TSTP Solution File: REL022-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL022-1 : 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 : n027.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 13:44:02 EDT 2023
% Result : Unsatisfiable 6.90s 1.23s
% Output : Proof 7.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL022-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 22:29:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 6.90/1.23 Command-line arguments: --flatten
% 6.90/1.23
% 6.90/1.23 % SZS status Unsatisfiable
% 6.90/1.23
% 6.90/1.38 % SZS output start Proof
% 6.90/1.38 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 6.90/1.38 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 6.90/1.38 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 6.90/1.38 Axiom 4 (goals_14): composition(sk1, top) = sk1.
% 6.90/1.38 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 6.90/1.38 Axiom 6 (def_top_12): top = join(X, complement(X)).
% 6.90/1.38 Axiom 7 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 6.90/1.38 Axiom 8 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 6.90/1.38 Axiom 9 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 6.90/1.38 Axiom 10 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 6.90/1.38 Axiom 11 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 6.90/1.38 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 6.90/1.38 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 6.90/1.38 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 6.90/1.38
% 6.90/1.38 Lemma 15: complement(top) = zero.
% 6.90/1.38 Proof:
% 6.90/1.38 complement(top)
% 6.90/1.38 = { by axiom 6 (def_top_12) }
% 6.90/1.38 complement(join(complement(X), complement(complement(X))))
% 6.90/1.38 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.38 meet(X, complement(X))
% 6.90/1.38 = { by axiom 5 (def_zero_13) R->L }
% 6.90/1.38 zero
% 6.90/1.38
% 6.90/1.38 Lemma 16: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 6.90/1.38 Proof:
% 6.90/1.38 converse(composition(converse(X), Y))
% 6.90/1.38 = { by axiom 9 (converse_multiplicativity_10) }
% 6.90/1.38 composition(converse(Y), converse(converse(X)))
% 6.90/1.38 = { by axiom 1 (converse_idempotence_8) }
% 6.90/1.38 composition(converse(Y), X)
% 6.90/1.38
% 6.90/1.38 Lemma 17: composition(converse(one), X) = X.
% 6.90/1.38 Proof:
% 6.90/1.38 composition(converse(one), X)
% 6.90/1.38 = { by lemma 16 R->L }
% 6.90/1.38 converse(composition(converse(X), one))
% 6.90/1.38 = { by axiom 3 (composition_identity_6) }
% 6.90/1.38 converse(converse(X))
% 6.90/1.38 = { by axiom 1 (converse_idempotence_8) }
% 6.90/1.38 X
% 6.90/1.38
% 6.90/1.38 Lemma 18: composition(one, X) = X.
% 6.90/1.38 Proof:
% 6.90/1.38 composition(one, X)
% 6.90/1.38 = { by lemma 17 R->L }
% 6.90/1.38 composition(converse(one), composition(one, X))
% 6.90/1.38 = { by axiom 10 (composition_associativity_5) }
% 6.90/1.38 composition(composition(converse(one), one), X)
% 6.90/1.38 = { by axiom 3 (composition_identity_6) }
% 6.90/1.38 composition(converse(one), X)
% 6.90/1.38 = { by lemma 17 }
% 6.90/1.38 X
% 6.90/1.38
% 6.90/1.38 Lemma 19: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 6.90/1.38 Proof:
% 6.90/1.38 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 6.90/1.38 = { by axiom 13 (converse_cancellativity_11) }
% 6.90/1.38 complement(X)
% 6.90/1.38
% 6.90/1.38 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 6.90/1.38 Proof:
% 6.90/1.38 join(complement(X), complement(X))
% 6.90/1.38 = { by lemma 17 R->L }
% 6.90/1.38 join(complement(X), composition(converse(one), complement(X)))
% 6.90/1.38 = { by lemma 18 R->L }
% 6.90/1.38 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 6.90/1.38 = { by lemma 19 }
% 6.90/1.38 complement(X)
% 6.90/1.38
% 6.90/1.38 Lemma 21: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 6.90/1.38 Proof:
% 6.90/1.38 join(meet(X, Y), complement(join(complement(X), Y)))
% 6.90/1.38 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 6.90/1.38 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 6.90/1.38 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 6.90/1.38 X
% 6.90/1.38
% 6.90/1.38 Lemma 22: join(zero, meet(X, X)) = X.
% 6.90/1.38 Proof:
% 6.90/1.38 join(zero, meet(X, X))
% 6.90/1.38 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 6.90/1.38 join(zero, complement(join(complement(X), complement(X))))
% 6.90/1.38 = { by axiom 5 (def_zero_13) }
% 6.90/1.38 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 6.90/1.38 = { by lemma 21 }
% 6.90/1.38 X
% 6.90/1.38
% 6.90/1.38 Lemma 23: join(zero, join(X, meet(Y, Y))) = join(X, Y).
