TSTP Solution File: REL033-3 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL033-3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:44:18 EDT 2023
% Result : Unsatisfiable 201.04s 25.96s
% Output : Proof 202.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL033-3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 21:38:38 EDT 2023
% 0.14/0.34 % CPUTime :
% 201.04/25.96 Command-line arguments: --flatten
% 201.04/25.96
% 201.04/25.96 % SZS status Unsatisfiable
% 201.04/25.96
% 201.76/26.05 % SZS output start Proof
% 201.76/26.05 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 201.76/26.05 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 201.76/26.05 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 201.76/26.05 Axiom 4 (goals_17): composition(sk1, top) = sk1.
% 201.76/26.05 Axiom 5 (def_top_12): top = join(X, complement(X)).
% 201.76/26.05 Axiom 6 (def_zero_13): zero = meet(X, complement(X)).
% 201.76/26.05 Axiom 7 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 201.76/26.05 Axiom 8 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 201.76/26.05 Axiom 9 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 201.76/26.05 Axiom 10 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 201.76/26.05 Axiom 11 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 201.76/26.05 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 201.76/26.05 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 201.76/26.05 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 201.76/26.05 Axiom 15 (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).
% 201.76/26.05 Axiom 16 (modular_law_2_16): join(meet(composition(X, Y), Z), meet(composition(meet(X, composition(Z, converse(Y))), Y), Z)) = meet(composition(meet(X, composition(Z, converse(Y))), Y), Z).
% 201.76/26.05
% 201.76/26.05 Lemma 17: complement(top) = zero.
% 201.76/26.05 Proof:
% 201.76/26.05 complement(top)
% 201.76/26.05 = { by axiom 5 (def_top_12) }
% 201.76/26.05 complement(join(complement(X), complement(complement(X))))
% 201.76/26.05 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.05 meet(X, complement(X))
% 201.76/26.05 = { by axiom 6 (def_zero_13) R->L }
% 201.76/26.05 zero
% 201.76/26.05
% 201.76/26.05 Lemma 18: join(X, join(Y, complement(X))) = join(Y, top).
% 201.76/26.05 Proof:
% 201.76/26.05 join(X, join(Y, complement(X)))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(X, join(complement(X), Y))
% 201.76/26.05 = { by axiom 8 (maddux2_join_associativity_2) }
% 201.76/26.05 join(join(X, complement(X)), Y)
% 201.76/26.05 = { by axiom 5 (def_top_12) R->L }
% 201.76/26.05 join(top, Y)
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.05 join(Y, top)
% 201.76/26.05
% 201.76/26.05 Lemma 19: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 201.76/26.05 Proof:
% 201.76/26.05 converse(composition(converse(X), Y))
% 201.76/26.05 = { by axiom 9 (converse_multiplicativity_10) }
% 201.76/26.05 composition(converse(Y), converse(converse(X)))
% 201.76/26.05 = { by axiom 1 (converse_idempotence_8) }
% 201.76/26.05 composition(converse(Y), X)
% 201.76/26.05
% 201.76/26.05 Lemma 20: composition(converse(one), X) = X.
% 201.76/26.05 Proof:
% 201.76/26.05 composition(converse(one), X)
% 201.76/26.05 = { by lemma 19 R->L }
% 201.76/26.05 converse(composition(converse(X), one))
% 201.76/26.05 = { by axiom 3 (composition_identity_6) }
% 201.76/26.05 converse(converse(X))
% 201.76/26.05 = { by axiom 1 (converse_idempotence_8) }
% 201.76/26.05 X
% 201.76/26.05
% 201.76/26.05 Lemma 21: composition(one, X) = X.
% 201.76/26.05 Proof:
% 201.76/26.05 composition(one, X)
% 201.76/26.05 = { by lemma 20 R->L }
% 201.76/26.05 composition(converse(one), composition(one, X))
% 201.76/26.05 = { by axiom 10 (composition_associativity_5) }
% 201.76/26.05 composition(composition(converse(one), one), X)
% 201.76/26.05 = { by axiom 3 (composition_identity_6) }
% 201.76/26.05 composition(converse(one), X)
% 201.76/26.05 = { by lemma 20 }
% 201.76/26.05 X
% 201.76/26.05
% 201.76/26.05 Lemma 22: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 201.76/26.05 Proof:
% 201.76/26.05 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 201.76/26.05 = { by axiom 13 (converse_cancellativity_11) }
% 201.76/26.05 complement(X)
% 201.76/26.05
% 201.76/26.05 Lemma 23: join(complement(X), complement(X)) = complement(X).
% 201.76/26.05 Proof:
% 201.76/26.05 join(complement(X), complement(X))
% 201.76/26.05 = { by lemma 20 R->L }
% 201.76/26.05 join(complement(X), composition(converse(one), complement(X)))
% 201.76/26.05 = { by lemma 21 R->L }
% 201.76/26.05 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 201.76/26.05 = { by lemma 22 }
% 201.76/26.05 complement(X)
% 201.76/26.05
% 201.76/26.05 Lemma 24: join(top, complement(X)) = top.
% 201.76/26.05 Proof:
% 201.76/26.05 join(top, complement(X))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(complement(X), top)
% 201.76/26.05 = { by lemma 18 R->L }
% 201.76/26.05 join(X, join(complement(X), complement(X)))
% 201.76/26.05 = { by lemma 23 }
% 201.76/26.05 join(X, complement(X))
% 201.76/26.05 = { by axiom 5 (def_top_12) R->L }
% 201.76/26.05 top
% 201.76/26.05
% 201.76/26.05 Lemma 25: join(Y, top) = join(X, top).
% 201.76/26.05 Proof:
% 201.76/26.05 join(Y, top)
% 201.76/26.05 = { by lemma 24 R->L }
% 201.76/26.05 join(Y, join(top, complement(Y)))
% 201.76/26.05 = { by lemma 18 }
% 201.76/26.05 join(top, top)
% 201.76/26.05 = { by lemma 18 R->L }
% 201.76/26.05 join(X, join(top, complement(X)))
% 201.76/26.05 = { by lemma 24 }
% 201.76/26.05 join(X, top)
% 201.76/26.05
% 201.76/26.05 Lemma 26: join(X, top) = top.
