2.73
% 17.91/2.73 Lemma 56: join(X, complement(meet(X, Y))) = top.
% 17.91/2.73 Proof:
% 17.91/2.73 join(X, complement(meet(X, Y)))
% 17.91/2.73 = { by lemma 48 R->L }
% 17.91/2.73 join(X, complement(join(meet(X, Y), complement(complement(meet(X, Y))))))
% 17.91/2.73 = { by lemma 40 }
% 17.91/2.73 join(X, complement(join(meet(X, Y), meet(X, Y))))
% 17.91/2.73 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.73 join(X, complement(join(complement(join(complement(X), complement(Y))), meet(X, Y))))
% 17.91/2.73 = { by lemma 37 R->L }
% 17.91/2.73 join(X, join(zero, complement(join(complement(join(complement(X), complement(Y))), meet(X, Y)))))
% 17.91/2.73 = { by lemma 50 R->L }
% 17.91/2.73 join(X, join(zero, meet(join(complement(X), complement(Y)), join(complement(X), complement(Y)))))
% 17.91/2.73 = { by lemma 30 }
% 17.91/2.73 join(X, join(complement(X), complement(Y)))
% 17.91/2.73 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.73 join(X, join(complement(Y), complement(X)))
% 17.91/2.73 = { by lemma 16 }
% 17.91/2.73 join(complement(Y), top)
% 17.91/2.73 = { by lemma 25 }
% 17.91/2.73 top
% 17.91/2.73
% 17.91/2.73 Lemma 57: join(X, complement(meet(Y, X))) = top.
% 17.91/2.73 Proof:
% 17.91/2.73 join(X, complement(meet(Y, X)))
% 17.91/2.73 = { by lemma 33 }
% 17.91/2.73 join(X, complement(meet(X, Y)))
% 17.91/2.73 = { by lemma 56 }
% 17.91/2.73 top
% 17.91/2.73
% 17.91/2.73 Lemma 58: meet(X, join(X, complement(Y))) = X.
% 17.91/2.73 Proof:
% 17.91/2.73 meet(X, join(X, complement(Y)))
% 17.91/2.73 = { by lemma 53 R->L }
% 17.91/2.73 meet(X, complement(meet(Y, complement(X))))
% 17.91/2.73 = { by lemma 52 R->L }
% 17.91/2.73 complement(join(complement(X), meet(Y, complement(X))))
% 17.91/2.73 = { by lemma 37 R->L }
% 17.91/2.73 join(zero, complement(join(complement(X), meet(Y, complement(X)))))
% 17.91/2.73 = { by lemma 15 R->L }
% 17.91/2.73 join(complement(top), complement(join(complement(X), meet(Y, complement(X)))))
% 17.91/2.73 = { by lemma 56 R->L }
% 17.91/2.73 join(complement(join(complement(X), complement(meet(complement(X), Y)))), complement(join(complement(X), meet(Y, complement(X)))))
% 17.91/2.73 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.73 join(meet(X, meet(complement(X), Y)), complement(join(complement(X), meet(Y, complement(X)))))
% 17.91/2.73 = { by lemma 33 R->L }
% 17.91/2.73 join(meet(X, meet(Y, complement(X))), complement(join(complement(X), meet(Y, complement(X)))))
% 17.91/2.73 = { by lemma 29 }
% 17.91/2.73 X
% 17.91/2.73
% 17.91/2.73 Lemma 59: composition(converse(X), complement(composition(X, top))) = zero.
% 17.91/2.73 Proof:
% 17.91/2.73 composition(converse(X), complement(composition(X, top)))
% 17.91/2.73 = { by lemma 39 R->L }
% 17.91/2.73 join(zero, composition(converse(X), complement(composition(X, top))))
% 17.91/2.73 = { by lemma 15 R->L }
% 17.91/2.73 join(complement(top), composition(converse(X), complement(composition(X, top))))
% 17.91/2.73 = { by lemma 21 }
% 17.91/2.73 complement(top)
% 17.91/2.73 = { by lemma 15 }
% 17.91/2.73 zero
% 17.91/2.73
% 17.91/2.73 Lemma 60: join(meet(X, Y), meet(Y, complement(X))) = Y.