% 6.90/1.38 Proof:
% 6.90/1.38 join(zero, join(X, meet(Y, Y)))
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 join(zero, join(meet(Y, Y), X))
% 6.90/1.38 = { by axiom 8 (maddux2_join_associativity_2) }
% 6.90/1.38 join(join(zero, meet(Y, Y)), X)
% 6.90/1.38 = { by lemma 22 }
% 6.90/1.38 join(Y, X)
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.38 join(X, Y)
% 6.90/1.38
% 6.90/1.38 Lemma 24: join(X, join(Y, complement(X))) = join(Y, top).
% 6.90/1.38 Proof:
% 6.90/1.38 join(X, join(Y, complement(X)))
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 join(X, join(complement(X), Y))
% 6.90/1.38 = { by axiom 8 (maddux2_join_associativity_2) }
% 6.90/1.38 join(join(X, complement(X)), Y)
% 6.90/1.38 = { by axiom 6 (def_top_12) R->L }
% 6.90/1.38 join(top, Y)
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.38 join(Y, top)
% 6.90/1.38
% 6.90/1.38 Lemma 25: join(top, complement(X)) = top.
% 6.90/1.38 Proof:
% 6.90/1.38 join(top, complement(X))
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 join(complement(X), top)
% 6.90/1.38 = { by lemma 24 R->L }
% 6.90/1.38 join(X, join(complement(X), complement(X)))
% 6.90/1.38 = { by lemma 20 }
% 6.90/1.38 join(X, complement(X))
% 6.90/1.38 = { by axiom 6 (def_top_12) R->L }
% 6.90/1.38 top
% 6.90/1.38
% 6.90/1.38 Lemma 26: join(Y, top) = join(X, top).
% 6.90/1.38 Proof:
% 6.90/1.38 join(Y, top)
% 6.90/1.38 = { by lemma 25 R->L }
% 6.90/1.38 join(Y, join(top, complement(Y)))
% 6.90/1.38 = { by lemma 24 }
% 6.90/1.38 join(top, top)
% 6.90/1.38 = { by lemma 24 R->L }
% 6.90/1.38 join(X, join(top, complement(X)))
% 6.90/1.38 = { by lemma 25 }
% 6.90/1.38 join(X, top)
% 6.90/1.38
% 6.90/1.38 Lemma 27: join(X, top) = top.
% 6.90/1.38 Proof:
% 6.90/1.38 join(X, top)
% 6.90/1.38 = { by lemma 26 }
% 6.90/1.38 join(zero, top)
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 join(top, zero)
% 6.90/1.38 = { by lemma 15 R->L }
% 6.90/1.38 join(top, complement(top))
% 6.90/1.38 = { by axiom 6 (def_top_12) R->L }
% 6.90/1.38 top
% 6.90/1.38
% 6.90/1.38 Lemma 28: join(X, join(complement(X), Y)) = top.
% 6.90/1.38 Proof:
% 6.90/1.38 join(X, join(complement(X), Y))
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 join(X, join(Y, complement(X)))
% 6.90/1.38 = { by lemma 24 }
% 6.90/1.38 join(Y, top)
% 6.90/1.38 = { by lemma 26 R->L }
% 6.90/1.38 join(Z, top)
% 6.90/1.38 = { by lemma 27 }
% 6.90/1.38 top
% 6.90/1.38
% 6.90/1.38 Lemma 29: join(X, complement(zero)) = top.
% 6.90/1.38 Proof:
% 6.90/1.38 join(X, complement(zero))
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 join(complement(zero), X)
% 6.90/1.38 = { by lemma 23 R->L }
% 6.90/1.38 join(zero, join(complement(zero), meet(X, X)))
% 6.90/1.38 = { by lemma 28 }
% 6.90/1.38 top
% 6.90/1.38
% 6.90/1.38 Lemma 30: complement(zero) = top.
% 6.90/1.38 Proof:
% 6.90/1.38 complement(zero)
% 6.90/1.38 = { by lemma 20 R->L }
% 6.90/1.38 join(complement(zero), complement(zero))
% 6.90/1.38 = { by lemma 29 }
% 6.90/1.38 top
% 6.90/1.38
% 6.90/1.38 Lemma 31: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 6.90/1.38 Proof:
% 6.90/1.38 converse(join(X, converse(Y)))
% 6.90/1.38 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.38 converse(join(converse(Y), X))
% 6.90/1.38 = { by axiom 7 (converse_additivity_9) }
% 6.90/1.38 join(converse(converse(Y)), converse(X))
% 6.90/1.38 = { by axiom 1 (converse_idempotence_8) }
% 6.90/1.39 join(Y, converse(X))
% 6.90/1.39
% 6.90/1.39 Lemma 32: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 6.90/1.39 Proof:
% 6.90/1.39 converse(join(converse(X), Y))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 converse(join(Y, converse(X)))
% 6.90/1.39 = { by lemma 31 }
% 6.90/1.39 join(X, converse(Y))
% 6.90/1.39
% 6.90/1.39 Lemma 33: join(X, converse(top)) = top.