% 201.76/26.05 Proof:
% 201.76/26.05 join(X, top)
% 201.76/26.05 = { by lemma 25 }
% 201.76/26.05 join(zero, top)
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(top, zero)
% 201.76/26.05 = { by lemma 17 R->L }
% 201.76/26.05 join(top, complement(top))
% 201.76/26.05 = { by axiom 5 (def_top_12) R->L }
% 201.76/26.05 top
% 201.76/26.05
% 201.76/26.05 Lemma 27: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 201.76/26.05 Proof:
% 201.76/26.05 converse(join(X, converse(Y)))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 converse(join(converse(Y), X))
% 201.76/26.05 = { by axiom 7 (converse_additivity_9) }
% 201.76/26.05 join(converse(converse(Y)), converse(X))
% 201.76/26.05 = { by axiom 1 (converse_idempotence_8) }
% 201.76/26.05 join(Y, converse(X))
% 201.76/26.05
% 201.76/26.05 Lemma 28: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 201.76/26.05 Proof:
% 201.76/26.05 converse(join(converse(X), Y))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 converse(join(Y, converse(X)))
% 201.76/26.05 = { by lemma 27 }
% 201.76/26.05 join(X, converse(Y))
% 201.76/26.05
% 201.76/26.05 Lemma 29: join(X, join(complement(X), Y)) = top.
% 201.76/26.05 Proof:
% 201.76/26.05 join(X, join(complement(X), Y))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(X, join(Y, complement(X)))
% 201.76/26.05 = { by lemma 18 }
% 201.76/26.05 join(Y, top)
% 201.76/26.05 = { by lemma 25 R->L }
% 201.76/26.05 join(Z, top)
% 201.76/26.05 = { by lemma 26 }
% 201.76/26.05 top
% 201.76/26.05
% 201.76/26.05 Lemma 30: join(X, converse(top)) = top.
% 201.76/26.05 Proof:
% 201.76/26.05 join(X, converse(top))
% 201.76/26.05 = { by axiom 5 (def_top_12) }
% 201.76/26.05 join(X, converse(join(converse(complement(X)), complement(converse(complement(X))))))
% 201.76/26.05 = { by lemma 28 }
% 201.76/26.05 join(X, join(complement(X), converse(complement(converse(complement(X))))))
% 201.76/26.05 = { by lemma 29 }
% 201.76/26.05 top
% 201.76/26.05
% 201.76/26.05 Lemma 31: converse(top) = top.
% 201.76/26.05 Proof:
% 201.76/26.05 converse(top)
% 201.76/26.05 = { by lemma 26 R->L }
% 201.76/26.05 converse(join(X, top))
% 201.76/26.05 = { by axiom 7 (converse_additivity_9) }
% 201.76/26.05 join(converse(X), converse(top))
% 201.76/26.05 = { by lemma 30 }
% 201.76/26.05 top
% 201.76/26.05
% 201.76/26.05 Lemma 32: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 201.76/26.05 Proof:
% 201.76/26.05 join(meet(X, Y), complement(join(complement(X), Y)))
% 201.76/26.05 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.05 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 201.76/26.05 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 201.76/26.05 X
% 201.76/26.05
% 201.76/26.05 Lemma 33: join(zero, meet(X, X)) = X.
% 201.76/26.05 Proof:
% 201.76/26.05 join(zero, meet(X, X))
% 201.76/26.05 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.05 join(zero, complement(join(complement(X), complement(X))))
% 201.76/26.05 = { by axiom 6 (def_zero_13) }
% 201.76/26.05 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 201.76/26.05 = { by lemma 32 }
% 201.76/26.05 X
% 201.76/26.05
% 201.76/26.05 Lemma 34: join(zero, join(X, complement(complement(Y)))) = join(X, Y).
% 201.76/26.05 Proof:
% 201.76/26.05 join(zero, join(X, complement(complement(Y))))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(zero, join(complement(complement(Y)), X))
% 201.76/26.05 = { by lemma 23 R->L }
% 201.76/26.05 join(zero, join(complement(join(complement(Y), complement(Y))), X))
% 201.76/26.05 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.05 join(zero, join(meet(Y, Y), X))
% 201.76/26.05 = { by axiom 8 (maddux2_join_associativity_2) }
% 201.76/26.05 join(join(zero, meet(Y, Y)), X)
% 201.76/26.05 = { by lemma 33 }
% 201.76/26.05 join(Y, X)
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.05 join(X, Y)
% 201.76/26.05
% 201.76/26.05 Lemma 35: join(zero, complement(complement(X))) = X.
% 201.76/26.05 Proof:
% 201.76/26.05 join(zero, complement(complement(X)))
% 201.76/26.05 = { by axiom 6 (def_zero_13) }
% 201.76/26.05 join(meet(X, complement(X)), complement(complement(X)))
% 201.76/26.05 = { by lemma 23 R->L }
% 201.76/26.05 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 201.76/26.05 = { by lemma 32 }
% 201.76/26.05 X
% 201.76/26.05
% 201.76/26.05 Lemma 36: join(X, zero) = join(X, X).
% 201.76/26.05 Proof:
% 201.76/26.05 join(X, zero)
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(zero, X)
% 201.76/26.05 = { by lemma 35 R->L }
% 201.76/26.05 join(zero, join(zero, complement(complement(X))))
% 201.76/26.05 = { by lemma 23 R->L }
% 201.76/26.05 join(zero, join(zero, join(complement(complement(X)), complement(complement(X)))))
% 201.76/26.05 = { by lemma 34 }
% 201.76/26.05 join(zero, join(complement(complement(X)), X))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.05 join(zero, join(X, complement(complement(X))))
% 201.76/26.05 = { by lemma 34 }
% 201.76/26.05 join(X, X)
% 201.76/26.05
% 201.76/26.05 Lemma 37: join(zero, complement(X)) = complement(X).
% 201.76/26.05 Proof:
% 201.76/26.05 join(zero, complement(X))
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(complement(X), zero)
% 201.76/26.05 = { by lemma 36 }
% 201.76/26.05 join(complement(X), complement(X))
% 201.76/26.05 = { by lemma 23 }
% 201.76/26.05 complement(X)
% 201.76/26.05
% 201.76/26.05 Lemma 38: join(X, zero) = X.
% 201.76/26.05 Proof:
% 201.76/26.05 join(X, zero)
% 201.76/26.05 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.05 join(zero, X)
% 201.76/26.05 = { by lemma 34 R->L }
% 201.76/26.05 join(zero, join(zero, complement(complement(X))))
% 201.76/26.05 = { by lemma 37 }
% 201.76/26.05 join(zero, complement(complement(X)))
% 201.76/26.05 = { by lemma 35 }
% 201.76/26.05 X
% 201.76/26.05
% 201.76/26.06 Lemma 39: join(zero, X) = X.
