TSTP Solution File: REL027-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL027-2 : 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 13:44:08 EDT 2023
% Result : Unsatisfiable 15.90s 2.38s
% Output : Proof 17.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL027-2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 19:00:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 15.90/2.38 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 15.90/2.38
% 15.90/2.38 % SZS status Unsatisfiable
% 15.90/2.38
% 16.38/2.50 % SZS output start Proof
% 16.38/2.50 Take the following subset of the input axioms:
% 16.38/2.50 fof(composition_associativity_5, axiom, ![A, B, C]: composition(A, composition(B, C))=composition(composition(A, B), C)).
% 16.38/2.50 fof(composition_distributivity_7, axiom, ![A2, B2, C2]: composition(join(A2, B2), C2)=join(composition(A2, C2), composition(B2, C2))).
% 16.38/2.50 fof(composition_identity_6, axiom, ![A2]: composition(A2, one)=A2).
% 16.38/2.50 fof(converse_additivity_9, axiom, ![A2, B2]: converse(join(A2, B2))=join(converse(A2), converse(B2))).
% 16.38/2.50 fof(converse_cancellativity_11, axiom, ![A2, B2]: join(composition(converse(A2), complement(composition(A2, B2))), complement(B2))=complement(B2)).
% 16.38/2.50 fof(converse_idempotence_8, axiom, ![A2]: converse(converse(A2))=A2).
% 16.38/2.50 fof(converse_multiplicativity_10, axiom, ![A2, B2]: converse(composition(A2, B2))=composition(converse(B2), converse(A2))).
% 16.38/2.50 fof(def_top_12, axiom, ![A2]: top=join(A2, complement(A2))).
% 16.38/2.50 fof(def_zero_13, axiom, ![A2]: zero=meet(A2, complement(A2))).
% 16.38/2.50 fof(goals_14, negated_conjecture, join(sk1, one)=one).
% 16.38/2.50 fof(goals_15, negated_conjecture, join(meet(complement(sk1), one), meet(complement(composition(sk1, top)), one))!=meet(complement(composition(sk1, top)), one) | join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one))!=meet(complement(sk1), one)).
% 16.38/2.50 fof(maddux1_join_commutativity_1, axiom, ![A2, B2]: join(A2, B2)=join(B2, A2)).
% 16.38/2.50 fof(maddux2_join_associativity_2, axiom, ![A2, B2, C2]: join(A2, join(B2, C2))=join(join(A2, B2), C2)).
% 16.38/2.50 fof(maddux3_a_kind_of_de_Morgan_3, axiom, ![A2, B2]: A2=join(complement(join(complement(A2), complement(B2))), complement(join(complement(A2), B2)))).
% 16.38/2.50 fof(maddux4_definiton_of_meet_4, axiom, ![A2, B2]: meet(A2, B2)=complement(join(complement(A2), complement(B2)))).
% 16.38/2.50
% 16.38/2.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.38/2.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.38/2.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.38/2.50 fresh(y, y, x1...xn) = u
% 16.38/2.50 C => fresh(s, t, x1...xn) = v
% 16.38/2.50 where fresh is a fresh function symbol and x1..xn are the free
% 16.38/2.50 variables of u and v.
% 16.38/2.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.38/2.50 input problem has no model of domain size 1).
% 16.38/2.50
% 16.38/2.50 The encoding turns the above axioms into the following unit equations and goals:
% 16.38/2.50
% 16.38/2.50 Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 16.38/2.50 Axiom 2 (goals_14): join(sk1, one) = one.
% 16.38/2.50 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 16.38/2.50 Axiom 4 (converse_idempotence_8): converse(converse(X)) = X.
% 16.38/2.50 Axiom 5 (def_top_12): top = join(X, complement(X)).
% 16.38/2.50 Axiom 6 (def_zero_13): zero = meet(X, complement(X)).
% 16.38/2.50 Axiom 7 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 16.38/2.50 Axiom 8 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 16.38/2.50 Axiom 9 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 16.38/2.50 Axiom 10 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 16.38/2.50 Axiom 11 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 16.38/2.50 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 16.38/2.50 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 16.38/2.50 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 16.38/2.50
% 16.38/2.50 Lemma 15: complement(top) = zero.