% 6.90/1.39 Proof:
% 6.90/1.39 join(X, converse(top))
% 6.90/1.39 = { by axiom 6 (def_top_12) }
% 6.90/1.39 join(X, converse(join(converse(complement(X)), complement(converse(complement(X))))))
% 6.90/1.39 = { by lemma 32 }
% 6.90/1.39 join(X, join(complement(X), converse(complement(converse(complement(X))))))
% 6.90/1.39 = { by lemma 28 }
% 6.90/1.39 top
% 6.90/1.39
% 6.90/1.39 Lemma 34: converse(top) = top.
% 6.90/1.39 Proof:
% 6.90/1.39 converse(top)
% 6.90/1.39 = { by lemma 27 R->L }
% 6.90/1.39 converse(join(X, top))
% 6.90/1.39 = { by axiom 7 (converse_additivity_9) }
% 6.90/1.39 join(converse(X), converse(top))
% 6.90/1.39 = { by lemma 33 }
% 6.90/1.39 top
% 6.90/1.39
% 6.90/1.39 Lemma 35: complement(complement(X)) = meet(X, X).
% 6.90/1.39 Proof:
% 6.90/1.39 complement(complement(X))
% 6.90/1.39 = { by lemma 20 R->L }
% 6.90/1.39 complement(join(complement(X), complement(X)))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.39 meet(X, X)
% 6.90/1.39
% 6.90/1.39 Lemma 36: meet(Y, X) = meet(X, Y).
% 6.90/1.39 Proof:
% 6.90/1.39 meet(Y, X)
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 6.90/1.39 complement(join(complement(Y), complement(X)))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 complement(join(complement(X), complement(Y)))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.39 meet(X, Y)
% 6.90/1.39
% 6.90/1.39 Lemma 37: complement(join(zero, complement(X))) = meet(X, top).
% 6.90/1.39 Proof:
% 6.90/1.39 complement(join(zero, complement(X)))
% 6.90/1.39 = { by lemma 15 R->L }
% 6.90/1.39 complement(join(complement(top), complement(X)))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.39 meet(top, X)
% 6.90/1.39 = { by lemma 36 R->L }
% 6.90/1.39 meet(X, top)
% 6.90/1.39
% 6.90/1.39 Lemma 38: join(meet(X, Y), meet(X, complement(Y))) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 join(meet(X, Y), meet(X, complement(Y)))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 join(meet(X, complement(Y)), meet(X, Y))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 6.90/1.39 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 6.90/1.39 = { by lemma 21 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 39: join(zero, meet(X, top)) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 join(zero, meet(X, top))
% 6.90/1.39 = { by lemma 30 R->L }
% 6.90/1.39 join(zero, meet(X, complement(zero)))
% 6.90/1.39 = { by lemma 15 R->L }
% 6.90/1.39 join(complement(top), meet(X, complement(zero)))
% 6.90/1.39 = { by lemma 29 R->L }
% 6.90/1.39 join(complement(join(complement(X), complement(zero))), meet(X, complement(zero)))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.39 join(meet(X, zero), meet(X, complement(zero)))
% 6.90/1.39 = { by lemma 38 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 40: join(zero, complement(X)) = complement(X).
% 6.90/1.39 Proof:
% 6.90/1.39 join(zero, complement(X))
% 6.90/1.39 = { by lemma 22 R->L }
% 6.90/1.39 join(zero, complement(join(zero, meet(X, X))))
% 6.90/1.39 = { by lemma 35 R->L }
% 6.90/1.39 join(zero, complement(join(zero, complement(complement(X)))))
% 6.90/1.39 = { by lemma 37 }
% 6.90/1.39 join(zero, meet(complement(X), top))
% 6.90/1.39 = { by lemma 39 }
% 6.90/1.39 complement(X)
% 6.90/1.39
% 6.90/1.39 Lemma 41: complement(complement(X)) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 complement(complement(X))
% 6.90/1.39 = { by lemma 40 R->L }
% 6.90/1.39 join(zero, complement(complement(X)))
% 6.90/1.39 = { by lemma 35 }
% 6.90/1.39 join(zero, meet(X, X))
% 6.90/1.39 = { by lemma 22 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 42: join(X, X) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 join(X, X)
% 6.90/1.39 = { by lemma 41 R->L }
% 6.90/1.39 join(X, complement(complement(X)))
% 6.90/1.39 = { by lemma 41 R->L }
% 6.90/1.39 join(complement(complement(X)), complement(complement(X)))
% 6.90/1.39 = { by lemma 20 }
% 6.90/1.39 complement(complement(X))
% 6.90/1.39 = { by lemma 41 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 43: join(X, zero) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 join(X, zero)
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 join(zero, X)
% 6.90/1.39 = { by lemma 41 R->L }
% 6.90/1.39 join(zero, complement(complement(X)))
% 6.90/1.39 = { by lemma 35 }
% 6.90/1.39 join(zero, meet(X, X))
% 6.90/1.39 = { by lemma 22 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 44: join(top, X) = top.
