%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL017-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:33:08 PM UTC 2026
% Result : Unsatisfiable 152.06s 19.64s
% Output : Proof 154.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL017-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 22:52:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 152.06/19.64 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
% 152.06/19.64
% 152.06/19.64 % SZS status Unsatisfiable
% 152.06/19.64
% 153.71/19.83 % SZS output start Proof
% 153.71/19.83 Axiom 1 (composition_identity_6): composition(X, one) = X.
% 153.71/19.83 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 153.71/19.83 Axiom 3 (def_top_12): top = join(X, complement(X)).
% 153.71/19.83 Axiom 4 (def_zero_13): zero = meet(X, complement(X)).
% 153.71/19.83 Axiom 5 (converse_idempotence_8): converse(converse(X)) = X.
% 153.71/19.83 Axiom 6 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 153.71/19.83 Axiom 7 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 153.71/19.83 Axiom 8 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 153.71/19.83 Axiom 9 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 153.71/19.83 Axiom 10 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 153.71/19.83 Axiom 11 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 153.71/19.83 Axiom 12 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 153.71/19.83 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 153.71/19.83 Axiom 14 (modular_law_1_15): 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).
% 153.71/19.83
% 153.71/19.83 Lemma 15: complement(top) = zero.
% 153.71/19.83 Proof:
% 153.71/19.83 complement(top)
% 153.71/19.83 = { by axiom 3 (def_top_12) }
% 153.71/19.83 complement(join(complement(X), complement(complement(X))))
% 153.71/19.83 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 153.71/19.83 meet(X, complement(X))
% 153.71/19.83 = { by axiom 4 (def_zero_13) R->L }
% 153.71/19.83 zero
% 153.71/19.83
% 153.71/19.83 Lemma 16: join(X, join(Y, Z)) = join(Y, join(X, Z)).
% 153.71/19.83 Proof:
% 153.71/19.83 join(X, join(Y, Z))
% 153.71/19.83 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.83 join(join(Y, Z), X)
% 153.71/19.83 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 153.71/19.83 join(Y, join(Z, X))
% 153.71/19.83 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.83 join(Y, join(X, Z))
% 153.71/19.83
% 153.71/19.83 Lemma 17: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 153.71/19.83 Proof:
% 153.71/19.83 join(meet(X, Y), complement(join(complement(X), Y)))
% 153.71/19.83 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.83 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 153.71/19.83 = { by axiom 12 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 153.71/19.83 X
% 153.71/19.83
% 153.71/19.83 Lemma 18: join(X, join(Y, complement(X))) = join(Y, top).
% 153.71/19.83 Proof:
% 153.71/19.83 join(X, join(Y, complement(X)))
% 153.71/19.83 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.83 join(X, join(complement(X), Y))
% 153.71/19.83 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.83 join(join(X, complement(X)), Y)
% 153.71/19.83 = { by axiom 3 (def_top_12) R->L }
% 153.71/19.83 join(top, Y)
% 153.71/19.83 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.83 join(Y, top)
% 153.71/19.83
% 153.71/19.84 Lemma 19: join(X, join(Y, complement(join(X, Y)))) = top.
% 153.71/19.84 Proof:
% 153.71/19.84 join(X, join(Y, complement(join(X, Y))))
% 153.71/19.84 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.84 join(join(X, Y), complement(join(X, Y)))
% 153.71/19.84 = { by axiom 3 (def_top_12) R->L }
% 153.71/19.84 top
% 153.71/19.84
% 153.71/19.84 Lemma 20: join(X, top) = top.