% 16.38/2.50 Proof:
% 16.38/2.50 complement(top)
% 16.38/2.50 = { by axiom 5 (def_top_12) }
% 16.38/2.50 complement(join(complement(X), complement(complement(X))))
% 16.38/2.50 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 16.38/2.50 meet(X, complement(X))
% 16.38/2.50 = { by axiom 6 (def_zero_13) R->L }
% 16.38/2.50 zero
% 16.38/2.50
% 16.38/2.50 Lemma 16: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 join(meet(X, Y), complement(join(complement(X), Y)))
% 16.38/2.50 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 16.38/2.50 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 16.38/2.50 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 17: join(zero, meet(X, X)) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 join(zero, meet(X, X))
% 16.38/2.50 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 16.38/2.50 join(zero, complement(join(complement(X), complement(X))))
% 16.38/2.50 = { by axiom 6 (def_zero_13) }
% 16.38/2.50 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 16.38/2.50 = { by lemma 16 }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 18: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 16.38/2.50 Proof:
% 16.38/2.50 converse(composition(converse(X), Y))
% 16.38/2.50 = { by axiom 9 (converse_multiplicativity_10) }
% 16.38/2.50 composition(converse(Y), converse(converse(X)))
% 16.38/2.50 = { by axiom 4 (converse_idempotence_8) }
% 16.38/2.50 composition(converse(Y), X)
% 16.38/2.50
% 16.38/2.50 Lemma 19: composition(converse(one), X) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 composition(converse(one), X)
% 16.38/2.50 = { by lemma 18 R->L }
% 16.38/2.50 converse(composition(converse(X), one))
% 16.38/2.50 = { by axiom 3 (composition_identity_6) }
% 16.38/2.50 converse(converse(X))
% 16.38/2.50 = { by axiom 4 (converse_idempotence_8) }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 20: composition(one, X) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 composition(one, X)
% 16.38/2.50 = { by lemma 19 R->L }
% 16.38/2.50 composition(converse(one), composition(one, X))
% 16.38/2.50 = { by axiom 10 (composition_associativity_5) }
% 16.38/2.50 composition(composition(converse(one), one), X)
% 16.38/2.50 = { by axiom 3 (composition_identity_6) }
% 16.38/2.50 composition(converse(one), X)
% 16.38/2.50 = { by lemma 19 }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 21: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 16.38/2.50 Proof:
% 16.38/2.50 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 16.38/2.50 = { by axiom 13 (converse_cancellativity_11) }
% 16.38/2.50 complement(X)
% 16.38/2.50
% 16.38/2.50 Lemma 22: join(complement(X), complement(X)) = complement(X).
% 16.38/2.50 Proof:
% 16.38/2.50 join(complement(X), complement(X))
% 16.38/2.50 = { by lemma 19 R->L }
% 16.38/2.50 join(complement(X), composition(converse(one), complement(X)))
% 16.38/2.50 = { by lemma 20 R->L }
% 16.38/2.50 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 16.38/2.50 = { by lemma 21 }
% 16.38/2.50 complement(X)
% 16.38/2.50
% 16.38/2.50 Lemma 23: join(zero, zero) = zero.
% 16.38/2.50 Proof:
% 16.38/2.50 join(zero, zero)
% 16.38/2.50 = { by lemma 15 R->L }
% 16.38/2.50 join(zero, complement(top))
% 16.38/2.50 = { by lemma 15 R->L }
% 16.38/2.50 join(complement(top), complement(top))
% 16.38/2.50 = { by lemma 22 }
% 16.38/2.50 complement(top)
% 16.38/2.50 = { by lemma 15 }
% 16.38/2.50 zero
% 16.38/2.50
% 16.38/2.50 Lemma 24: join(zero, join(zero, X)) = join(X, zero).
% 16.38/2.50 Proof:
% 16.38/2.50 join(zero, join(zero, X))
% 16.38/2.50 = { by axiom 8 (maddux2_join_associativity_2) }
% 16.38/2.50 join(join(zero, zero), X)
% 16.38/2.50 = { by lemma 23 }
% 16.38/2.50 join(zero, X)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) }
% 16.38/2.50 join(X, zero)
% 16.38/2.50
% 16.38/2.50 Lemma 25: join(zero, complement(complement(X))) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 join(zero, complement(complement(X)))
% 16.38/2.50 = { by axiom 6 (def_zero_13) }
% 16.38/2.50 join(meet(X, complement(X)), complement(complement(X)))
% 16.38/2.50 = { by lemma 22 R->L }
% 16.38/2.50 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 16.38/2.50 = { by lemma 16 }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 26: join(X, zero) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 join(X, zero)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 join(zero, X)
% 16.38/2.50 = { by lemma 17 R->L }
% 16.38/2.50 join(zero, join(zero, meet(X, X)))
% 16.38/2.50 = { by lemma 24 }
% 16.38/2.50 join(meet(X, X), zero)
% 16.38/2.50 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 16.38/2.50 join(complement(join(complement(X), complement(X))), zero)
% 16.38/2.50 = { by lemma 22 }
% 16.38/2.50 join(complement(complement(X)), zero)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) }
% 16.38/2.50 join(zero, complement(complement(X)))
% 16.38/2.50 = { by lemma 25 }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 27: join(zero, X) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 join(zero, X)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 join(X, zero)
% 16.38/2.50 = { by lemma 26 }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 28: complement(zero) = top.