% 6.90/1.39 Proof:
% 6.90/1.39 join(top, X)
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 join(X, top)
% 6.90/1.39 = { by lemma 26 R->L }
% 6.90/1.39 join(Y, top)
% 6.90/1.39 = { by lemma 27 }
% 6.90/1.39 top
% 6.90/1.39
% 6.90/1.39 Lemma 45: join(zero, X) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 join(zero, X)
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 join(X, zero)
% 6.90/1.39 = { by lemma 43 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 46: meet(X, X) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 meet(X, X)
% 6.90/1.39 = { by lemma 35 R->L }
% 6.90/1.39 complement(complement(X))
% 6.90/1.39 = { by lemma 41 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 47: meet(X, top) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 meet(X, top)
% 6.90/1.39 = { by lemma 37 R->L }
% 6.90/1.39 complement(join(zero, complement(X)))
% 6.90/1.39 = { by lemma 40 R->L }
% 6.90/1.39 join(zero, complement(join(zero, complement(X))))
% 6.90/1.39 = { by lemma 37 }
% 6.90/1.39 join(zero, meet(X, top))
% 6.90/1.39 = { by lemma 39 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 48: composition(join(X, one), Y) = join(Y, composition(X, Y)).
% 6.90/1.39 Proof:
% 6.90/1.39 composition(join(X, one), Y)
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 composition(join(one, X), Y)
% 6.90/1.39 = { by axiom 12 (composition_distributivity_7) }
% 6.90/1.39 join(composition(one, Y), composition(X, Y))
% 6.90/1.39 = { by lemma 18 }
% 6.90/1.39 join(Y, composition(X, Y))
% 6.90/1.39
% 6.90/1.39 Lemma 49: join(X, composition(top, X)) = composition(top, X).
% 6.90/1.39 Proof:
% 6.90/1.39 join(X, composition(top, X))
% 6.90/1.39 = { by lemma 34 R->L }
% 6.90/1.39 join(X, composition(converse(top), X))
% 6.90/1.39 = { by lemma 48 R->L }
% 6.90/1.39 composition(join(converse(top), one), X)
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.39 composition(join(one, converse(top)), X)
% 6.90/1.39 = { by lemma 33 }
% 6.90/1.39 composition(top, X)
% 6.90/1.39
% 6.90/1.39 Lemma 50: composition(top, zero) = zero.
% 6.90/1.39 Proof:
% 6.90/1.39 composition(top, zero)
% 6.90/1.39 = { by lemma 34 R->L }
% 6.90/1.39 composition(converse(top), zero)
% 6.90/1.39 = { by lemma 45 R->L }
% 6.90/1.39 join(zero, composition(converse(top), zero))
% 6.90/1.39 = { by lemma 15 R->L }
% 6.90/1.39 join(complement(top), composition(converse(top), zero))
% 6.90/1.39 = { by lemma 15 R->L }
% 6.90/1.39 join(complement(top), composition(converse(top), complement(top)))
% 6.90/1.39 = { by lemma 44 R->L }
% 6.90/1.39 join(complement(top), composition(converse(top), complement(join(top, composition(top, top)))))
% 6.90/1.39 = { by lemma 49 }
% 6.90/1.39 join(complement(top), composition(converse(top), complement(composition(top, top))))
% 6.90/1.39 = { by lemma 19 }
% 6.90/1.39 complement(top)
% 6.90/1.39 = { by lemma 15 }
% 6.90/1.39 zero
% 6.90/1.39
% 6.90/1.39 Lemma 51: complement(join(complement(X), meet(Y, Z))) = meet(X, join(complement(Y), complement(Z))).
% 6.90/1.39 Proof:
% 6.90/1.39 complement(join(complement(X), meet(Y, Z)))
% 6.90/1.39 = { by lemma 36 }
% 6.90/1.39 complement(join(complement(X), meet(Z, Y)))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 complement(join(meet(Z, Y), complement(X)))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 6.90/1.39 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.39 meet(join(complement(Z), complement(Y)), X)
% 6.90/1.39 = { by lemma 36 R->L }
% 6.90/1.39 meet(X, join(complement(Z), complement(Y)))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.39 meet(X, join(complement(Y), complement(Z)))
% 6.90/1.39
% 6.90/1.39 Lemma 52: complement(join(zero, meet(X, Y))) = join(complement(X), complement(Y)).