% 201.76/26.06 Proof:
% 201.76/26.06 join(zero, X)
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 join(X, zero)
% 201.76/26.06 = { by lemma 38 }
% 201.76/26.06 X
% 201.76/26.06
% 201.76/26.06 Lemma 40: meet(Y, X) = meet(X, Y).
% 201.76/26.06 Proof:
% 201.76/26.06 meet(Y, X)
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.06 complement(join(complement(Y), complement(X)))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 complement(join(complement(X), complement(Y)))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.06 meet(X, Y)
% 201.76/26.06
% 201.76/26.06 Lemma 41: complement(join(zero, complement(X))) = meet(X, top).
% 201.76/26.06 Proof:
% 201.76/26.06 complement(join(zero, complement(X)))
% 201.76/26.06 = { by lemma 17 R->L }
% 201.76/26.06 complement(join(complement(top), complement(X)))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.06 meet(top, X)
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 meet(X, top)
% 201.76/26.06
% 201.76/26.06 Lemma 42: join(X, complement(zero)) = top.
% 201.76/26.06 Proof:
% 201.76/26.06 join(X, complement(zero))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 join(complement(zero), X)
% 201.76/26.06 = { by lemma 34 R->L }
% 201.76/26.06 join(zero, join(complement(zero), complement(complement(X))))
% 201.76/26.06 = { by lemma 29 }
% 201.76/26.06 top
% 201.76/26.06
% 201.76/26.06 Lemma 43: meet(X, zero) = zero.
% 201.76/26.06 Proof:
% 201.76/26.06 meet(X, zero)
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.06 complement(join(complement(X), complement(zero)))
% 201.76/26.06 = { by lemma 42 }
% 201.76/26.06 complement(top)
% 201.76/26.06 = { by lemma 17 }
% 201.76/26.06 zero
% 201.76/26.06
% 201.76/26.06 Lemma 44: join(meet(X, Y), meet(X, complement(Y))) = X.
% 201.76/26.06 Proof:
% 201.76/26.06 join(meet(X, Y), meet(X, complement(Y)))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 join(meet(X, complement(Y)), meet(X, Y))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.06 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 201.76/26.06 = { by lemma 32 }
% 201.76/26.06 X
% 201.76/26.06
% 201.76/26.06 Lemma 45: meet(X, top) = X.
% 201.76/26.06 Proof:
% 201.76/26.06 meet(X, top)
% 201.76/26.06 = { by lemma 41 R->L }
% 201.76/26.06 complement(join(zero, complement(X)))
% 201.76/26.06 = { by lemma 37 R->L }
% 201.76/26.06 join(zero, complement(join(zero, complement(X))))
% 201.76/26.06 = { by lemma 41 }
% 201.76/26.06 join(zero, meet(X, top))
% 201.76/26.06 = { by lemma 42 R->L }
% 201.76/26.06 join(zero, meet(X, join(complement(zero), complement(zero))))
% 201.76/26.06 = { by lemma 23 }
% 201.76/26.06 join(zero, meet(X, complement(zero)))
% 201.76/26.06 = { by lemma 43 R->L }
% 201.76/26.06 join(meet(X, zero), meet(X, complement(zero)))
% 201.76/26.06 = { by lemma 44 }
% 201.76/26.06 X
% 201.76/26.06
% 201.76/26.06 Lemma 46: join(meet(X, Y), meet(X, Y)) = meet(X, Y).
% 201.76/26.06 Proof:
% 201.76/26.06 join(meet(X, Y), meet(X, Y))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 join(meet(Y, X), meet(X, Y))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 join(meet(Y, X), meet(Y, X))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.06 join(meet(Y, X), complement(join(complement(Y), complement(X))))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.06 join(complement(join(complement(Y), complement(X))), complement(join(complement(Y), complement(X))))
% 201.76/26.06 = { by lemma 23 }
% 201.76/26.06 complement(join(complement(Y), complement(X)))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.06 meet(Y, X)
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 meet(X, Y)
% 201.76/26.06
% 201.76/26.06 Lemma 47: converse(zero) = zero.
% 201.76/26.06 Proof:
% 201.76/26.06 converse(zero)
% 201.76/26.06 = { by lemma 39 R->L }
% 201.76/26.06 join(zero, converse(zero))
% 201.76/26.06 = { by lemma 28 R->L }
% 201.76/26.06 converse(join(converse(zero), zero))
% 201.76/26.06 = { by lemma 36 }
% 201.76/26.06 converse(join(converse(zero), converse(zero)))
% 201.76/26.06 = { by lemma 27 }
% 201.76/26.06 join(zero, converse(converse(zero)))
% 201.76/26.06 = { by axiom 1 (converse_idempotence_8) }
% 201.76/26.06 join(zero, zero)
% 201.76/26.06 = { by lemma 45 R->L }
% 201.76/26.06 join(zero, meet(zero, top))
% 201.76/26.06 = { by lemma 45 R->L }
% 201.76/26.06 join(meet(zero, top), meet(zero, top))
% 201.76/26.06 = { by lemma 46 }
% 201.76/26.06 meet(zero, top)
% 201.76/26.06 = { by lemma 45 }
% 201.76/26.06 zero
% 201.76/26.06
% 201.76/26.06 Lemma 48: join(top, X) = top.
% 201.76/26.06 Proof:
% 201.76/26.06 join(top, X)
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 join(X, top)
% 201.76/26.06 = { by lemma 25 R->L }
% 201.76/26.06 join(Y, top)
% 201.76/26.06 = { by lemma 26 }
% 201.76/26.06 top
% 201.76/26.06
% 201.76/26.06 Lemma 49: complement(complement(X)) = X.
% 201.76/26.06 Proof:
% 201.76/26.06 complement(complement(X))
% 201.76/26.06 = { by lemma 37 R->L }
% 201.76/26.06 join(zero, complement(complement(X)))
% 201.76/26.06 = { by lemma 35 }
% 201.76/26.06 X
% 201.76/26.06
% 201.76/26.06 Lemma 50: meet(zero, X) = zero.
% 201.76/26.06 Proof:
% 201.76/26.06 meet(zero, X)
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 meet(X, zero)
% 201.76/26.06 = { by lemma 43 }
% 201.76/26.06 zero
% 201.76/26.06
% 201.76/26.06 Lemma 51: composition(top, zero) = zero.