% 16.38/2.50 Proof:
% 16.38/2.50 complement(zero)
% 16.38/2.50 = { by lemma 27 R->L }
% 16.38/2.50 join(zero, complement(zero))
% 16.38/2.50 = { by axiom 5 (def_top_12) R->L }
% 16.38/2.50 top
% 16.38/2.50
% 16.38/2.50 Lemma 29: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 16.38/2.50 Proof:
% 16.38/2.50 converse(join(X, converse(Y)))
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 converse(join(converse(Y), X))
% 16.38/2.50 = { by axiom 7 (converse_additivity_9) }
% 16.38/2.50 join(converse(converse(Y)), converse(X))
% 16.38/2.50 = { by axiom 4 (converse_idempotence_8) }
% 16.38/2.50 join(Y, converse(X))
% 16.38/2.50
% 16.38/2.50 Lemma 30: join(X, join(Y, complement(X))) = join(Y, top).
% 16.38/2.50 Proof:
% 16.38/2.50 join(X, join(Y, complement(X)))
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 join(X, join(complement(X), Y))
% 16.38/2.50 = { by axiom 8 (maddux2_join_associativity_2) }
% 16.38/2.50 join(join(X, complement(X)), Y)
% 16.38/2.50 = { by axiom 5 (def_top_12) R->L }
% 16.38/2.50 join(top, Y)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) }
% 16.38/2.50 join(Y, top)
% 16.38/2.50
% 16.38/2.50 Lemma 31: join(top, complement(X)) = top.
% 16.38/2.50 Proof:
% 16.38/2.50 join(top, complement(X))
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 join(complement(X), top)
% 16.38/2.50 = { by lemma 30 R->L }
% 16.38/2.50 join(X, join(complement(X), complement(X)))
% 16.38/2.50 = { by lemma 22 }
% 16.38/2.50 join(X, complement(X))
% 16.38/2.50 = { by axiom 5 (def_top_12) R->L }
% 16.38/2.50 top
% 16.38/2.50
% 16.38/2.50 Lemma 32: join(Y, top) = join(X, top).
% 16.38/2.50 Proof:
% 16.38/2.50 join(Y, top)
% 16.38/2.50 = { by lemma 31 R->L }
% 16.38/2.50 join(Y, join(top, complement(Y)))
% 16.38/2.50 = { by lemma 30 }
% 16.38/2.50 join(top, top)
% 16.38/2.50 = { by lemma 30 R->L }
% 16.38/2.50 join(X, join(top, complement(X)))
% 16.38/2.50 = { by lemma 31 }
% 16.38/2.50 join(X, top)
% 16.38/2.50
% 16.38/2.50 Lemma 33: join(sk1, join(one, X)) = join(X, one).
% 16.38/2.50 Proof:
% 16.38/2.50 join(sk1, join(one, X))
% 16.38/2.50 = { by axiom 8 (maddux2_join_associativity_2) }
% 16.38/2.50 join(join(sk1, one), X)
% 16.38/2.50 = { by axiom 2 (goals_14) }
% 16.38/2.50 join(one, X)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) }
% 16.38/2.50 join(X, one)
% 16.38/2.50
% 16.38/2.50 Lemma 34: join(X, top) = top.
% 16.38/2.50 Proof:
% 16.38/2.50 join(X, top)
% 16.38/2.50 = { by lemma 32 }
% 16.38/2.50 join(sk1, top)
% 16.38/2.50 = { by axiom 5 (def_top_12) }
% 16.38/2.50 join(sk1, join(one, complement(one)))
% 16.38/2.50 = { by lemma 33 }
% 16.38/2.50 join(complement(one), one)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) }
% 16.38/2.50 join(one, complement(one))
% 16.38/2.50 = { by axiom 5 (def_top_12) R->L }
% 16.38/2.50 top
% 16.38/2.50
% 16.38/2.50 Lemma 35: join(top, X) = top.
% 16.38/2.50 Proof:
% 16.38/2.50 join(top, X)
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 join(X, top)
% 16.38/2.50 = { by lemma 32 R->L }
% 16.38/2.50 join(Y, top)
% 16.38/2.50 = { by lemma 34 }
% 16.38/2.50 top
% 16.38/2.50
% 16.38/2.50 Lemma 36: join(X, converse(top)) = converse(top).
% 16.38/2.50 Proof:
% 16.38/2.50 join(X, converse(top))
% 16.38/2.50 = { by lemma 29 R->L }
% 16.38/2.50 converse(join(top, converse(X)))
% 16.38/2.50 = { by lemma 35 }
% 16.38/2.50 converse(top)
% 16.38/2.50
% 16.38/2.50 Lemma 37: converse(top) = top.