% 153.71/19.84 Proof:
% 153.71/19.84 join(X, top)
% 153.71/19.84 = { by axiom 3 (def_top_12) }
% 153.71/19.84 join(X, join(composition(Y, Z), complement(composition(Y, Z))))
% 153.71/19.84 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.84 join(X, join(complement(composition(Y, Z)), composition(Y, Z)))
% 153.71/19.84 = { by lemma 16 R->L }
% 153.71/19.84 join(complement(composition(Y, Z)), join(X, composition(Y, Z)))
% 153.71/19.84 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.84 join(join(complement(composition(Y, Z)), X), composition(Y, Z))
% 153.71/19.84 = { by lemma 17 R->L }
% 153.71/19.84 join(join(complement(composition(Y, Z)), X), join(meet(composition(Y, Z), X), complement(join(complement(composition(Y, Z)), X))))
% 153.71/19.84 = { by lemma 18 }
% 153.71/19.84 join(meet(composition(Y, Z), X), top)
% 153.71/19.84 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.84 join(top, meet(composition(Y, Z), X))
% 153.71/19.84 = { by axiom 1 (composition_identity_6) R->L }
% 153.71/19.84 join(top, meet(composition(Y, Z), composition(X, one)))
% 153.71/19.84 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.84 join(meet(composition(Y, Z), composition(X, one)), top)
% 153.71/19.84 = { by axiom 3 (def_top_12) }
% 153.71/19.84 join(meet(composition(Y, Z), composition(X, one)), join(meet(composition(Y, meet(Z, composition(converse(Y), composition(X, one)))), composition(X, one)), complement(meet(composition(Y, meet(Z, composition(converse(Y), composition(X, one)))), composition(X, one)))))
% 153.71/19.84 = { by axiom 14 (modular_law_1_15) R->L }
% 153.71/19.84 join(meet(composition(Y, Z), composition(X, one)), join(meet(composition(Y, meet(Z, composition(converse(Y), composition(X, one)))), composition(X, one)), complement(join(meet(composition(Y, Z), composition(X, one)), meet(composition(Y, meet(Z, composition(converse(Y), composition(X, one)))), composition(X, one))))))
% 153.71/19.84 = { by lemma 19 }
% 153.71/19.84 top
% 153.71/19.84
% 153.71/19.84 Lemma 21: join(meet(X, Y), join(Z, complement(join(complement(X), Y)))) = join(X, Z).
% 153.71/19.84 Proof:
% 153.71/19.84 join(meet(X, Y), join(Z, complement(join(complement(X), Y))))
% 153.71/19.84 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.84 join(meet(X, Y), join(complement(join(complement(X), Y)), Z))
% 153.71/19.84 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.84 join(join(meet(X, Y), complement(join(complement(X), Y))), Z)
% 153.71/19.84 = { by lemma 17 }
% 153.71/19.84 join(X, Z)
% 153.71/19.84
% 153.71/19.84 Lemma 22: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 153.71/19.84 Proof:
% 153.71/19.84 converse(composition(converse(X), Y))
% 153.71/19.84 = { by axiom 7 (converse_multiplicativity_10) }
% 153.71/19.84 composition(converse(Y), converse(converse(X)))
% 153.71/19.84 = { by axiom 5 (converse_idempotence_8) }
% 153.71/19.84 composition(converse(Y), X)
% 153.71/19.84
% 153.71/19.84 Lemma 23: composition(converse(one), X) = X.
% 153.71/19.84 Proof:
% 153.71/19.84 composition(converse(one), X)
% 153.71/19.84 = { by lemma 22 R->L }
% 153.71/19.84 converse(composition(converse(X), one))
% 153.71/19.84 = { by axiom 1 (composition_identity_6) }
% 153.71/19.84 converse(converse(X))
% 153.71/19.84 = { by axiom 5 (converse_idempotence_8) }
% 153.71/19.84 X
% 153.71/19.84
% 153.71/19.84 Lemma 24: join(complement(X), complement(X)) = complement(X).
% 153.71/19.84 Proof:
% 153.71/19.84 join(complement(X), complement(X))
% 153.71/19.84 = { by lemma 23 R->L }
% 153.71/19.84 join(complement(X), complement(composition(converse(one), X)))
% 153.71/19.84 = { by axiom 1 (composition_identity_6) R->L }
% 153.71/19.84 join(complement(X), complement(composition(composition(converse(one), one), X)))
% 153.71/19.84 = { by axiom 8 (composition_associativity_5) R->L }
% 153.71/19.84 join(complement(X), complement(composition(converse(one), composition(one, X))))
% 153.71/19.84 = { by lemma 23 }
% 153.71/19.84 join(complement(X), complement(composition(one, X)))
% 153.71/19.84 = { by axiom 5 (converse_idempotence_8) R->L }
% 153.71/19.84 join(complement(X), complement(composition(converse(converse(one)), X)))
% 153.71/19.84 = { by lemma 23 R->L }
% 153.71/19.84 join(complement(X), composition(converse(one), complement(composition(converse(converse(one)), X))))
% 153.71/19.84 = { by axiom 5 (converse_idempotence_8) R->L }
% 153.71/19.84 join(complement(X), composition(converse(converse(converse(one))), complement(composition(converse(converse(one)), X))))
% 153.71/19.84 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.84 join(composition(converse(converse(converse(one))), complement(composition(converse(converse(one)), X))), complement(X))
% 153.71/19.84 = { by axiom 13 (converse_cancellativity_11) }
% 153.71/19.84 complement(X)
% 153.71/19.84
% 153.71/19.84 Lemma 25: meet(Y, X) = meet(X, Y).