% 201.76/26.06 Proof:
% 201.76/26.06 composition(top, zero)
% 201.76/26.06 = { by lemma 31 R->L }
% 201.76/26.06 composition(converse(top), zero)
% 201.76/26.06 = { by lemma 39 R->L }
% 201.76/26.06 join(zero, composition(converse(top), zero))
% 201.76/26.06 = { by lemma 17 R->L }
% 201.76/26.06 join(complement(top), composition(converse(top), zero))
% 201.76/26.06 = { by lemma 17 R->L }
% 201.76/26.06 join(complement(top), composition(converse(top), complement(top)))
% 201.76/26.06 = { by lemma 48 R->L }
% 201.76/26.06 join(complement(top), composition(converse(top), complement(join(top, composition(top, top)))))
% 201.76/26.06 = { by lemma 31 R->L }
% 201.76/26.06 join(complement(top), composition(converse(top), complement(join(top, composition(converse(top), top)))))
% 201.76/26.06 = { by lemma 21 R->L }
% 201.76/26.06 join(complement(top), composition(converse(top), complement(join(composition(one, top), composition(converse(top), top)))))
% 201.76/26.06 = { by axiom 12 (composition_distributivity_7) R->L }
% 201.76/26.06 join(complement(top), composition(converse(top), complement(composition(join(one, converse(top)), top))))
% 201.76/26.06 = { by lemma 30 }
% 201.76/26.06 join(complement(top), composition(converse(top), complement(composition(top, top))))
% 201.76/26.06 = { by lemma 22 }
% 201.76/26.06 complement(top)
% 201.76/26.06 = { by lemma 17 }
% 201.76/26.06 zero
% 201.76/26.06
% 201.76/26.06 Lemma 52: composition(X, zero) = zero.
% 201.76/26.06 Proof:
% 201.76/26.06 composition(X, zero)
% 201.76/26.06 = { by lemma 39 R->L }
% 201.76/26.06 join(zero, composition(X, zero))
% 201.76/26.06 = { by lemma 51 R->L }
% 201.76/26.06 join(composition(top, zero), composition(X, zero))
% 201.76/26.06 = { by axiom 12 (composition_distributivity_7) R->L }
% 201.76/26.06 composition(join(top, X), zero)
% 201.76/26.06 = { by lemma 48 }
% 201.76/26.06 composition(top, zero)
% 201.76/26.06 = { by lemma 51 }
% 201.76/26.06 zero
% 201.76/26.06
% 201.76/26.06 Lemma 53: composition(zero, X) = zero.
% 201.76/26.06 Proof:
% 201.76/26.06 composition(zero, X)
% 201.76/26.06 = { by lemma 47 R->L }
% 201.76/26.06 composition(converse(zero), X)
% 201.76/26.06 = { by lemma 19 R->L }
% 201.76/26.06 converse(composition(converse(X), zero))
% 201.76/26.06 = { by lemma 52 }
% 201.76/26.06 converse(zero)
% 201.76/26.06 = { by lemma 47 }
% 201.76/26.06 zero
% 201.76/26.06
% 201.76/26.06 Lemma 54: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 201.76/26.06 Proof:
% 201.76/26.06 meet(X, join(complement(Y), complement(Z)))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 meet(X, join(complement(Z), complement(Y)))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 meet(join(complement(Z), complement(Y)), X)
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.06 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.06 complement(join(meet(Z, Y), complement(X)))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.06 complement(join(complement(X), meet(Z, Y)))
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 complement(join(complement(X), meet(Y, Z)))
% 201.76/26.06
% 201.76/26.06 Lemma 55: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 201.76/26.06 Proof:
% 201.76/26.06 join(complement(X), complement(Y))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 join(complement(Y), complement(X))
% 201.76/26.06 = { by lemma 33 R->L }
% 201.76/26.06 join(zero, meet(join(complement(Y), complement(X)), join(complement(Y), complement(X))))
% 201.76/26.06 = { by lemma 54 }
% 201.76/26.06 join(zero, complement(join(complement(join(complement(Y), complement(X))), meet(Y, X))))
% 201.76/26.06 = { by lemma 37 }
% 201.76/26.06 complement(join(complement(join(complement(Y), complement(X))), meet(Y, X)))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.06 complement(join(meet(Y, X), meet(Y, X)))
% 201.76/26.06 = { by lemma 46 }
% 201.76/26.06 complement(meet(Y, X))
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 complement(meet(X, Y))
% 201.76/26.06
% 201.76/26.06 Lemma 56: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 201.76/26.06 Proof:
% 201.76/26.06 complement(join(X, complement(Y)))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 complement(join(complement(Y), X))
% 201.76/26.06 = { by lemma 45 R->L }
% 201.76/26.06 complement(join(complement(Y), meet(X, top)))
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 complement(join(complement(Y), meet(top, X)))
% 201.76/26.06 = { by lemma 54 R->L }
% 201.76/26.06 meet(Y, join(complement(top), complement(X)))
% 201.76/26.06 = { by lemma 17 }
% 201.76/26.06 meet(Y, join(zero, complement(X)))
% 201.76/26.06 = { by lemma 37 }
% 201.76/26.06 meet(Y, complement(X))
% 201.76/26.06
% 201.76/26.06 Lemma 57: complement(join(complement(X), Y)) = meet(X, complement(Y)).
% 201.76/26.06 Proof:
% 201.76/26.06 complement(join(complement(X), Y))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 complement(join(Y, complement(X)))
% 201.76/26.06 = { by lemma 56 }
% 201.76/26.06 meet(X, complement(Y))
% 201.76/26.06
% 201.76/26.06 Lemma 58: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 201.76/26.06 Proof:
% 201.76/26.06 complement(meet(X, complement(Y)))
% 201.76/26.06 = { by lemma 39 R->L }
% 201.76/26.06 complement(join(zero, meet(X, complement(Y))))
% 201.76/26.06 = { by lemma 56 R->L }
% 201.76/26.06 complement(join(zero, complement(join(Y, complement(X)))))
% 201.76/26.06 = { by lemma 41 }
% 201.76/26.06 meet(join(Y, complement(X)), top)
% 201.76/26.06 = { by lemma 45 }
% 201.76/26.06 join(Y, complement(X))
% 201.76/26.06
% 201.76/26.06 Lemma 59: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 201.76/26.06 Proof:
% 201.76/26.06 complement(meet(complement(X), Y))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 complement(meet(Y, complement(X)))
% 201.76/26.06 = { by lemma 58 }
% 201.76/26.06 join(X, complement(Y))
% 201.76/26.06
% 201.76/26.06 Lemma 60: meet(complement(X), complement(Y)) = complement(join(X, Y)).