% 16.38/2.50 Proof:
% 16.38/2.50 converse(top)
% 16.38/2.50 = { by lemma 36 R->L }
% 16.38/2.50 join(X, converse(top))
% 16.38/2.50 = { by lemma 36 R->L }
% 16.38/2.50 join(X, join(complement(X), converse(top)))
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 join(X, join(converse(top), complement(X)))
% 16.38/2.50 = { by lemma 30 }
% 16.38/2.50 join(converse(top), top)
% 16.38/2.50 = { by lemma 34 }
% 16.38/2.50 top
% 16.38/2.50
% 16.38/2.50 Lemma 38: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 16.38/2.50 Proof:
% 16.38/2.50 converse(join(converse(X), Y))
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 converse(join(Y, converse(X)))
% 16.38/2.50 = { by lemma 29 }
% 16.38/2.50 join(X, converse(Y))
% 16.38/2.50
% 16.38/2.50 Lemma 39: converse(zero) = zero.
% 16.38/2.50 Proof:
% 16.38/2.50 converse(zero)
% 16.38/2.50 = { by lemma 26 R->L }
% 16.38/2.50 join(converse(zero), zero)
% 16.38/2.50 = { by lemma 24 R->L }
% 16.38/2.50 join(zero, join(zero, converse(zero)))
% 16.38/2.50 = { by lemma 38 R->L }
% 16.38/2.50 join(zero, converse(join(converse(zero), zero)))
% 16.38/2.50 = { by lemma 26 }
% 16.38/2.50 join(zero, converse(converse(zero)))
% 16.38/2.50 = { by axiom 4 (converse_idempotence_8) }
% 16.38/2.50 join(zero, zero)
% 16.38/2.50 = { by lemma 23 }
% 16.38/2.50 zero
% 16.38/2.50
% 16.38/2.50 Lemma 40: complement(complement(X)) = X.
% 16.38/2.50 Proof:
% 16.38/2.50 complement(complement(X))
% 16.38/2.50 = { by lemma 27 R->L }
% 16.38/2.50 join(zero, complement(complement(X)))
% 16.38/2.50 = { by lemma 25 }
% 16.38/2.50 X
% 16.38/2.50
% 16.38/2.50 Lemma 41: meet(Y, X) = meet(X, Y).
% 16.38/2.50 Proof:
% 16.38/2.50 meet(Y, X)
% 16.38/2.50 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 16.38/2.50 complement(join(complement(Y), complement(X)))
% 16.38/2.50 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.50 complement(join(complement(X), complement(Y)))
% 16.38/2.50 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 16.38/2.50 meet(X, Y)
% 16.38/2.50
% 16.38/2.50 Lemma 42: complement(join(zero, complement(X))) = meet(X, top).
% 16.38/2.50 Proof:
% 16.38/2.50 complement(join(zero, complement(X)))
% 16.38/2.50 = { by lemma 15 R->L }
% 16.38/2.50 complement(join(complement(top), complement(X)))
% 16.38/2.50 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 16.38/2.50 meet(top, X)
% 16.38/2.50 = { by lemma 41 R->L }
% 16.38/2.50 meet(X, top)
% 16.38/2.51
% 16.38/2.51 Lemma 43: meet(X, top) = X.
% 16.38/2.51 Proof:
% 16.38/2.51 meet(X, top)
% 16.38/2.51 = { by lemma 42 R->L }
% 16.38/2.51 complement(join(zero, complement(X)))
% 16.38/2.51 = { by lemma 27 }
% 16.38/2.51 complement(complement(X))
% 16.38/2.51 = { by lemma 40 }
% 16.38/2.51 X
% 16.38/2.51
% 16.38/2.51 Lemma 44: composition(join(X, one), Y) = join(Y, composition(X, Y)).
% 16.38/2.51 Proof:
% 16.38/2.51 composition(join(X, one), Y)
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.51 composition(join(one, X), Y)
% 16.38/2.51 = { by axiom 12 (composition_distributivity_7) }
% 16.38/2.51 join(composition(one, Y), composition(X, Y))
% 16.38/2.51 = { by lemma 20 }
% 16.38/2.51 join(Y, composition(X, Y))
% 16.38/2.51
% 16.38/2.51 Lemma 45: composition(join(one, Y), X) = join(X, composition(Y, X)).
% 16.38/2.51 Proof:
% 16.38/2.51 composition(join(one, Y), X)
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.51 composition(join(Y, one), X)
% 16.38/2.51 = { by lemma 44 }
% 16.38/2.51 join(X, composition(Y, X))
% 16.38/2.51
% 16.38/2.51 Lemma 46: composition(top, zero) = zero.