% 6.90/1.39 Proof:
% 6.90/1.39 complement(join(zero, meet(X, Y)))
% 6.90/1.39 = { by lemma 36 }
% 6.90/1.39 complement(join(zero, meet(Y, X)))
% 6.90/1.39 = { by lemma 15 R->L }
% 6.90/1.39 complement(join(complement(top), meet(Y, X)))
% 6.90/1.39 = { by lemma 51 }
% 6.90/1.39 meet(top, join(complement(Y), complement(X)))
% 6.90/1.39 = { by lemma 36 }
% 6.90/1.39 meet(join(complement(Y), complement(X)), top)
% 6.90/1.39 = { by lemma 47 }
% 6.90/1.39 join(complement(Y), complement(X))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.39 join(complement(X), complement(Y))
% 6.90/1.39
% 6.90/1.39 Lemma 53: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 6.90/1.39 Proof:
% 6.90/1.39 join(complement(X), complement(Y))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.39 join(complement(Y), complement(X))
% 6.90/1.39 = { by lemma 52 R->L }
% 6.90/1.39 complement(join(zero, meet(Y, X)))
% 6.90/1.39 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.39 complement(join(meet(Y, X), zero))
% 6.90/1.39 = { by lemma 43 }
% 6.90/1.39 complement(meet(Y, X))
% 6.90/1.39 = { by lemma 36 R->L }
% 6.90/1.39 complement(meet(X, Y))
% 6.90/1.39
% 6.90/1.39 Lemma 54: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 6.90/1.39 Proof:
% 6.90/1.39 complement(meet(X, complement(Y)))
% 6.90/1.39 = { by lemma 36 }
% 6.90/1.39 complement(meet(complement(Y), X))
% 6.90/1.39 = { by lemma 40 R->L }
% 6.90/1.39 complement(meet(join(zero, complement(Y)), X))
% 6.90/1.39 = { by lemma 53 R->L }
% 6.90/1.39 join(complement(join(zero, complement(Y))), complement(X))
% 6.90/1.39 = { by lemma 37 }
% 6.90/1.39 join(meet(Y, top), complement(X))
% 6.90/1.39 = { by lemma 47 }
% 6.90/1.39 join(Y, complement(X))
% 6.90/1.39
% 6.90/1.39 Lemma 55: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 6.90/1.39 Proof:
% 6.90/1.39 complement(meet(complement(X), Y))
% 6.90/1.39 = { by lemma 36 }
% 6.90/1.39 complement(meet(Y, complement(X)))
% 6.90/1.39 = { by lemma 54 }
% 6.90/1.39 join(X, complement(Y))
% 6.90/1.39
% 6.90/1.39 Lemma 56: meet(X, join(X, complement(Y))) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 meet(X, join(X, complement(Y)))
% 6.90/1.39 = { by lemma 54 R->L }
% 6.90/1.39 meet(X, complement(meet(Y, complement(X))))
% 6.90/1.39 = { by lemma 53 R->L }
% 6.90/1.39 meet(X, join(complement(Y), complement(complement(X))))
% 6.90/1.39 = { by lemma 51 R->L }
% 6.90/1.39 complement(join(complement(X), meet(Y, complement(X))))
% 6.90/1.39 = { by lemma 40 R->L }
% 6.90/1.39 join(zero, complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by lemma 15 R->L }
% 6.90/1.39 join(complement(top), complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by lemma 27 R->L }
% 6.90/1.39 join(complement(join(complement(Y), top)), complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by lemma 24 R->L }
% 6.90/1.39 join(complement(join(complement(X), join(complement(Y), complement(complement(X))))), complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by lemma 53 }
% 6.90/1.39 join(complement(join(complement(X), complement(meet(Y, complement(X))))), complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by lemma 36 R->L }
% 6.90/1.39 join(complement(join(complement(X), complement(meet(complement(X), Y)))), complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.39 join(meet(X, meet(complement(X), Y)), complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by lemma 36 R->L }
% 6.90/1.39 join(meet(X, meet(Y, complement(X))), complement(join(complement(X), meet(Y, complement(X)))))
% 6.90/1.39 = { by lemma 21 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.39 Lemma 57: join(X, meet(X, Y)) = X.