% 17.91/2.73 Proof:
% 17.91/2.73 join(meet(X, Y), meet(Y, complement(X)))
% 17.91/2.73 = { by lemma 33 }
% 17.91/2.73 join(meet(Y, X), meet(Y, complement(X)))
% 17.91/2.73 = { by lemma 42 }
% 17.91/2.73 Y
% 17.91/2.73
% 17.91/2.73 Lemma 61: meet(composition(X, Y), complement(composition(X, top))) = zero.
% 17.91/2.73 Proof:
% 17.91/2.73 meet(composition(X, Y), complement(composition(X, top)))
% 17.91/2.73 = { by lemma 38 R->L }
% 17.91/2.73 join(meet(composition(X, Y), complement(composition(X, top))), zero)
% 17.91/2.73 = { by lemma 44 R->L }
% 17.91/2.73 join(meet(composition(X, Y), complement(composition(X, top))), meet(zero, complement(composition(X, top))))
% 17.91/2.73 = { by lemma 47 R->L }
% 17.91/2.73 join(meet(composition(X, Y), complement(composition(X, top))), meet(composition(X, zero), complement(composition(X, top))))
% 17.91/2.73 = { by lemma 43 R->L }
% 17.91/2.73 join(meet(composition(X, Y), complement(composition(X, top))), meet(composition(X, meet(Y, zero)), complement(composition(X, top))))
% 17.91/2.73 = { by lemma 59 R->L }
% 17.91/2.73 join(meet(composition(X, Y), complement(composition(X, top))), meet(composition(X, meet(Y, composition(converse(X), complement(composition(X, top))))), complement(composition(X, top))))
% 17.91/2.73 = { by axiom 14 (modular_law_1) }
% 17.91/2.73 meet(composition(X, meet(Y, composition(converse(X), complement(composition(X, top))))), complement(composition(X, top)))
% 17.91/2.73 = { by lemma 59 }
% 17.91/2.73 meet(composition(X, meet(Y, zero)), complement(composition(X, top)))
% 17.91/2.73 = { by lemma 43 }
% 17.91/2.73 meet(composition(X, zero), complement(composition(X, top)))
% 17.91/2.73 = { by lemma 47 }
% 17.91/2.73 meet(zero, complement(composition(X, top)))
% 17.91/2.73 = { by lemma 44 }
% 17.91/2.73 zero
% 17.91/2.73
% 17.91/2.73 Lemma 62: join(meet(composition(x0, top), X), composition(x0, X)) = meet(composition(x0, top), X).
% 17.91/2.73 Proof:
% 17.91/2.73 join(meet(composition(x0, top), X), composition(x0, X))
% 17.91/2.73 = { by lemma 29 R->L }
% 17.91/2.73 join(meet(composition(x0, top), X), join(meet(composition(x0, X), complement(composition(x0, top))), complement(join(complement(composition(x0, X)), complement(composition(x0, top))))))
% 17.91/2.73 = { by lemma 61 }
% 17.91/2.73 join(meet(composition(x0, top), X), join(zero, complement(join(complement(composition(x0, X)), complement(composition(x0, top))))))
% 17.91/2.73 = { by lemma 37 }
% 17.91/2.73 join(meet(composition(x0, top), X), complement(join(complement(composition(x0, X)), complement(composition(x0, top)))))
% 17.91/2.74 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, X), composition(x0, top)))
% 17.91/2.74 = { by lemma 33 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), composition(x0, X)))
% 17.91/2.74 = { by lemma 29 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(meet(composition(x0, X), complement(X)), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by lemma 51 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(join(X, complement(composition(x0, X)))), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by lemma 20 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(join(composition(join(x0, one), X), complement(composition(x0, X)))), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by axiom 11 (composition_distributivity) }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(join(join(composition(x0, X), composition(one, X)), complement(composition(x0, X)))), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by axiom 3 (goals) R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(join(join(composition(x0, X), composition(join(x0, one), X)), complement(composition(x0, X)))), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by lemma 20 