% 153.71/19.84 Proof:
% 153.71/19.84 meet(Y, X)
% 153.71/19.84 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.84 complement(join(complement(Y), complement(X)))
% 153.71/19.84 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.84 complement(join(complement(X), complement(Y)))
% 153.71/19.84 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 153.71/19.84 meet(X, Y)
% 153.71/19.84
% 153.71/19.84 Lemma 26: complement(join(zero, complement(X))) = meet(X, top).
% 153.71/19.84 Proof:
% 153.71/19.84 complement(join(zero, complement(X)))
% 153.71/19.85 = { by lemma 15 R->L }
% 153.71/19.85 complement(join(complement(top), complement(X)))
% 153.71/19.85 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 153.71/19.85 meet(top, X)
% 153.71/19.85 = { by lemma 25 R->L }
% 153.71/19.85 meet(X, top)
% 153.71/19.85
% 153.71/19.85 Lemma 27: join(meet(X, Y), complement(join(complement(Y), X))) = Y.
% 153.71/19.85 Proof:
% 153.71/19.85 join(meet(X, Y), complement(join(complement(Y), X)))
% 153.71/19.85 = { by lemma 25 }
% 153.71/19.85 join(meet(Y, X), complement(join(complement(Y), X)))
% 153.71/19.85 = { by lemma 17 }
% 153.71/19.85 Y
% 153.71/19.85
% 153.71/19.85 Lemma 28: meet(join(X, complement(Y)), join(complement(X), complement(Y))) = complement(Y).
% 153.71/19.85 Proof:
% 153.71/19.85 meet(join(X, complement(Y)), join(complement(X), complement(Y)))
% 153.71/19.85 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.85 meet(join(X, complement(Y)), join(complement(Y), complement(X)))
% 153.71/19.85 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.85 meet(join(complement(Y), X), join(complement(Y), complement(X)))
% 153.71/19.85 = { by lemma 25 }
% 153.71/19.85 meet(join(complement(Y), complement(X)), join(complement(Y), X))
% 153.71/19.85 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.85 complement(join(complement(join(complement(Y), complement(X))), complement(join(complement(Y), X))))
% 153.71/19.85 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 153.71/19.85 complement(join(meet(Y, X), complement(join(complement(Y), X))))
% 153.71/19.85 = { by lemma 17 }
% 153.71/19.85 complement(Y)
% 153.71/19.85
% 153.71/19.85 Lemma 29: join(zero, complement(X)) = complement(X).
% 153.71/19.85 Proof:
% 153.71/19.85 join(zero, complement(X))
% 153.71/19.85 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.85 join(complement(X), zero)
% 153.71/19.85 = { by lemma 15 R->L }
% 153.71/19.85 join(complement(X), complement(top))
% 153.71/19.85 = { by lemma 24 R->L }
% 153.71/19.85 join(complement(X), join(complement(top), complement(top)))
% 153.71/19.85 = { by lemma 15 }
% 153.71/19.85 join(complement(X), join(zero, complement(top)))
% 153.71/19.85 = { by lemma 20 R->L }
% 153.71/19.85 join(complement(X), join(zero, complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 15 R->L }
% 153.71/19.85 join(complement(X), join(complement(top), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 20 R->L }
% 153.71/19.85 join(complement(X), join(complement(join(complement(join(complement(zero), complement(X))), top)), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 18 R->L }
% 153.71/19.85 join(complement(X), join(complement(join(meet(zero, complement(X)), join(complement(join(complement(zero), complement(X))), complement(meet(zero, complement(X)))))), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.85 join(complement(X), join(complement(join(meet(zero, complement(X)), join(complement(meet(zero, complement(X))), complement(join(complement(zero), complement(X)))))), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 21 }
% 153.71/19.85 join(complement(X), join(complement(join(zero, complement(meet(zero, complement(X))))), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 26 }
% 153.71/19.85 join(complement(X), join(meet(meet(zero, complement(X)), top), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 25 R->L }
% 153.71/19.85 join(complement(X), join(meet(top, meet(zero, complement(X))), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 25 R->L }
% 153.71/19.85 join(complement(X), join(meet(top, meet(complement(X), zero)), complement(join(complement(meet(complement(X), zero)), top))))
% 153.71/19.85 = { by lemma 27 }
% 153.71/19.85 join(complement(X), meet(complement(X), zero))
% 153.71/19.85 = { by lemma 15 R->L }
% 153.71/19.85 join(complement(X), meet(complement(X), complement(top)))
% 153.71/19.85 = { by lemma 28 R->L }
% 153.71/19.85 join(meet(join(X, complement(X)), join(complement(X), complement(X))), meet(complement(X), complement(top)))
% 153.71/19.85 = { by axiom 3 (def_top_12) R->L }
% 153.71/19.85 join(meet(top, join(complement(X), complement(X))), meet(complement(X), complement(top)))
% 153.71/19.85 = { by lemma 24 }
% 153.71/19.85 join(meet(top, complement(X)), meet(complement(X), complement(top)))
% 153.71/19.85 = { by lemma 25 }
% 153.71/19.85 join(meet(complement(X), top), meet(complement(X), complement(top)))
% 153.71/19.85 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.85 join(meet(complement(X), complement(top)), meet(complement(X), top))
% 153.71/19.85 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.85 join(meet(complement(X), complement(top)), complement(join(complement(complement(X)), complement(top))))
% 153.71/19.85 = { by lemma 17 }
% 153.71/19.85 complement(X)
% 153.71/19.85
% 153.71/19.85 Lemma 30: join(X, zero) = X.