% 16.38/2.51 Proof:
% 16.38/2.51 composition(top, zero)
% 16.38/2.51 = { by lemma 37 R->L }
% 16.38/2.51 composition(converse(top), zero)
% 16.38/2.51 = { by lemma 27 R->L }
% 16.38/2.51 join(zero, composition(converse(top), zero))
% 16.38/2.51 = { by lemma 15 R->L }
% 16.38/2.51 join(complement(top), composition(converse(top), zero))
% 16.38/2.51 = { by lemma 15 R->L }
% 16.38/2.51 join(complement(top), composition(converse(top), complement(top)))
% 16.38/2.51 = { by lemma 35 R->L }
% 16.38/2.51 join(complement(top), composition(converse(top), complement(join(top, composition(complement(sk1), top)))))
% 16.38/2.51 = { by lemma 45 R->L }
% 16.38/2.51 join(complement(top), composition(converse(top), complement(composition(join(one, complement(sk1)), top))))
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.51 join(complement(top), composition(converse(top), complement(composition(join(complement(sk1), one), top))))
% 16.38/2.51 = { by lemma 33 R->L }
% 16.38/2.51 join(complement(top), composition(converse(top), complement(composition(join(sk1, join(one, complement(sk1))), top))))
% 16.38/2.51 = { by lemma 30 }
% 16.38/2.51 join(complement(top), composition(converse(top), complement(composition(join(one, top), top))))
% 16.38/2.51 = { by lemma 34 }
% 16.38/2.51 join(complement(top), composition(converse(top), complement(composition(top, top))))
% 16.38/2.51 = { by lemma 21 }
% 16.38/2.51 complement(top)
% 16.38/2.51 = { by lemma 15 }
% 16.38/2.51 zero
% 16.38/2.51
% 16.38/2.51 Lemma 47: converse(composition(top, X)) = composition(converse(X), top).
% 16.38/2.51 Proof:
% 16.38/2.51 converse(composition(top, X))
% 16.38/2.51 = { by axiom 9 (converse_multiplicativity_10) }
% 16.38/2.51 composition(converse(X), converse(top))
% 16.38/2.51 = { by lemma 37 }
% 16.38/2.51 composition(converse(X), top)
% 16.38/2.51
% 16.38/2.51 Lemma 48: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 16.38/2.51 Proof:
% 16.38/2.51 meet(X, join(complement(Y), complement(Z)))
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.51 meet(X, join(complement(Z), complement(Y)))
% 16.38/2.51 = { by lemma 41 }
% 16.38/2.51 meet(join(complement(Z), complement(Y)), X)
% 16.38/2.51 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 16.38/2.51 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 16.38/2.51 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 16.38/2.51 complement(join(meet(Z, Y), complement(X)))
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) }
% 16.38/2.51 complement(join(complement(X), meet(Z, Y)))
% 16.38/2.51 = { by lemma 41 R->L }
% 16.38/2.51 complement(join(complement(X), meet(Y, Z)))
% 16.38/2.51
% 16.38/2.51 Lemma 49: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 16.38/2.51 Proof:
% 16.38/2.51 complement(join(X, complement(Y)))
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.51 complement(join(complement(Y), X))
% 16.38/2.51 = { by lemma 43 R->L }
% 16.38/2.51 complement(join(complement(Y), meet(X, top)))
% 16.38/2.51 = { by lemma 41 R->L }
% 16.38/2.51 complement(join(complement(Y), meet(top, X)))
% 16.38/2.51 = { by lemma 48 R->L }
% 16.38/2.51 meet(Y, join(complement(top), complement(X)))
% 16.38/2.51 = { by lemma 15 }
% 16.38/2.51 meet(Y, join(zero, complement(X)))
% 16.38/2.51 = { by lemma 27 }
% 16.38/2.51 meet(Y, complement(X))
% 16.38/2.51
% 16.38/2.51 Lemma 50: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 16.38/2.51 Proof:
% 16.38/2.51 complement(meet(X, complement(Y)))
% 16.38/2.51 = { by lemma 27 R->L }
% 16.38/2.51 complement(join(zero, meet(X, complement(Y))))
% 16.38/2.51 = { by lemma 49 R->L }
% 16.38/2.51 complement(join(zero, complement(join(Y, complement(X)))))
% 16.38/2.51 = { by lemma 42 }
% 16.38/2.51 meet(join(Y, complement(X)), top)
% 16.38/2.51 = { by lemma 43 }
% 16.38/2.51 join(Y, complement(X))
% 16.38/2.51
% 16.38/2.51 Lemma 51: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 16.38/2.51 Proof:
% 16.38/2.51 complement(meet(complement(X), Y))
% 16.38/2.51 = { by lemma 41 }
% 16.38/2.51 complement(meet(Y, complement(X)))
% 16.38/2.51 = { by lemma 50 }
% 16.38/2.51 join(X, complement(Y))
% 16.38/2.51
% 16.38/2.51 Lemma 52: converse(composition(X, converse(Y))) = composition(Y, converse(X)).