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(join(join(composition(x0, X), X), complement(composition(x0, X)))), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by axiom 9 (maddux2_join_associativity) R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(join(composition(x0, X), join(X, complement(composition(x0, X))))), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(join(composition(x0, X), join(complement(composition(x0, X)), X))), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by lemma 26 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(complement(top), complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by lemma 15 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), join(zero, complement(join(complement(composition(x0, X)), complement(X))))))
% 17.91/2.74 = { by lemma 37 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), complement(join(complement(composition(x0, X)), complement(X)))))
% 17.91/2.74 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, top), meet(composition(x0, X), X)))
% 17.91/2.74 = { by lemma 41 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(meet(composition(x0, top), top), meet(composition(x0, X), X)))
% 17.91/2.74 = { by lemma 34 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(complement(join(zero, complement(composition(x0, top)))), meet(composition(x0, X), X)))
% 17.91/2.74 = { by lemma 33 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(meet(composition(x0, X), X), complement(join(zero, complement(composition(x0, top))))))
% 17.91/2.74 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(complement(join(complement(composition(x0, X)), complement(X))), complement(join(zero, complement(composition(x0, top))))))
% 17.91/2.74 = { by lemma 55 }
% 17.91/2.74 join(meet(composition(x0, top), X), complement(join(join(complement(composition(x0, X)), complement(X)), join(zero, complement(composition(x0, top))))))
% 17.91/2.74 = { by axiom 9 (maddux2_join_associativity) R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), complement(join(complement(composition(x0, X)), join(complement(X), join(zero, complement(composition(x0, top)))))))
% 17.91/2.74 = { by lemma 52 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, X), complement(join(complement(X), join(zero, complement(composition(x0, top)))))))
% 17.91/2.74 = { by lemma 52 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, X), meet(X, complement(join(zero, complement(composition(x0, top)))))))
% 17.91/2.74 = { by lemma 34 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, X), meet(X, meet(composition(x0, top), top))))
% 17.91/2.74 = { by lemma 41 }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, X), meet(X, composition(x0, top))))
% 17.91/2.74 = { by lemma 33 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(composition(x0, X), meet(composition(x0, top), X)))
% 17.91/2.74 = { by lemma 33 R->L }
% 17.91/2.74 join(meet(composition(x0, top), X), meet(meet(composition(x0, top), X), composition(x0, X)))
% 17.91/2.74 = { by axiom 10 (maddux4_definiton_of_meet) }
% 17.91/2.74 join(meet(composition(x0, top), X), complement(join(complement(meet(composition(x0, top), X)), complement(composition(x0, X)))))
% 17.91/2.74 = { by lemma 54 R->L }
% 17.91/2.74 complement(meet(complement(meet(composition(x0, top), X)), join(complement(meet(composition(x0, top), X)), complement(composition(x0, X)))))
% 17.91/2.74 = { by lemma 58 }
% 17.91/2.74 complement(complement(meet(composition(x0, top), X)))
% 17.91/2.74 = { by lemma 40 }
% 17.91/2.74 meet(composition(x0, top), X)
% 17.91/2.74
% 17.91/2.74 Goal 1 (goals_1): tuple(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, x1), meet(composition(x0, top), x1))) = tuple(composition(x0, x1), meet(composition(x0, top), x1)).