% 153.71/19.85 Proof:
% 153.71/19.85 join(X, zero)
% 153.71/19.85 = { by lemma 21 R->L }
% 153.71/19.85 join(meet(X, Y), join(zero, complement(join(complement(X), Y))))
% 153.71/19.85 = { by lemma 29 }
% 153.71/19.85 join(meet(X, Y), complement(join(complement(X), Y)))
% 153.71/19.85 = { by lemma 17 }
% 153.71/19.85 X
% 153.71/19.85
% 153.71/19.85 Lemma 31: complement(complement(X)) = X.
% 153.71/19.85 Proof:
% 153.71/19.85 complement(complement(X))
% 153.71/19.85 = { by lemma 24 R->L }
% 153.71/19.85 complement(join(complement(X), complement(X)))
% 153.71/19.85 = { by lemma 29 R->L }
% 153.71/19.85 join(zero, complement(join(complement(X), complement(X))))
% 153.71/19.85 = { by axiom 4 (def_zero_13) }
% 153.71/19.85 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 153.71/19.85 = { by lemma 17 }
% 153.71/19.85 X
% 153.71/19.85
% 153.71/19.85 Lemma 32: meet(X, top) = X.
% 153.71/19.85 Proof:
% 153.71/19.85 meet(X, top)
% 153.71/19.85 = { by lemma 26 R->L }
% 153.71/19.85 complement(join(zero, complement(X)))
% 153.71/19.85 = { by lemma 29 R->L }
% 153.71/19.85 join(zero, complement(join(zero, complement(X))))
% 153.71/19.85 = { by lemma 26 }
% 153.71/19.85 join(zero, meet(X, top))
% 153.71/19.85 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.85 join(meet(X, top), zero)
% 153.71/19.85 = { by lemma 15 R->L }
% 153.71/19.85 join(meet(X, top), complement(top))
% 153.71/19.85 = { by lemma 20 R->L }
% 153.71/19.85 join(meet(X, top), complement(join(complement(X), top)))
% 153.71/19.85 = { by lemma 17 }
% 153.71/19.85 X
% 153.71/19.85
% 153.71/19.85 Lemma 33: join(zero, meet(X, X)) = X.
% 153.71/19.85 Proof:
% 153.71/19.85 join(zero, meet(X, X))
% 153.71/19.85 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.85 join(zero, complement(join(complement(X), complement(X))))
% 153.71/19.85 = { by axiom 4 (def_zero_13) }
% 153.71/19.86 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 153.71/19.86 = { by lemma 17 }
% 153.71/19.86 X
% 153.71/19.86
% 153.71/19.86 Lemma 34: join(join(X, Y), Z) = join(join(Z, Y), X).
% 153.71/19.86 Proof:
% 153.71/19.86 join(join(X, Y), Z)
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 join(Z, join(X, Y))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 join(Z, join(Y, X))
% 153.71/19.86 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.86 join(join(Z, Y), X)
% 153.71/19.86
% 153.71/19.86 Lemma 35: join(complement(X), join(X, Y)) = top.
% 153.71/19.86 Proof:
% 153.71/19.86 join(complement(X), join(X, Y))
% 153.71/19.86 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.86 join(join(complement(X), X), Y)
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 join(join(X, complement(X)), Y)
% 153.71/19.86 = { by axiom 3 (def_top_12) R->L }
% 153.71/19.86 join(top, Y)
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.86 join(Y, top)
% 153.71/19.86 = { by lemma 20 }
% 153.71/19.86 top
% 153.71/19.86
% 153.71/19.86 Lemma 36: join(join(X, Y), join(Z, W)) = join(Z, join(join(W, Y), X)).