% 16.38/2.51 Proof:
% 16.38/2.51 converse(composition(X, converse(Y)))
% 16.38/2.51 = { by axiom 9 (converse_multiplicativity_10) }
% 16.38/2.51 composition(converse(converse(Y)), converse(X))
% 16.38/2.51 = { by axiom 4 (converse_idempotence_8) }
% 16.38/2.51 composition(Y, converse(X))
% 16.38/2.51
% 16.38/2.51 Lemma 53: composition(converse(X), complement(composition(X, top))) = zero.
% 16.38/2.51 Proof:
% 16.38/2.51 composition(converse(X), complement(composition(X, top)))
% 16.38/2.51 = { by lemma 27 R->L }
% 16.38/2.51 join(zero, composition(converse(X), complement(composition(X, top))))
% 16.38/2.51 = { by lemma 15 R->L }
% 16.38/2.51 join(complement(top), composition(converse(X), complement(composition(X, top))))
% 16.38/2.51 = { by lemma 21 }
% 16.38/2.51 complement(top)
% 16.38/2.51 = { by lemma 15 }
% 16.38/2.51 zero
% 16.38/2.51
% 16.38/2.51 Lemma 54: join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)) = meet(complement(sk1), one).
% 16.38/2.51 Proof:
% 16.38/2.51 join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one))
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.51 join(meet(complement(sk1), one), meet(complement(composition(sk1, top)), one))
% 16.38/2.51 = { by lemma 16 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(meet(meet(complement(composition(sk1, top)), one), complement(meet(complement(sk1), one))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 49 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(meet(complement(sk1), one), complement(meet(complement(composition(sk1, top)), one)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 41 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(meet(complement(sk1), one), complement(meet(one, complement(composition(sk1, top)))))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 50 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(meet(complement(sk1), one), join(composition(sk1, top), complement(one)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(meet(complement(sk1), one), join(complement(one), composition(sk1, top)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by axiom 8 (maddux2_join_associativity_2) }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(meet(complement(sk1), one), complement(one)), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by axiom 2 (goals_14) R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(meet(complement(sk1), one), complement(join(sk1, one))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 40 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(meet(complement(sk1), one), complement(join(complement(complement(sk1)), one))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 16 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(complement(sk1), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 21 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), composition(converse(converse(complement(composition(sk1, top)))), complement(composition(converse(complement(composition(sk1, top))), sk1)))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 18 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(composition(converse(sk1), complement(composition(sk1, top))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 53 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(zero)))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 39 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), composition(converse(converse(complement(composition(sk1, top)))), complement(zero))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by axiom 4 (converse_idempotence_8) }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), composition(complement(composition(sk1, top)), complement(zero))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 28 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), composition(complement(composition(sk1, top)), top)), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by axiom 4 (converse_idempotence_8) R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), composition(converse(converse(complement(composition(sk1, top)))), top)), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 47 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), converse(composition(top, converse(complement(composition(sk1, top)))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 34 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), converse(composition(join(one, top), converse(complement(composition(sk1, top)))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 45 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), converse(join(converse(complement(composition(sk1, top))), composition(top, converse(complement(composition(sk1, top))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 38 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), converse(composition(top, converse(complement(composition(sk1, top))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 47 }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), top))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by axiom 4 (converse_idempotence_8) }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), top))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.51 = { by lemma 28 R->L }
% 16.38/2.51 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(zero)))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by axiom 4 (converse_idempotence_8) R->L }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(zero)))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 39 R->L }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(zero))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 46 R->L }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(composition(top, zero)))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 35 R->L }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(composition(join(top, converse(top)), zero)))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by axiom 12 (composition_distributivity_7) }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(join(composition(top, zero), composition(converse(top), zero))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 46 }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(join(zero, composition(converse(top), zero))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 27 }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(composition(converse(top), zero)))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 53 R->L }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(composition(converse(top), composition(converse(sk1), complement(composition(sk1, top))))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by axiom 10 (composition_associativity_5) }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(composition(composition(converse(top), converse(sk1)), complement(composition(sk1, top)))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(converse(composition(converse(composition(sk1, top)), complement(composition(sk1, top)))))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 18 }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(composition(converse(complement(composition(sk1, top))), composition(sk1, top)))))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 16.38/2.52 = { by lemma 21 }