% 201.76/26.06 Proof:
% 201.76/26.06 meet(complement(X), complement(Y))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 meet(complement(Y), complement(X))
% 201.76/26.06 = { by lemma 37 R->L }
% 201.76/26.06 meet(join(zero, complement(Y)), complement(X))
% 201.76/26.06 = { by lemma 56 R->L }
% 201.76/26.06 complement(join(X, complement(join(zero, complement(Y)))))
% 201.76/26.06 = { by lemma 41 }
% 201.76/26.06 complement(join(X, meet(Y, top)))
% 201.76/26.06 = { by lemma 45 }
% 201.76/26.06 complement(join(X, Y))
% 201.76/26.06
% 201.76/26.06 Lemma 61: meet(complement(Z), meet(Y, X)) = meet(X, meet(Y, complement(Z))).
% 201.76/26.06 Proof:
% 201.76/26.06 meet(complement(Z), meet(Y, X))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 meet(complement(Z), meet(X, Y))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 meet(meet(X, Y), complement(Z))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 201.76/26.06 meet(complement(join(complement(X), complement(Y))), complement(Z))
% 201.76/26.06 = { by lemma 60 }
% 201.76/26.06 complement(join(join(complement(X), complement(Y)), Z))
% 201.76/26.06 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 201.76/26.06 complement(join(complement(X), join(complement(Y), Z)))
% 201.76/26.06 = { by lemma 57 }
% 201.76/26.06 meet(X, complement(join(complement(Y), Z)))
% 201.76/26.06 = { by lemma 57 }
% 201.76/26.06 meet(X, meet(Y, complement(Z)))
% 201.76/26.06
% 201.76/26.06 Lemma 62: meet(Y, meet(Z, X)) = meet(X, meet(Y, Z)).
% 201.76/26.06 Proof:
% 201.76/26.06 meet(Y, meet(Z, X))
% 201.76/26.06 = { by lemma 45 R->L }
% 201.76/26.06 meet(meet(Y, top), meet(Z, X))
% 201.76/26.06 = { by lemma 41 R->L }
% 201.76/26.06 meet(complement(join(zero, complement(Y))), meet(Z, X))
% 201.76/26.06 = { by lemma 61 }
% 201.76/26.06 meet(X, meet(Z, complement(join(zero, complement(Y)))))
% 201.76/26.06 = { by lemma 41 }
% 201.76/26.06 meet(X, meet(Z, meet(Y, top)))
% 201.76/26.06 = { by lemma 45 }
% 201.76/26.06 meet(X, meet(Z, Y))
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 meet(X, meet(Y, Z))
% 201.76/26.06
% 201.76/26.06 Lemma 63: join(X, complement(meet(X, Y))) = top.
% 201.76/26.06 Proof:
% 201.76/26.06 join(X, complement(meet(X, Y)))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 join(X, complement(meet(Y, X)))
% 201.76/26.06 = { by lemma 55 R->L }
% 201.76/26.06 join(X, join(complement(Y), complement(X)))
% 201.76/26.06 = { by lemma 18 }
% 201.76/26.06 join(complement(Y), top)
% 201.76/26.06 = { by lemma 26 }
% 201.76/26.06 top
% 201.76/26.06
% 201.76/26.06 Lemma 64: join(X, complement(meet(Y, X))) = top.
% 201.76/26.06 Proof:
% 201.76/26.06 join(X, complement(meet(Y, X)))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 join(X, complement(meet(X, Y)))
% 201.76/26.06 = { by lemma 63 }
% 201.76/26.06 top
% 201.76/26.06
% 201.76/26.06 Lemma 65: meet(X, join(X, complement(Y))) = X.
% 201.76/26.06 Proof:
% 201.76/26.06 meet(X, join(X, complement(Y)))
% 201.76/26.06 = { by lemma 58 R->L }
% 201.76/26.06 meet(X, complement(meet(Y, complement(X))))
% 201.76/26.06 = { by lemma 57 R->L }
% 201.76/26.06 complement(join(complement(X), meet(Y, complement(X))))
% 201.76/26.06 = { by lemma 37 R->L }
% 201.76/26.06 join(zero, complement(join(complement(X), meet(Y, complement(X)))))
% 201.76/26.06 = { by lemma 17 R->L }
% 201.76/26.06 join(complement(top), complement(join(complement(X), meet(Y, complement(X)))))
% 201.76/26.06 = { by lemma 63 R->L }
% 201.76/26.06 join(complement(join(complement(X), complement(meet(complement(X), Y)))), complement(join(complement(X), meet(Y, complement(X)))))
% 201.76/26.06 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.06 join(meet(X, meet(complement(X), Y)), complement(join(complement(X), meet(Y, complement(X)))))
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 join(meet(X, meet(Y, complement(X))), complement(join(complement(X), meet(Y, complement(X)))))
% 201.76/26.06 = { by lemma 32 }
% 201.76/26.06 X
% 201.76/26.06
% 201.76/26.06 Lemma 66: join(complement(X), meet(Y, complement(Z))) = complement(meet(X, join(Z, complement(Y)))).
% 201.76/26.06 Proof:
% 201.76/26.06 join(complement(X), meet(Y, complement(Z)))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 join(meet(Y, complement(Z)), complement(X))
% 201.76/26.06 = { by lemma 56 R->L }
% 201.76/26.06 join(complement(join(Z, complement(Y))), complement(X))
% 201.76/26.06 = { by lemma 55 }
% 201.76/26.06 complement(meet(join(Z, complement(Y)), X))
% 201.76/26.06 = { by lemma 40 R->L }
% 201.76/26.06 complement(meet(X, join(Z, complement(Y))))
% 201.76/26.06
% 201.76/26.06 Lemma 67: complement(join(X, join(Y, complement(Z)))) = meet(Z, complement(join(X, Y))).
% 201.76/26.06 Proof:
% 201.76/26.06 complement(join(X, join(Y, complement(Z))))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.06 complement(join(X, join(complement(Z), Y)))
% 201.76/26.06 = { by axiom 8 (maddux2_join_associativity_2) }
% 201.76/26.06 complement(join(join(X, complement(Z)), Y))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.06 complement(join(Y, join(X, complement(Z))))
% 201.76/26.06 = { by axiom 8 (maddux2_join_associativity_2) }
% 201.76/26.06 complement(join(join(Y, X), complement(Z)))
% 201.76/26.06 = { by lemma 56 }
% 201.76/26.06 meet(Z, complement(join(Y, X)))
% 201.76/26.06 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.06 meet(Z, complement(join(X, Y)))
% 201.76/26.06
% 201.76/26.06 Lemma 68: join(meet(X, Y), meet(Y, complement(X))) = Y.