% 153.71/19.86 Proof:
% 153.71/19.86 join(join(X, Y), join(Z, W))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 join(join(X, Y), join(W, Z))
% 153.71/19.86 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.86 join(join(join(X, Y), W), Z)
% 153.71/19.86 = { by lemma 34 }
% 153.71/19.86 join(join(join(W, Y), X), Z)
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.86 join(Z, join(join(W, Y), X))
% 153.71/19.86
% 153.71/19.86 Lemma 37: join(composition(X, Y), composition(X, Z)) = composition(X, join(Z, Y)).
% 153.71/19.86 Proof:
% 153.71/19.86 join(composition(X, Y), composition(X, Z))
% 153.71/19.86 = { by axiom 5 (converse_idempotence_8) R->L }
% 153.71/19.86 join(composition(X, Y), composition(converse(converse(X)), Z))
% 153.71/19.86 = { by axiom 5 (converse_idempotence_8) R->L }
% 153.71/19.86 join(converse(converse(composition(X, Y))), composition(converse(converse(X)), Z))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 join(composition(converse(converse(X)), Z), converse(converse(composition(X, Y))))
% 153.71/19.86 = { by lemma 22 R->L }
% 153.71/19.86 join(converse(composition(converse(Z), converse(X))), converse(converse(composition(X, Y))))
% 153.71/19.86 = { by axiom 9 (converse_additivity_9) R->L }
% 153.71/19.86 converse(join(composition(converse(Z), converse(X)), converse(composition(X, Y))))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 converse(join(converse(composition(X, Y)), composition(converse(Z), converse(X))))
% 153.71/19.86 = { by axiom 7 (converse_multiplicativity_10) }
% 153.71/19.86 converse(join(composition(converse(Y), converse(X)), composition(converse(Z), converse(X))))
% 153.71/19.86 = { by axiom 11 (composition_distributivity_7) R->L }
% 153.71/19.86 converse(composition(join(converse(Y), converse(Z)), converse(X)))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.86 converse(composition(join(converse(Z), converse(Y)), converse(X)))
% 153.71/19.86 = { by axiom 7 (converse_multiplicativity_10) }
% 153.71/19.86 composition(converse(converse(X)), converse(join(converse(Z), converse(Y))))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 composition(converse(converse(X)), converse(join(converse(Y), converse(Z))))
% 153.71/19.86 = { by axiom 9 (converse_additivity_9) }
% 153.71/19.86 composition(converse(converse(X)), join(converse(converse(Y)), converse(converse(Z))))
% 153.71/19.86 = { by axiom 5 (converse_idempotence_8) }
% 153.71/19.86 composition(converse(converse(X)), join(Y, converse(converse(Z))))
% 153.71/19.86 = { by axiom 5 (converse_idempotence_8) }
% 153.71/19.86 composition(X, join(Y, converse(converse(Z))))
% 153.71/19.86 = { by axiom 5 (converse_idempotence_8) }
% 153.71/19.86 composition(X, join(Y, Z))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.86 composition(X, join(Z, Y))
% 153.71/19.86
% 153.71/19.86 Lemma 38: join(join(join(X, W), Y), Z) = join(X, join(join(Y, Z), W)).
% 153.71/19.86 Proof:
% 153.71/19.86 join(join(join(X, W), Y), Z)
% 153.71/19.86 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 153.71/19.86 join(join(X, W), join(Y, Z))
% 153.71/19.86 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 153.71/19.86 join(X, join(W, join(Y, Z)))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.86 join(X, join(join(Y, Z), W))
% 153.71/19.86
% 153.71/19.86 Lemma 39: meet(join(X, complement(Y)), join(X, Y)) = X.
% 153.71/19.86 Proof:
% 153.71/19.86 meet(join(X, complement(Y)), join(X, Y))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 meet(join(X, complement(Y)), join(Y, X))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 meet(join(complement(Y), X), join(Y, X))
% 153.71/19.86 = { by lemma 32 R->L }
% 153.71/19.86 meet(join(complement(Y), X), join(Y, meet(X, top)))
% 153.71/19.86 = { by lemma 26 R->L }
% 153.71/19.86 meet(join(complement(Y), X), join(Y, complement(join(zero, complement(X)))))
% 153.71/19.86 = { by lemma 32 R->L }
% 153.71/19.86 meet(join(complement(Y), meet(X, top)), join(Y, complement(join(zero, complement(X)))))
% 153.71/19.86 = { by lemma 26 R->L }
% 153.71/19.86 meet(join(complement(Y), complement(join(zero, complement(X)))), join(Y, complement(join(zero, complement(X)))))
% 153.71/19.86 = { by lemma 25 }
% 153.71/19.86 meet(join(Y, complement(join(zero, complement(X)))), join(complement(Y), complement(join(zero, complement(X)))))
% 153.71/19.86 = { by lemma 28 }
% 153.71/19.86 complement(join(zero, complement(X)))
% 153.71/19.86 = { by lemma 26 }
% 153.71/19.86 meet(X, top)
% 153.71/19.86 = { by lemma 32 }
% 153.71/19.86 X
% 153.71/19.86
% 153.71/19.86 Lemma 40: join(meet(X, Y), complement(join(X, complement(Y)))) = Y.