% 6.90/1.39 Proof:
% 6.90/1.39 join(X, meet(X, Y))
% 6.90/1.39 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 6.90/1.39 join(X, complement(join(complement(X), complement(Y))))
% 6.90/1.39 = { by lemma 55 R->L }
% 6.90/1.39 complement(meet(complement(X), join(complement(X), complement(Y))))
% 6.90/1.39 = { by lemma 56 }
% 6.90/1.39 complement(complement(X))
% 6.90/1.39 = { by lemma 41 }
% 6.90/1.39 X
% 6.90/1.39
% 6.90/1.40 Lemma 58: join(meet(X, Y), Y) = Y.
% 6.90/1.40 Proof:
% 6.90/1.40 join(meet(X, Y), Y)
% 6.90/1.40 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.40 join(Y, meet(X, Y))
% 6.90/1.40 = { by lemma 36 }
% 6.90/1.40 join(Y, meet(Y, X))
% 6.90/1.40 = { by lemma 57 }
% 6.90/1.40 Y
% 6.90/1.40
% 6.90/1.40 Lemma 59: meet(X, join(X, Y)) = X.
% 6.90/1.40 Proof:
% 6.90/1.40 meet(X, join(X, Y))
% 6.90/1.40 = { by lemma 46 R->L }
% 6.90/1.40 meet(X, join(X, meet(Y, Y)))
% 6.90/1.40 = { by lemma 35 R->L }
% 6.90/1.40 meet(X, join(X, complement(complement(Y))))
% 6.90/1.40 = { by lemma 56 }
% 6.90/1.40 X
% 6.90/1.40
% 6.90/1.40 Lemma 60: meet(meet(X, Y), Z) = meet(X, meet(Z, Y)).
% 6.90/1.40 Proof:
% 6.90/1.40 meet(meet(X, Y), Z)
% 6.90/1.40 = { by lemma 36 }
% 6.90/1.40 meet(Z, meet(X, Y))
% 6.90/1.40 = { by lemma 46 R->L }
% 6.90/1.40 meet(meet(Z, meet(X, Y)), meet(Z, meet(X, Y)))
% 6.90/1.40 = { by lemma 35 R->L }
% 6.90/1.40 complement(complement(meet(Z, meet(X, Y))))
% 6.90/1.40 = { by lemma 36 }
% 6.90/1.40 complement(complement(meet(Z, meet(Y, X))))
% 6.90/1.40 = { by lemma 53 R->L }
% 6.90/1.40 complement(join(complement(Z), complement(meet(Y, X))))
% 6.90/1.40 = { by lemma 53 R->L }
% 6.90/1.40 complement(join(complement(Z), join(complement(Y), complement(X))))
% 6.90/1.40 = { by axiom 8 (maddux2_join_associativity_2) }
% 6.90/1.40 complement(join(join(complement(Z), complement(Y)), complement(X)))
% 6.90/1.40 = { by lemma 54 R->L }
% 6.90/1.40 complement(complement(meet(X, complement(join(complement(Z), complement(Y))))))
% 6.90/1.40 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 6.90/1.40 complement(complement(meet(X, meet(Z, Y))))
% 6.90/1.40 = { by lemma 36 R->L }
% 6.90/1.40 complement(complement(meet(X, meet(Y, Z))))
% 6.90/1.40 = { by lemma 41 }
% 6.90/1.40 meet(X, meet(Y, Z))
% 6.90/1.40 = { by lemma 36 R->L }
% 6.90/1.40 meet(X, meet(Z, Y))
% 6.90/1.40
% 6.90/1.40 Lemma 61: meet(X, meet(Y, complement(meet(X, Y)))) = zero.
% 6.90/1.40 Proof:
% 6.90/1.40 meet(X, meet(Y, complement(meet(X, Y))))
% 6.90/1.40 = { by lemma 53 R->L }
% 6.90/1.40 meet(X, meet(Y, join(complement(X), complement(Y))))
% 6.90/1.40 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 6.90/1.40 complement(join(complement(X), complement(meet(Y, join(complement(X), complement(Y))))))
% 6.90/1.40 = { by lemma 53 R->L }
% 6.90/1.40 complement(join(complement(X), join(complement(Y), complement(join(complement(X), complement(Y))))))
% 6.90/1.40 = { by axiom 8 (maddux2_join_associativity_2) }
% 6.90/1.40 complement(join(join(complement(X), complement(Y)), complement(join(complement(X), complement(Y)))))
% 6.90/1.40 = { by axiom 6 (def_top_12) R->L }
% 6.90/1.40 complement(top)
% 6.90/1.40 = { by lemma 15 }
% 6.90/1.40 zero
% 6.90/1.40
% 6.90/1.40 Lemma 62: meet(X, join(Y, complement(X))) = meet(X, Y).