% 201.76/26.06 Proof:
% 201.76/26.06 join(meet(X, Y), meet(Y, complement(X)))
% 201.76/26.06 = { by lemma 40 }
% 201.76/26.06 join(meet(Y, X), meet(Y, complement(X)))
% 201.76/26.07 = { by lemma 44 }
% 201.76/26.07 Y
% 201.76/26.07
% 201.76/26.07 Lemma 69: join(meet(X, Y), meet(complement(X), Y)) = Y.
% 201.76/26.07 Proof:
% 201.76/26.07 join(meet(X, Y), meet(complement(X), Y))
% 201.76/26.07 = { by lemma 40 }
% 201.76/26.07 join(meet(X, Y), meet(Y, complement(X)))
% 201.76/26.07 = { by lemma 68 }
% 201.76/26.07 Y
% 201.76/26.07
% 201.76/26.07 Lemma 70: complement(meet(Y, join(X, complement(Y)))) = complement(meet(X, join(Y, complement(X)))).
% 201.76/26.07 Proof:
% 201.76/26.07 complement(meet(Y, join(X, complement(Y))))
% 201.76/26.07 = { by lemma 66 R->L }
% 201.76/26.07 join(complement(Y), meet(Y, complement(X)))
% 201.76/26.07 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.07 join(meet(Y, complement(X)), complement(Y))
% 201.76/26.07 = { by lemma 69 R->L }
% 201.76/26.07 join(meet(Y, complement(X)), join(meet(X, complement(Y)), meet(complement(X), complement(Y))))
% 201.76/26.07 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.07 join(meet(Y, complement(X)), join(meet(complement(X), complement(Y)), meet(X, complement(Y))))
% 201.76/26.07 = { by axiom 8 (maddux2_join_associativity_2) }
% 201.76/26.07 join(join(meet(Y, complement(X)), meet(complement(X), complement(Y))), meet(X, complement(Y)))
% 201.76/26.07 = { by lemma 68 }
% 201.76/26.07 join(complement(X), meet(X, complement(Y)))
% 201.76/26.07 = { by lemma 66 }
% 201.76/26.07 complement(meet(X, join(Y, complement(X))))
% 201.76/26.07
% 201.76/26.07 Lemma 71: composition(converse(complement(composition(sk1, top))), composition(sk1, top)) = zero.
% 201.76/26.07 Proof:
% 201.76/26.07 composition(converse(complement(composition(sk1, top))), composition(sk1, top))
% 201.76/26.07 = { by lemma 19 R->L }
% 201.76/26.07 converse(composition(converse(composition(sk1, top)), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 38 R->L }
% 201.76/26.07 converse(join(composition(converse(composition(sk1, top)), complement(composition(sk1, top))), zero))
% 201.76/26.07 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.07 converse(join(zero, composition(converse(composition(sk1, top)), complement(composition(sk1, top)))))
% 201.76/26.07 = { by lemma 17 R->L }
% 201.76/26.07 converse(join(complement(top), composition(converse(composition(sk1, top)), complement(composition(sk1, top)))))
% 201.76/26.07 = { by axiom 4 (goals_17) R->L }
% 201.76/26.07 converse(join(complement(top), composition(converse(composition(sk1, top)), complement(composition(composition(sk1, top), top)))))
% 201.76/26.07 = { by lemma 22 }
% 201.76/26.07 converse(complement(top))
% 201.76/26.07 = { by lemma 17 }
% 201.76/26.07 converse(zero)
% 201.76/26.07 = { by lemma 47 }
% 201.76/26.07 zero
% 201.76/26.07
% 201.76/26.07 Lemma 72: meet(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), X)) = composition(complement(composition(sk1, top)), X).
% 201.76/26.07 Proof:
% 201.76/26.07 meet(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), X))
% 201.76/26.07 = { by lemma 40 }
% 201.76/26.07 meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top)))
% 201.76/26.07 = { by lemma 39 R->L }
% 201.76/26.07 join(zero, meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 50 R->L }
% 201.76/26.07 join(meet(zero, composition(sk1, top)), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 52 R->L }
% 201.76/26.07 join(meet(composition(complement(composition(sk1, top)), zero), composition(sk1, top)), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 43 R->L }
% 201.76/26.07 join(meet(composition(complement(composition(sk1, top)), meet(X, zero)), composition(sk1, top)), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 71 R->L }
% 201.76/26.07 join(meet(composition(complement(composition(sk1, top)), meet(X, composition(converse(complement(composition(sk1, top))), composition(sk1, top)))), composition(sk1, top)), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by axiom 15 (modular_law_1_15) R->L }
% 201.76/26.07 join(join(meet(composition(complement(composition(sk1, top)), X), composition(sk1, top)), meet(composition(complement(composition(sk1, top)), meet(X, composition(converse(complement(composition(sk1, top))), composition(sk1, top)))), composition(sk1, top))), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 71 }
% 201.76/26.07 join(join(meet(composition(complement(composition(sk1, top)), X), composition(sk1, top)), meet(composition(complement(composition(sk1, top)), meet(X, zero)), composition(sk1, top))), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 43 }
% 201.76/26.07 join(join(meet(composition(complement(composition(sk1, top)), X), composition(sk1, top)), meet(composition(complement(composition(sk1, top)), zero), composition(sk1, top))), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 52 }
% 201.76/26.07 join(join(meet(composition(complement(composition(sk1, top)), X), composition(sk1, top)), meet(zero, composition(sk1, top))), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 50 }
% 201.76/26.07 join(join(meet(composition(complement(composition(sk1, top)), X), composition(sk1, top)), zero), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 38 }
% 201.76/26.07 join(meet(composition(complement(composition(sk1, top)), X), composition(sk1, top)), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 40 R->L }
% 201.76/26.07 join(meet(composition(sk1, top), composition(complement(composition(sk1, top)), X)), meet(composition(complement(composition(sk1, top)), X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 68 }
% 201.76/26.07 composition(complement(composition(sk1, top)), X)
% 201.76/26.07
% 201.76/26.07 Lemma 73: meet(meet(sk1, X), composition(complement(composition(sk1, top)), Y)) = zero.