% 17.91/2.75 Proof:
% 17.91/2.75 tuple(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, x1), meet(composition(x0, top), x1)))
% 17.91/2.75 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.75 tuple(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 39 R->L }
% 17.91/2.75 tuple(join(zero, join(meet(composition(x0, top), x1), composition(x0, x1))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 49 }
% 17.91/2.75 tuple(join(meet(composition(x0, top), x1), join(zero, composition(x0, x1))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 48 R->L }
% 17.91/2.75 tuple(join(meet(composition(x0, top), x1), join(zero, join(composition(x0, x1), complement(complement(composition(x0, x1)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 31 }
% 17.91/2.75 tuple(join(meet(composition(x0, top), x1), join(composition(x0, x1), composition(x0, x1))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 49 R->L }
% 17.91/2.75 tuple(join(composition(x0, x1), join(meet(composition(x0, top), x1), composition(x0, x1))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 41 R->L }
% 17.91/2.75 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), top)), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 57 R->L }
% 17.91/2.75 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), composition(x0, top)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 41 R->L }
% 17.91/2.75 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), meet(composition(x0, top), top)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 34 R->L }
% 17.91/2.75 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, complement(composition(x0, top))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 60 R->L }
% 17.91/2.75 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, join(meet(meet(composition(x0, top), x1), complement(composition(x0, top))), meet(complement(composition(x0, top)), complement(meet(composition(x0, top), x1))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.75 = { by lemma 51 R->L }
% 17.91/2.75 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, join(complement(join(composition(x0, top), complement(meet(composition(x0, top), x1)))), meet(complement(composition(x0, top)), complement(meet(composition(x0, top), x1))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 56 }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, join(complement(top), meet(complement(composition(x0, top)), complement(meet(composition(x0, top), x1))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 15 }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, join(zero, meet(complement(composition(x0, top)), complement(meet(composition(x0, top), x1))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 39 }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, meet(complement(composition(x0, top)), complement(meet(composition(x0, top), x1)))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 55 }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, complement(join(composition(x0, top), meet(composition(x0, top), x1)))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, complement(join(meet(composition(x0, top), x1), composition(x0, top)))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 34 }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), meet(join(meet(composition(x0, top), x1), composition(x0, top)), top)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 41 }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, top))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 41 R->L }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), meet(composition(x0, top), top))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 34 R->L }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), complement(join(zero, complement(composition(x0, top)))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 60 R->L }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), complement(join(zero, join(meet(composition(x0, x1), complement(composition(x0, top))), meet(complement(composition(x0, top)), complement(composition(x0, x1)))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.76 = { by lemma 61 }
% 17.91/2.76 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), complement(join(zero, join(zero, meet(complement(composition(x0, top)), complement(composition(x0, x1)))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 39 }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), complement(join(zero, meet(complement(composition(x0, top)), complement(composition(x0, x1))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 55 }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), complement(join(zero, complement(join(composition(x0, top), composition(x0, x1))))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 34 }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), meet(join(composition(x0, top), composition(x0, x1)), top))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 41 }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(meet(composition(x0, top), x1), join(composition(x0, top), composition(x0, x1)))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 49 R->L }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), join(meet(composition(x0, top), x1), composition(x0, x1)))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(join(meet(composition(x0, top), x1), composition(x0, x1)), composition(x0, top))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 41 R->L }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(join(meet(composition(x0, top), x1), composition(x0, x1)), meet(composition(x0, top), top))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 34 R->L }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(join(zero, complement(composition(x0, top)))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 58 }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, top), complement(join(meet(composition(x0, top), x1), composition(x0, x1)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, top)))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by lemma 57 R->L }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, join(x1, complement(meet(composition(x0, top), x1))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by axiom 1 (converse_idempotence) R->L }