% 153.71/19.86 Proof:
% 153.71/19.86 join(meet(X, Y), complement(join(X, complement(Y))))
% 153.71/19.86 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.86 join(meet(X, Y), complement(join(complement(Y), X)))
% 153.71/19.86 = { by lemma 27 }
% 153.71/19.86 Y
% 153.71/19.86
% 153.71/19.86 Lemma 41: join(join(join(complement(X), Y), complement(Z)), Y) = join(join(complement(X), Y), complement(Z)).
% 153.71/19.87 Proof:
% 153.71/19.87 join(join(join(complement(X), Y), complement(Z)), Y)
% 153.71/19.87 = { by lemma 39 R->L }
% 153.71/19.87 meet(join(join(join(join(complement(X), Y), complement(Z)), Y), complement(X)), join(join(join(join(complement(X), Y), complement(Z)), Y), X))
% 153.71/19.87 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.87 meet(join(join(join(join(complement(X), Y), complement(Z)), Y), complement(X)), join(X, join(join(join(complement(X), Y), complement(Z)), Y)))
% 153.71/19.87 = { by lemma 38 }
% 153.71/19.87 meet(join(join(join(join(complement(X), Y), complement(Z)), Y), complement(X)), join(X, join(complement(X), join(join(complement(Z), Y), Y))))
% 153.71/19.87 = { by lemma 16 }
% 153.71/19.87 meet(join(join(join(join(complement(X), Y), complement(Z)), Y), complement(X)), join(complement(X), join(X, join(join(complement(Z), Y), Y))))
% 153.71/19.87 = { by lemma 35 }
% 153.71/19.87 meet(join(join(join(join(complement(X), Y), complement(Z)), Y), complement(X)), top)
% 153.71/19.87 = { by lemma 32 }
% 153.71/19.87 join(join(join(join(complement(X), Y), complement(Z)), Y), complement(X))
% 153.71/19.87 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.87 join(complement(X), join(join(join(complement(X), Y), complement(Z)), Y))
% 153.71/19.87 = { by lemma 16 }
% 153.71/19.87 join(join(join(complement(X), Y), complement(Z)), join(complement(X), Y))
% 153.71/19.87 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.87 join(join(complement(X), Y), join(join(complement(X), Y), complement(Z)))
% 153.71/19.87 = { by lemma 24 R->L }
% 153.71/19.87 join(join(complement(X), Y), join(join(complement(X), Y), join(complement(Z), complement(Z))))
% 153.71/19.87 = { by lemma 36 }
% 153.71/19.87 join(join(complement(X), Y), join(complement(Z), join(join(complement(Z), Y), complement(X))))
% 153.71/19.87 = { by lemma 34 }
% 153.71/19.87 join(join(complement(X), Y), join(complement(Z), join(join(complement(X), Y), complement(Z))))
% 153.71/19.87 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.87 join(join(complement(X), Y), join(join(join(complement(X), Y), complement(Z)), complement(Z)))
% 153.71/19.87 = { by lemma 36 }
% 153.71/19.87 join(join(join(complement(X), Y), complement(Z)), join(join(complement(Z), Y), complement(X)))
% 153.71/19.87 = { by lemma 34 }
% 153.71/19.87 join(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z)))
% 153.71/19.87 = { by lemma 31 R->L }
% 153.71/19.87 join(complement(complement(join(join(complement(X), Y), complement(Z)))), join(join(complement(X), Y), complement(Z)))
% 153.71/19.87 = { by lemma 24 R->L }
% 153.71/19.87 join(complement(join(complement(join(join(complement(X), Y), complement(Z))), complement(join(join(complement(X), Y), complement(Z))))), join(join(complement(X), Y), complement(Z)))
% 153.71/19.87 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 153.71/19.87 join(meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z))), join(join(complement(X), Y), complement(Z)))
% 153.71/19.87 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.87 join(join(join(complement(X), Y), complement(Z)), meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z))))
% 153.71/19.87 = { by lemma 33 R->L }
% 153.71/19.87 join(join(zero, meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z)))), meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z))))
% 153.71/19.87 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 153.71/19.87 join(zero, join(meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z))), meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z)))))
% 153.71/19.87 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.87 join(zero, join(meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z))), complement(join(complement(join(join(complement(X), Y), complement(Z))), complement(join(join(complement(X), Y), complement(Z)))))))
% 153.71/19.87 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.87 join(zero, join(complement(join(complement(join(join(complement(X), Y), complement(Z))), complement(join(join(complement(X), Y), complement(Z))))), complement(join(complement(join(join(complement(X), Y), complement(Z))), complement(join(join(complement(X), Y), complement(Z)))))))
% 153.71/19.87 = { by lemma 24 }
% 153.71/19.87 join(zero, complement(join(complement(join(join(complement(X), Y), complement(Z))), complement(join(join(complement(X), Y), complement(Z))))))
% 153.71/19.87 = { by axiom 6 (maddux4_definiton_of_meet_4) R->L }
% 153.71/19.87 join(zero, meet(join(join(complement(X), Y), complement(Z)), join(join(complement(X), Y), complement(Z))))
% 153.71/19.87 = { by lemma 33 }
% 153.71/19.87 join(join(complement(X), Y), complement(Z))
% 153.71/19.87
% 153.71/19.87 Lemma 42: join(composition(X, meet(Y, complement(Z))), composition(X, Z)) = join(composition(X, Y), composition(X, Z)).