% 16.38/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(sk1), complement(composition(sk1, top))), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by axiom 1 (maddux1_join_commutativity_1) }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(composition(sk1, top)), complement(sk1)), composition(sk1, top))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(join(complement(composition(sk1, top)), join(complement(sk1), composition(sk1, top)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by axiom 1 (maddux1_join_commutativity_1) }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(join(complement(composition(sk1, top)), join(composition(sk1, top), complement(sk1)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by axiom 8 (maddux2_join_associativity_2) }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(join(join(complement(composition(sk1, top)), composition(sk1, top)), complement(sk1))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(join(join(composition(sk1, top), complement(composition(sk1, top))), complement(sk1))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by axiom 5 (def_top_12) R->L }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(join(top, complement(sk1))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by axiom 1 (maddux1_join_commutativity_1) }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(join(complement(sk1), top)), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by lemma 34 }
% 17.04/2.52 join(meet(complement(sk1), one), join(complement(top), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by lemma 15 }
% 17.04/2.52 join(meet(complement(sk1), one), join(zero, complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one))))))
% 17.04/2.52 = { by lemma 27 }
% 17.04/2.52 join(meet(complement(sk1), one), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(meet(complement(sk1), one)))))
% 17.04/2.52 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.04/2.52 join(meet(complement(sk1), one), meet(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))
% 17.04/2.52 = { by lemma 41 }
% 17.04/2.52 join(meet(complement(sk1), one), meet(meet(complement(sk1), one), meet(complement(composition(sk1, top)), one)))
% 17.04/2.52 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.04/2.52 join(meet(complement(sk1), one), complement(join(complement(meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.52 = { by lemma 51 R->L }
% 17.04/2.52 complement(meet(complement(meet(complement(sk1), one)), join(complement(meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.52 = { by lemma 26 R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), join(complement(meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))), zero))
% 17.04/2.52 = { by lemma 15 R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), join(complement(meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))), complement(top)))
% 17.04/2.52 = { by lemma 51 R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(top)))
% 17.04/2.52 = { by lemma 34 R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), top))))
% 17.04/2.52 = { by lemma 30 R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), join(complement(meet(complement(composition(sk1, top)), one)), complement(complement(complement(meet(complement(sk1), one)))))))))
% 17.04/2.52 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), join(complement(complement(complement(meet(complement(sk1), one)))), complement(meet(complement(composition(sk1, top)), one)))))))
% 17.04/2.52 = { by lemma 17 R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), join(zero, meet(join(complement(complement(complement(meet(complement(sk1), one)))), complement(meet(complement(composition(sk1, top)), one))), join(complement(complement(complement(meet(complement(sk1), one)))), complement(meet(complement(composition(sk1, top)), one)))))))))
% 17.04/2.52 = { by lemma 48 }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), join(zero, complement(join(complement(join(complement(complement(complement(meet(complement(sk1), one)))), complement(meet(complement(composition(sk1, top)), one)))), meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))))))))
% 17.04/2.52 = { by lemma 27 }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(join(complement(join(complement(complement(complement(meet(complement(sk1), one)))), complement(meet(complement(composition(sk1, top)), one)))), meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one))))))))
% 17.04/2.52 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(join(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)), meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one))))))))
% 17.04/2.52 = { by lemma 41 }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(join(meet(meet(complement(composition(sk1, top)), one), complement(complement(meet(complement(sk1), one)))), meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one))))))))
% 17.04/2.52 = { by lemma 41 }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(join(meet(meet(complement(composition(sk1, top)), one), complement(complement(meet(complement(sk1), one)))), meet(meet(complement(composition(sk1, top)), one), complement(complement(meet(complement(sk1), one))))))))))
% 17.04/2.52 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(join(meet(meet(complement(composition(sk1, top)), one), complement(complement(meet(complement(sk1), one)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(complement(complement(meet(complement(sk1), one))))))))))))
% 17.04/2.52 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(join(complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(complement(complement(meet(complement(sk1), one)))))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(complement(complement(meet(complement(sk1), one))))))))))))
% 17.04/2.52 = { by lemma 22 }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(complement(complement(meet(complement(sk1), one)))))))))))
% 17.04/2.52 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(meet(meet(complement(composition(sk1, top)), one), complement(complement(meet(complement(sk1), one)))))))))
% 17.04/2.52 = { by lemma 41 R->L }
% 17.04/2.52 complement(join(meet(complement(meet(complement(sk1), one)), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))), complement(join(complement(complement(meet(complement(sk1), one))), complement(meet(complement(complement(meet(complement(sk1), one))), meet(complement(composition(sk1, top)), one)))))))
% 17.04/2.52 = { by lemma 16 }
% 17.04/2.52 complement(complement(meet(complement(sk1), one)))
% 17.04/2.52 = { by lemma 40 }
% 17.04/2.53 meet(complement(sk1), one)
% 17.04/2.53
% 17.04/2.53 Goal 1 (goals_15): tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(sk1), one), meet(complement(composition(sk1, top)), one))) = tuple(meet(complement(sk1), one), meet(complement(composition(sk1, top)), one)).