% 6.90/1.40 Proof:
% 6.90/1.40 meet(X, join(Y, complement(X)))
% 6.90/1.40 = { by lemma 55 R->L }
% 6.90/1.40 meet(X, complement(meet(complement(Y), X)))
% 6.90/1.40 = { by lemma 38 R->L }
% 6.90/1.40 join(meet(meet(X, complement(meet(complement(Y), X))), Y), meet(meet(X, complement(meet(complement(Y), X))), complement(Y)))
% 6.90/1.40 = { by lemma 36 R->L }
% 6.90/1.40 join(meet(meet(X, complement(meet(complement(Y), X))), Y), meet(complement(Y), meet(X, complement(meet(complement(Y), X)))))
% 6.90/1.40 = { by lemma 61 }
% 6.90/1.40 join(meet(meet(X, complement(meet(complement(Y), X))), Y), zero)
% 6.90/1.40 = { by lemma 43 }
% 6.90/1.40 meet(meet(X, complement(meet(complement(Y), X))), Y)
% 6.90/1.40 = { by lemma 60 }
% 6.90/1.40 meet(X, meet(Y, complement(meet(complement(Y), X))))
% 6.90/1.40 = { by lemma 55 }
% 6.90/1.40 meet(X, meet(Y, join(Y, complement(X))))
% 6.90/1.40 = { by lemma 56 }
% 6.90/1.40 meet(X, Y)
% 6.90/1.40
% 6.90/1.40 Lemma 63: converse(composition(X, converse(Y))) = composition(Y, converse(X)).
% 6.90/1.40 Proof:
% 6.90/1.40 converse(composition(X, converse(Y)))
% 6.90/1.40 = { by axiom 9 (converse_multiplicativity_10) }
% 6.90/1.40 composition(converse(converse(Y)), converse(X))
% 6.90/1.40 = { by axiom 1 (converse_idempotence_8) }
% 6.90/1.40 composition(Y, converse(X))
% 6.90/1.40
% 6.90/1.40 Lemma 64: join(meet(X, Y), meet(Y, complement(X))) = Y.
% 6.90/1.40 Proof:
% 6.90/1.40 join(meet(X, Y), meet(Y, complement(X)))
% 6.90/1.40 = { by lemma 36 }
% 6.90/1.40 join(meet(Y, X), meet(Y, complement(X)))
% 6.90/1.40 = { by lemma 38 }
% 6.90/1.40 Y
% 6.90/1.40
% 6.90/1.40 Lemma 65: composition(complement(composition(sk1, top)), top) = complement(composition(sk1, top)).
% 6.90/1.40 Proof:
% 6.90/1.40 composition(complement(composition(sk1, top)), top)
% 6.90/1.40 = { by lemma 34 R->L }
% 6.90/1.40 composition(complement(composition(sk1, top)), converse(top))
% 6.90/1.40 = { by lemma 63 R->L }
% 6.90/1.40 converse(composition(top, converse(complement(composition(sk1, top)))))
% 6.90/1.40 = { by lemma 49 R->L }
% 6.90/1.40 converse(join(converse(complement(composition(sk1, top))), composition(top, converse(complement(composition(sk1, top))))))
% 6.90/1.40 = { by lemma 32 }
% 6.90/1.40 join(complement(composition(sk1, top)), converse(composition(top, converse(complement(composition(sk1, top))))))
% 6.90/1.40 = { by lemma 63 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), converse(top)))
% 6.90/1.40 = { by lemma 34 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), top))
% 6.90/1.40 = { by lemma 30 R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(zero)))
% 6.90/1.40 = { by lemma 42 R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(join(zero, zero))))
% 6.90/1.40 = { by axiom 1 (converse_idempotence_8) R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(join(zero, converse(converse(zero))))))
% 6.90/1.40 = { by lemma 31 R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(converse(zero), converse(zero))))))
% 6.90/1.40 = { by lemma 23 R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(zero, join(converse(zero), meet(converse(zero), converse(zero))))))))
% 6.90/1.40 = { by lemma 57 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(zero, converse(zero))))))
% 6.90/1.40 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(converse(zero), zero)))))
% 6.90/1.40 = { by lemma 32 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(join(zero, converse(zero)))))
% 6.90/1.40 = { by lemma 45 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(zero))))
% 6.90/1.40 = { by lemma 15 R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(complement(top)))))
% 6.90/1.40 = { by lemma 19 R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(complement(top), composition(converse(composition(sk1, top)), complement(composition(composition(sk1, top), top))))))))
% 6.90/1.40 = { by axiom 4 (goals_14) }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(complement(top), composition(converse(composition(sk1, top)), complement(composition(sk1, top))))))))
% 6.90/1.40 = { by lemma 15 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(zero, composition(converse(composition(sk1, top)), complement(composition(sk1, top))))))))
% 6.90/1.40 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(join(composition(converse(composition(sk1, top)), complement(composition(sk1, top))), zero)))))
% 6.90/1.40 = { by lemma 43 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(converse(composition(converse(composition(sk1, top)), complement(composition(sk1, top)))))))
% 6.90/1.40 = { by lemma 16 }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(complement(composition(sk1, top)), complement(composition(converse(complement(composition(sk1, top))), composition(sk1, top)))))
% 6.90/1.40 = { by axiom 1 (converse_idempotence_8) R->L }
% 6.90/1.40 join(complement(composition(sk1, top)), composition(converse(converse(complement(composition(sk1, top)))), complement(composition(converse(complement(composition(sk1, top))), composition(sk1, top)))))
% 6.90/1.40 = { by lemma 19 }
% 6.90/1.40 complement(composition(sk1, top))
% 6.90/1.40
% 6.90/1.40 Lemma 66: composition(join(X, complement(composition(sk1, top))), top) = join(complement(composition(sk1, top)), composition(X, top)).