% 153.71/19.87 Proof:
% 153.71/19.87 join(composition(X, meet(Y, complement(Z))), composition(X, Z))
% 153.71/19.87 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.87 join(composition(X, Z), composition(X, meet(Y, complement(Z))))
% 153.71/19.87 = { by lemma 37 }
% 153.71/19.87 composition(X, join(meet(Y, complement(Z)), Z))
% 153.71/19.87 = { by lemma 31 R->L }
% 153.71/19.87 composition(X, join(meet(Y, complement(Z)), complement(complement(Z))))
% 153.71/19.88 = { by lemma 17 R->L }
% 153.71/19.88 composition(X, join(join(meet(meet(Y, complement(Z)), join(join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))), complement(join(complement(meet(Y, complement(Z))), join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))))))), complement(join(complement(meet(Y, complement(Z))), join(join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))), complement(join(complement(meet(Y, complement(Z))), join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))))))))), complement(complement(Z))))
% 153.71/19.88 = { by lemma 19 }
% 153.71/19.88 composition(X, join(join(meet(meet(Y, complement(Z)), join(join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))), complement(join(complement(meet(Y, complement(Z))), join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))))))), complement(top)), complement(complement(Z))))
% 153.71/19.88 = { by lemma 15 }
% 153.71/19.88 composition(X, join(join(meet(meet(Y, complement(Z)), join(join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))), complement(join(complement(meet(Y, complement(Z))), join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))))))), zero), complement(complement(Z))))
% 153.71/19.88 = { by lemma 30 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))), complement(join(complement(meet(Y, complement(Z))), join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))))))), complement(complement(Z))))
% 153.71/19.88 = { by lemma 18 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(join(Z, meet(Z, Y)), complement(complement(meet(Y, complement(Z))))), complement(join(join(Z, meet(Z, Y)), top)))), complement(complement(Z))))
% 153.71/19.88 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(Z, meet(Z, Y)), join(complement(complement(meet(Y, complement(Z)))), complement(join(join(Z, meet(Z, Y)), top))))), complement(complement(Z))))
% 153.71/19.88 = { by lemma 31 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(Z, meet(Z, Y)), join(meet(Y, complement(Z)), complement(join(join(Z, meet(Z, Y)), top))))), complement(complement(Z))))
% 153.71/19.88 = { by lemma 20 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(Z, meet(Z, Y)), join(meet(Y, complement(Z)), complement(top)))), complement(complement(Z))))
% 153.71/19.88 = { by lemma 15 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(Z, meet(Z, Y)), join(meet(Y, complement(Z)), zero))), complement(complement(Z))))
% 153.71/19.88 = { by lemma 30 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(Z, meet(Z, Y)), meet(Y, complement(Z)))), complement(complement(Z))))
% 153.71/19.88 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(meet(Y, complement(Z)), join(Z, meet(Z, Y)))), complement(complement(Z))))
% 153.71/19.88 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(meet(Y, complement(Z)), join(meet(Z, Y), Z))), complement(complement(Z))))
% 153.71/19.88 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(meet(Y, complement(Z)), meet(Z, Y)), Z)), complement(complement(Z))))
% 153.71/19.88 = { by axiom 6 (maddux4_definiton_of_meet_4) }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(meet(Y, complement(Z)), complement(join(complement(Z), complement(Y)))), Z)), complement(complement(Z))))
% 153.71/19.88 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(join(meet(Y, complement(Z)), complement(join(complement(Y), complement(Z)))), Z)), complement(complement(Z))))
% 153.71/19.88 = { by lemma 17 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(Y, Z)), complement(complement(Z))))
% 153.71/19.88 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(complement(Z))))
% 153.71/19.88 = { by lemma 40 R->L }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(meet(Y, complement(Z)), complement(join(Y, complement(complement(Z))))))))
% 153.71/19.88 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(complement(join(Y, complement(complement(Z)))), meet(Y, complement(Z))))))
% 153.71/19.88 = { by lemma 31 }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(complement(join(Y, Z)), meet(Y, complement(Z))))))
% 153.71/19.88 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(meet(Y, complement(Z)), complement(join(Y, Z))))))
% 153.71/19.88 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.88 composition(X, join(meet(meet(Y, complement(Z)), join(Z, Y)), complement(join(meet(Y, complement(Z)), complement(join(Z, Y))))))
% 153.71/19.88 = { by lemma 40 }
% 153.71/19.88 composition(X, join(Z, Y))
% 153.71/19.88 = { by lemma 37 R->L }
% 153.71/19.89 join(composition(X, Y), composition(X, Z))
% 153.71/19.89
% 153.71/19.89 Goal 1 (goals_17): tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), composition(sk1, sk3))) = tuple(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3))).