% 201.76/26.07 Proof:
% 201.76/26.07 meet(meet(sk1, X), composition(complement(composition(sk1, top)), Y))
% 201.76/26.07 = { by lemma 72 R->L }
% 201.76/26.07 meet(meet(sk1, X), meet(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), Y)))
% 201.76/26.07 = { by lemma 40 }
% 201.76/26.07 meet(meet(sk1, X), meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 62 }
% 201.76/26.07 meet(complement(composition(sk1, top)), meet(meet(sk1, X), composition(complement(composition(sk1, top)), Y)))
% 201.76/26.07 = { by lemma 61 }
% 201.76/26.07 meet(composition(complement(composition(sk1, top)), Y), meet(meet(sk1, X), complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 56 R->L }
% 201.76/26.07 meet(composition(complement(composition(sk1, top)), Y), complement(join(composition(sk1, top), complement(meet(sk1, X)))))
% 201.76/26.07 = { by axiom 4 (goals_17) }
% 201.76/26.07 meet(composition(complement(composition(sk1, top)), Y), complement(join(sk1, complement(meet(sk1, X)))))
% 201.76/26.07 = { by lemma 63 }
% 201.76/26.07 meet(composition(complement(composition(sk1, top)), Y), complement(top))
% 201.76/26.07 = { by lemma 17 }
% 201.76/26.07 meet(composition(complement(composition(sk1, top)), Y), zero)
% 201.76/26.07 = { by lemma 43 }
% 201.76/26.07 zero
% 201.76/26.07
% 201.76/26.07 Lemma 74: meet(composition(sk1, top), join(X, composition(complement(composition(sk1, top)), Y))) = meet(X, composition(sk1, top)).
% 201.76/26.07 Proof:
% 201.76/26.07 meet(composition(sk1, top), join(X, composition(complement(composition(sk1, top)), Y)))
% 201.76/26.07 = { by lemma 49 R->L }
% 201.76/26.07 meet(complement(complement(composition(sk1, top))), join(X, composition(complement(composition(sk1, top)), Y)))
% 201.76/26.07 = { by lemma 72 R->L }
% 201.76/26.07 meet(complement(complement(composition(sk1, top))), join(X, meet(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), Y))))
% 201.76/26.07 = { by lemma 40 }
% 201.76/26.07 meet(complement(complement(composition(sk1, top))), join(X, meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))))
% 201.76/26.07 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.07 meet(complement(complement(composition(sk1, top))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X))
% 201.76/26.07 = { by lemma 40 }
% 201.76/26.07 meet(join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), complement(complement(composition(sk1, top))))
% 201.76/26.07 = { by lemma 68 R->L }
% 201.76/26.07 meet(join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), complement(join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))))))
% 201.76/26.07 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 201.76/26.07 meet(join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))))))
% 201.76/26.07 = { by lemma 67 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)))))
% 201.76/26.07 = { by lemma 60 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), complement(X)))))
% 201.76/26.07 = { by lemma 56 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(join(X, complement(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))))))))))
% 201.76/26.07 = { by lemma 59 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), complement(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), join(X, complement(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))))))))))
% 201.76/26.07 = { by lemma 70 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), complement(meet(X, join(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), complement(X))))))
% 201.76/26.07 = { by lemma 55 }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), complement(meet(X, complement(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X))))))
% 201.76/26.07 = { by lemma 58 }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), complement(X))))
% 201.76/26.07 = { by lemma 69 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), complement(join(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X))))))
% 201.76/26.07 = { by lemma 60 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), meet(complement(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)), complement(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X))))))
% 201.76/26.07 = { by lemma 56 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), complement(join(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X), complement(complement(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X))))))))
% 201.76/26.07 = { by lemma 59 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), complement(meet(complement(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)), join(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X), complement(complement(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X))))))))
% 201.76/26.07 = { by lemma 70 }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), complement(meet(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X), join(complement(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)), complement(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X)))))))
% 201.76/26.07 = { by lemma 55 }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), complement(meet(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X), complement(meet(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X)))))))
% 201.76/26.07 = { by lemma 58 }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X)), complement(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X)))))
% 201.76/26.07 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(complement(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X)), meet(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X)))))
% 201.76/26.07 = { by lemma 40 R->L }
% 201.76/26.07 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(complement(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X)), meet(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X), meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)))))
% 201.76/26.08 = { by lemma 59 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(X)), meet(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X), meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)))))
% 201.76/26.08 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), join(complement(X), meet(meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X), meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X))))))
% 201.76/26.08 = { by lemma 40 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), join(complement(X), meet(meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X), meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X))))))
% 201.76/26.08 = { by lemma 62 R->L }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), join(complement(X), meet(complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), meet(X, meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)))))))
% 201.76/26.08 = { by lemma 40 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), join(complement(X), meet(meet(X, meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)), complement(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))))))))
% 201.76/26.08 = { by lemma 66 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, meet(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), X)))))))))
% 201.76/26.08 = { by lemma 40 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, meet(X, meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))))))))))))
% 201.76/26.08 = { by lemma 40 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(meet(X, meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), X))))))))
% 201.76/26.08 = { by lemma 32 R->L }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(meet(X, meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), join(meet(X, meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))), complement(join(complement(X), meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))))))))))))))
% 201.76/26.08 = { by lemma 65 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top)))))))))))
% 201.76/26.08 = { by lemma 64 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(meet(X, top)))))
% 201.76/26.08 = { by lemma 45 }
% 201.76/26.08 complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), complement(X))))
% 201.76/26.08 = { by lemma 67 }
% 201.76/26.08 meet(X, complement(join(meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))), meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))))))
% 201.76/26.08 = { by axiom 2 (maddux1_join_commutativity_1) }
% 201.76/26.08 meet(X, complement(join(meet(composition(complement(composition(sk1, top)), Y), complement(composition(sk1, top))), meet(complement(composition(sk1, top)), complement(composition(complement(composition(sk1, top)), Y))))))
% 201.76/26.08 = { by lemma 68 }
% 201.76/26.08 meet(X, complement(complement(composition(sk1, top))))
% 201.76/26.08 = { by lemma 49 }
% 201.76/26.08 meet(X, composition(sk1, top))
% 201.76/26.08
% 201.76/26.08 Goal 1 (goals_18): composition(meet(sk1, sk2), sk3) = meet(sk1, composition(sk2, sk3)).