% 17.91/2.77 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, join(x1, converse(converse(complement(meet(composition(x0, top), x1))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.77 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, join(converse(converse(complement(meet(composition(x0, top), x1)))), x1))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 1 (converse_idempotence) R->L }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, join(converse(converse(complement(meet(composition(x0, top), x1)))), converse(converse(x1))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 5 (converse_additivity) R->L }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, converse(join(converse(complement(meet(composition(x0, top), x1))), converse(x1))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 1 (converse_idempotence) R->L }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(converse(converse(x0)), converse(join(converse(complement(meet(composition(x0, top), x1))), converse(x1))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 6 (converse_multiplicativity) R->L }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), converse(composition(join(converse(complement(meet(composition(x0, top), x1))), converse(x1)), converse(x0)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), converse(composition(join(converse(x1), converse(complement(meet(composition(x0, top), x1)))), converse(x0)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 11 (composition_distributivity) }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), converse(join(composition(converse(x1), converse(x0)), composition(converse(complement(meet(composition(x0, top), x1))), converse(x0))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 6 (converse_multiplicativity) R->L }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), converse(join(converse(composition(x0, x1)), composition(converse(complement(meet(composition(x0, top), x1))), converse(x0))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 5 (converse_additivity) }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), join(converse(converse(composition(x0, x1))), converse(composition(converse(complement(meet(composition(x0, top), x1))), converse(x0))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 1 (converse_idempotence) }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), join(composition(x0, x1), converse(composition(converse(complement(meet(composition(x0, top), x1))), converse(x0))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 6 (converse_multiplicativity) }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), join(composition(x0, x1), composition(converse(converse(x0)), converse(converse(complement(meet(composition(x0, top), x1))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.78 = { by axiom 1 (converse_idempotence) }
% 17.91/2.78 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), join(composition(x0, x1), composition(x0, converse(converse(complement(meet(composition(x0, top), x1))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by axiom 1 (converse_idempotence) }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), join(composition(x0, x1), composition(x0, complement(meet(composition(x0, top), x1))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 62 R->L }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), join(composition(x0, x1), composition(x0, complement(join(meet(composition(x0, top), x1), composition(x0, x1)))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), join(composition(x0, complement(join(meet(composition(x0, top), x1), composition(x0, x1)))), composition(x0, x1))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by axiom 9 (maddux2_join_associativity) }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, complement(join(meet(composition(x0, top), x1), composition(x0, x1))))), composition(x0, x1)))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 45 R->L }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(join(join(x0, one), x0), complement(join(meet(composition(x0, top), x1), composition(x0, x1)))), composition(x0, x1)))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(join(x0, join(x0, one)), complement(join(meet(composition(x0, top), x1), composition(x0, x1)))), composition(x0, x1)))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by axiom 3 (goals) }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(join(x0, one), complement(join(meet(composition(x0, top), x1), composition(x0, x1)))), composition(x0, x1)))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 20 }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), composition(x0, x1)))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by axiom 2 (maddux1_join_commutativity) }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), join(composition(x0, x1), complement(join(meet(composition(x0, top), x1), composition(x0, x1)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 53 R->L }
% 17.91/2.79 tuple(join(composition(x0, x1), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(composition(x0, x1)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 52 R->L }
% 17.91/2.79 tuple(join(composition(x0, x1), complement(join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(composition(x0, x1)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 54 R->L }
% 17.91/2.79 tuple(complement(meet(complement(composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(join(meet(composition(x0, top), x1), composition(x0, x1)), complement(composition(x0, x1)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 33 }
% 17.91/2.79 tuple(complement(meet(complement(composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1)))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.79 = { by lemma 38 R->L }
% 17.91/2.79 tuple(complement(join(meet(complement(composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1))))), zero)), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.80 = { by lemma 15 R->L }
% 17.91/2.80 tuple(complement(join(meet(complement(composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1))))), complement(top))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 17.91/2.80 = { by axiom 8 (def_top) }
% 18.63/2.80 tuple(complement(join(meet(complement(composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1))))), complement(join(join(complement(complement(composition(x0, x1))), complement(join(meet(composition(x0, top), x1), composition(x0, x1)))), complement(join(complement(complement(composition(x0, x1))), complement(join(meet(composition(x0, top), x1), composition(x0, x1))))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 18.63/2.80 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 18.63/2.80 tuple(complement(join(meet(complement(composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1))))), complement(join(join(complement(complement(composition(x0, x1))), complement(join(meet(composition(x0, top), x1), composition(x0, x1)))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 18.63/2.81 = { by axiom 9 (maddux2_join_associativity) R->L }
% 18.63/2.81 tuple(complement(join(meet(complement(composition(x0, x1)), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1))))), complement(join(complement(complement(composition(x0, x1))), join(complement(join(meet(composition(x0, top), x1), composition(x0, x1))), meet(complement(composition(x0, x1)), join(meet(composition(x0, top), x1), composition(x0, x1)))))))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 18.63/2.81 = { by lemma 29 }
% 18.63/2.81 tuple(complement(complement(composition(x0, x1))), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 18.63/2.81 = { by lemma 40 }
% 18.63/2.81 tuple(composition(x0, x1), join(meet(composition(x0, top), x1), composition(x0, x1)))
% 18.63/2.81 = { by lemma 62 }
% 18.63/2.81 tuple(composition(x0, x1), meet(composition(x0, top), x1))
% 18.63/2.81 % SZS output end Proof
% 18.63/2.81
% 18.63/2.81 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------