% 153.71/19.89 Proof:
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), composition(sk1, sk3)))
% 153.71/19.89 = { by lemma 38 }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(complement(composition(sk1, sk2)), join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), composition(sk1, sk3))))
% 153.71/19.89 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), composition(sk1, sk3)), complement(composition(sk1, sk2))))
% 153.71/19.89 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), join(composition(sk1, sk3), complement(composition(sk1, sk2)))))
% 153.71/19.89 = { by axiom 2 (maddux1_join_commutativity_1) }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), join(complement(composition(sk1, sk2)), composition(sk1, sk3))))
% 153.71/19.89 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3))))
% 153.71/19.89 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), join(composition(sk1, sk3), complement(composition(sk1, meet(sk2, complement(sk3)))))))
% 153.71/19.89 = { by axiom 10 (maddux2_join_associativity_2) }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))))
% 153.71/19.89 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 153.71/19.89 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(complement(composition(sk1, meet(sk2, complement(sk3)))), join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), composition(sk1, sk3))))
% 153.71/19.89 = { by lemma 38 R->L }
% 153.71/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)))
% 153.71/19.90 = { by lemma 41 }
% 153.71/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))))
% 153.71/19.90 = { by lemma 32 R->L }
% 153.71/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), meet(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), top))
% 154.41/19.90 = { by lemma 35 R->L }
% 154.41/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), meet(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), join(composition(sk1, meet(sk2, complement(sk3))), composition(sk1, sk3)))))
% 154.41/19.90 = { by lemma 42 }
% 154.41/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), meet(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), join(composition(sk1, sk2), composition(sk1, sk3)))))
% 154.41/19.90 = { by lemma 16 }
% 154.41/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), meet(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), join(composition(sk1, sk2), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))))
% 154.41/19.90 = { by axiom 2 (maddux1_join_commutativity_1) }
% 154.41/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), meet(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), composition(sk1, sk2))))
% 154.41/19.90 = { by lemma 39 }
% 154.41/19.90 tuple(join(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), composition(sk1, sk3)), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by lemma 41 }
% 154.41/19.90 tuple(join(join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)), complement(composition(sk1, sk2))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by lemma 34 R->L }
% 154.41/19.90 tuple(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by lemma 32 R->L }
% 154.41/19.90 tuple(meet(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), top), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by lemma 35 R->L }
% 154.41/19.90 tuple(meet(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), join(complement(composition(sk1, sk2)), join(composition(sk1, sk2), composition(sk1, sk3)))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by lemma 42 R->L }
% 154.41/19.90 tuple(meet(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), join(complement(composition(sk1, sk2)), join(composition(sk1, meet(sk2, complement(sk3))), composition(sk1, sk3)))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by lemma 16 }
% 154.41/19.90 tuple(meet(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), join(composition(sk1, meet(sk2, complement(sk3))), join(complement(composition(sk1, sk2)), composition(sk1, sk3)))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by axiom 2 (maddux1_join_commutativity_1) }
% 154.41/19.90 tuple(meet(join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), complement(composition(sk1, meet(sk2, complement(sk3))))), join(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), composition(sk1, meet(sk2, complement(sk3))))), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 = { by lemma 39 }
% 154.41/19.90 tuple(join(complement(composition(sk1, sk2)), composition(sk1, sk3)), join(complement(composition(sk1, meet(sk2, complement(sk3)))), composition(sk1, sk3)))
% 154.41/19.90 % SZS output end Proof
% 154.41/19.90
% 154.41/19.90 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------