% 201.76/26.08 Proof:
% 201.76/26.08 composition(meet(sk1, sk2), sk3)
% 201.76/26.08 = { by lemma 32 R->L }
% 201.76/26.08 join(meet(composition(meet(sk1, sk2), sk3), complement(composition(sk1, top))), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 38 R->L }
% 201.76/26.08 join(join(meet(composition(meet(sk1, sk2), sk3), complement(composition(sk1, top))), zero), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 50 R->L }
% 201.76/26.08 join(join(meet(composition(meet(sk1, sk2), sk3), complement(composition(sk1, top))), meet(zero, complement(composition(sk1, top)))), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 53 R->L }
% 201.76/26.08 join(join(meet(composition(meet(sk1, sk2), sk3), complement(composition(sk1, top))), meet(composition(zero, sk3), complement(composition(sk1, top)))), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 73 R->L }
% 201.76/26.08 join(join(meet(composition(meet(sk1, sk2), sk3), complement(composition(sk1, top))), meet(composition(meet(meet(sk1, sk2), composition(complement(composition(sk1, top)), converse(sk3))), sk3), complement(composition(sk1, top)))), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by axiom 16 (modular_law_2_16) }
% 201.76/26.08 join(meet(composition(meet(meet(sk1, sk2), composition(complement(composition(sk1, top)), converse(sk3))), sk3), complement(composition(sk1, top))), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 73 }
% 201.76/26.08 join(meet(composition(zero, sk3), complement(composition(sk1, top))), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 53 }
% 201.76/26.08 join(meet(zero, complement(composition(sk1, top))), complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 50 }
% 201.76/26.08 join(zero, complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top)))))
% 201.76/26.08 = { by lemma 37 }
% 201.76/26.08 complement(join(complement(composition(meet(sk1, sk2), sk3)), complement(composition(sk1, top))))
% 201.76/26.08 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 201.76/26.08 meet(composition(meet(sk1, sk2), sk3), composition(sk1, top))
% 201.76/26.08 = { by lemma 74 R->L }
% 201.76/26.08 meet(composition(sk1, top), join(composition(meet(sk1, sk2), sk3), composition(complement(composition(sk1, top)), sk3)))
% 201.76/26.08 = { by axiom 12 (composition_distributivity_7) R->L }
% 201.76/26.08 meet(composition(sk1, top), composition(join(meet(sk1, sk2), complement(composition(sk1, top))), sk3))
% 201.76/26.08 = { by lemma 49 R->L }
% 201.76/26.08 meet(composition(sk1, top), composition(complement(complement(join(meet(sk1, sk2), complement(composition(sk1, top))))), sk3))
% 201.76/26.08 = { by lemma 65 R->L }
% 201.76/26.08 meet(composition(sk1, top), composition(complement(meet(complement(join(meet(sk1, sk2), complement(composition(sk1, top)))), join(complement(join(meet(sk1, sk2), complement(composition(sk1, top)))), complement(sk2)))), sk3))
% 202.48/26.08 = { by lemma 59 }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), complement(join(complement(join(meet(sk1, sk2), complement(composition(sk1, top)))), complement(sk2)))), sk3))
% 202.48/26.08 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), meet(join(meet(sk1, sk2), complement(composition(sk1, top))), sk2)), sk3))
% 202.48/26.08 = { by lemma 40 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), meet(sk2, join(meet(sk1, sk2), complement(composition(sk1, top))))), sk3))
% 202.48/26.08 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), meet(sk2, join(complement(composition(sk1, top)), meet(sk1, sk2)))), sk3))
% 202.48/26.08 = { by axiom 4 (goals_17) }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), meet(sk2, join(complement(sk1), meet(sk1, sk2)))), sk3))
% 202.48/26.08 = { by lemma 40 }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), meet(sk2, join(complement(sk1), meet(sk2, sk1)))), sk3))
% 202.48/26.08 = { by lemma 38 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), join(meet(sk2, join(complement(sk1), meet(sk2, sk1))), zero)), sk3))
% 202.48/26.08 = { by lemma 17 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), join(meet(sk2, join(complement(sk1), meet(sk2, sk1))), complement(top))), sk3))
% 202.48/26.08 = { by axiom 5 (def_top_12) }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), join(meet(sk2, join(complement(sk1), meet(sk2, sk1))), complement(join(join(complement(sk2), complement(sk1)), complement(join(complement(sk2), complement(sk1))))))), sk3))
% 202.48/26.08 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), join(meet(sk2, join(complement(sk1), meet(sk2, sk1))), complement(join(join(complement(sk2), complement(sk1)), meet(sk2, sk1))))), sk3))
% 202.48/26.08 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), join(meet(sk2, join(complement(sk1), meet(sk2, sk1))), complement(join(complement(sk2), join(complement(sk1), meet(sk2, sk1)))))), sk3))
% 202.48/26.08 = { by lemma 32 }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), complement(composition(sk1, top))), sk2), sk3))
% 202.48/26.08 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(meet(sk1, sk2), join(complement(composition(sk1, top)), sk2)), sk3))
% 202.48/26.08 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(meet(sk1, sk2), join(sk2, complement(composition(sk1, top)))), sk3))
% 202.48/26.08 = { by axiom 8 (maddux2_join_associativity_2) }
% 202.48/26.08 meet(composition(sk1, top), composition(join(join(meet(sk1, sk2), sk2), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 45 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(meet(join(meet(sk1, sk2), sk2), top), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 41 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, complement(join(meet(sk1, sk2), sk2)))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, complement(join(sk2, meet(sk1, sk2))))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 60 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, meet(complement(sk2), complement(meet(sk1, sk2))))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 39 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, join(zero, meet(complement(sk2), complement(meet(sk1, sk2)))))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 17 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, join(complement(top), meet(complement(sk2), complement(meet(sk1, sk2)))))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 64 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, join(complement(join(sk2, complement(meet(sk1, sk2)))), meet(complement(sk2), complement(meet(sk1, sk2)))))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 56 }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, join(meet(meet(sk1, sk2), complement(sk2)), meet(complement(sk2), complement(meet(sk1, sk2)))))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 68 }
% 202.48/26.08 meet(composition(sk1, top), composition(join(complement(join(zero, complement(sk2))), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 41 }
% 202.48/26.08 meet(composition(sk1, top), composition(join(meet(sk2, top), complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by lemma 45 }
% 202.48/26.08 meet(composition(sk1, top), composition(join(sk2, complement(composition(sk1, top))), sk3))
% 202.48/26.08 = { by axiom 12 (composition_distributivity_7) }
% 202.48/26.08 meet(composition(sk1, top), join(composition(sk2, sk3), composition(complement(composition(sk1, top)), sk3)))
% 202.48/26.08 = { by lemma 74 }
% 202.48/26.08 meet(composition(sk2, sk3), composition(sk1, top))
% 202.48/26.08 = { by lemma 40 R->L }
% 202.48/26.08 meet(composition(sk1, top), composition(sk2, sk3))
% 202.48/26.08 = { by axiom 4 (goals_17) }
% 202.48/26.08 meet(sk1, composition(sk2, sk3))
% 202.48/26.08 % SZS output end Proof
% 202.48/26.08
% 202.48/26.08 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------