% 17.04/2.53 Proof:
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(sk1), one), meet(complement(composition(sk1, top)), one)))
% 17.04/2.53 = { by axiom 1 (maddux1_join_commutativity_1) }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))
% 17.04/2.53 = { by lemma 16 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one))), complement(join(complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one))), complement(meet(complement(composition(sk1, top)), one))))))
% 17.04/2.53 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), meet(complement(composition(sk1, top)), one))))
% 17.04/2.53 = { by axiom 1 (maddux1_join_commutativity_1) }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), meet(complement(composition(sk1, top)), one)), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 41 }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(meet(complement(composition(sk1, top)), one), join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 27 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(zero, complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 15 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(complement(top), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 35 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(complement(join(top, meet(complement(sk1), one))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(complement(join(meet(complement(sk1), one), top)), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 30 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(complement(join(meet(complement(composition(sk1, top)), one), join(meet(complement(sk1), one), complement(meet(complement(composition(sk1, top)), one))))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by axiom 8 (maddux2_join_associativity_2) }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(complement(join(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 49 }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(meet(meet(complement(composition(sk1, top)), one), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))), complement(join(complement(meet(complement(composition(sk1, top)), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)))))), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 16 }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(composition(sk1, top)), one)))))
% 17.04/2.53 = { by lemma 41 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(one, complement(composition(sk1, top)))))))
% 17.04/2.53 = { by lemma 50 }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(composition(sk1, top), complement(one)))))
% 17.04/2.53 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), composition(sk1, top)))))
% 17.04/2.53 = { by axiom 5 (def_top_12) }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), composition(sk1, join(one, complement(one)))))))
% 17.04/2.53 = { by axiom 4 (converse_idempotence_8) R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), composition(sk1, join(one, converse(converse(complement(one)))))))))
% 17.04/2.53 = { by lemma 19 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), composition(sk1, join(composition(converse(one), one), converse(converse(complement(one)))))))))
% 17.04/2.53 = { by axiom 3 (composition_identity_6) }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), composition(sk1, join(converse(one), converse(converse(complement(one)))))))))
% 17.04/2.53 = { by axiom 7 (converse_additivity_9) R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), composition(sk1, converse(join(one, converse(complement(one)))))))))
% 17.04/2.53 = { by axiom 1 (maddux1_join_commutativity_1) }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), composition(sk1, converse(join(converse(complement(one)), one)))))))
% 17.04/2.53 = { by lemma 52 R->L }
% 17.04/2.53 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), converse(composition(join(converse(complement(one)), one), converse(sk1)))))))
% 17.04/2.54 = { by lemma 44 }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), converse(join(converse(sk1), composition(converse(complement(one)), converse(sk1))))))))
% 17.04/2.54 = { by lemma 38 }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), join(sk1, converse(composition(converse(complement(one)), converse(sk1))))))))
% 17.04/2.54 = { by lemma 52 }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), join(sk1, composition(sk1, converse(converse(complement(one)))))))))
% 17.04/2.54 = { by axiom 4 (converse_idempotence_8) }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), join(sk1, composition(sk1, complement(one)))))))
% 17.04/2.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), join(composition(sk1, complement(one)), sk1)))))
% 17.04/2.54 = { by axiom 8 (maddux2_join_associativity_2) }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(join(complement(one), composition(sk1, complement(one))), sk1))))
% 17.04/2.54 = { by lemma 44 R->L }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(composition(join(sk1, one), complement(one)), sk1))))
% 17.04/2.54 = { by axiom 2 (goals_14) }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(composition(one, complement(one)), sk1))))
% 17.04/2.54 = { by lemma 20 }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(complement(one), sk1))))
% 17.04/2.54 = { by axiom 1 (maddux1_join_commutativity_1) }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(sk1, complement(one)))))
% 17.04/2.54 = { by lemma 50 R->L }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(one, complement(sk1))))))
% 17.04/2.54 = { by lemma 41 }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(meet(complement(sk1), one)))))
% 17.04/2.54 = { by lemma 54 R->L }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), meet(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), complement(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one))))))
% 17.04/2.54 = { by axiom 6 (def_zero_13) R->L }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), join(meet(complement(composition(sk1, top)), one), zero))
% 17.04/2.54 = { by lemma 26 }
% 17.04/2.54 tuple(join(meet(complement(composition(sk1, top)), one), meet(complement(sk1), one)), meet(complement(composition(sk1, top)), one))
% 17.04/2.54 = { by lemma 54 }
% 17.04/2.54 tuple(meet(complement(sk1), one), meet(complement(composition(sk1, top)), one))
% 17.04/2.54 % SZS output end Proof
% 17.04/2.54
% 17.04/2.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------