% 6.90/1.40 Proof:
% 6.90/1.40 composition(join(X, complement(composition(sk1, top))), top)
% 6.90/1.40 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.40 composition(join(complement(composition(sk1, top)), X), top)
% 6.90/1.40 = { by axiom 12 (composition_distributivity_7) }
% 6.90/1.40 join(composition(complement(composition(sk1, top)), top), composition(X, top))
% 6.90/1.40 = { by lemma 65 }
% 6.90/1.41 join(complement(composition(sk1, top)), composition(X, top))
% 6.90/1.41
% 6.90/1.41 Lemma 67: composition(meet(sk1, one), X) = meet(sk1, X).
% 6.90/1.41 Proof:
% 6.90/1.41 composition(meet(sk1, one), X)
% 6.90/1.41 = { by lemma 59 R->L }
% 6.90/1.41 meet(composition(meet(sk1, one), X), join(composition(meet(sk1, one), X), X))
% 6.90/1.41 = { by lemma 18 R->L }
% 6.90/1.41 meet(composition(meet(sk1, one), X), join(composition(meet(sk1, one), X), composition(one, X)))
% 6.90/1.41 = { by axiom 12 (composition_distributivity_7) R->L }
% 6.90/1.41 meet(composition(meet(sk1, one), X), composition(join(meet(sk1, one), one), X))
% 6.90/1.41 = { by lemma 58 }
% 6.90/1.41 meet(composition(meet(sk1, one), X), composition(one, X))
% 6.90/1.41 = { by lemma 18 }
% 6.90/1.41 meet(composition(meet(sk1, one), X), X)
% 6.90/1.41 = { by lemma 36 }
% 6.90/1.41 meet(X, composition(meet(sk1, one), X))
% 6.90/1.41 = { by lemma 62 R->L }
% 6.90/1.41 meet(X, join(composition(meet(sk1, one), X), complement(X)))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.41 meet(X, join(complement(X), composition(meet(sk1, one), X)))
% 6.90/1.41 = { by lemma 18 R->L }
% 6.90/1.41 meet(X, join(composition(one, complement(X)), composition(meet(sk1, one), X)))
% 6.90/1.41 = { by lemma 58 R->L }
% 6.90/1.41 meet(X, join(composition(join(meet(sk1, one), one), complement(X)), composition(meet(sk1, one), X)))
% 6.90/1.41 = { by lemma 48 }
% 6.90/1.41 meet(X, join(join(complement(X), composition(meet(sk1, one), complement(X))), composition(meet(sk1, one), X)))
% 6.90/1.41 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 6.90/1.41 meet(X, join(complement(X), join(composition(meet(sk1, one), complement(X)), composition(meet(sk1, one), X))))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.41 meet(X, join(complement(X), join(composition(meet(sk1, one), X), composition(meet(sk1, one), complement(X)))))
% 6.90/1.41 = { by axiom 1 (converse_idempotence_8) R->L }
% 6.90/1.41 meet(X, join(complement(X), join(composition(meet(sk1, one), X), composition(meet(sk1, one), converse(converse(complement(X)))))))
% 6.90/1.41 = { by axiom 1 (converse_idempotence_8) R->L }
% 6.90/1.41 meet(X, join(complement(X), converse(converse(join(composition(meet(sk1, one), X), composition(meet(sk1, one), converse(converse(complement(X)))))))))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.41 meet(X, join(complement(X), converse(converse(join(composition(meet(sk1, one), converse(converse(complement(X)))), composition(meet(sk1, one), X))))))
% 6.90/1.41 = { by axiom 7 (converse_additivity_9) }
% 6.90/1.41 meet(X, join(complement(X), converse(join(converse(composition(meet(sk1, one), converse(converse(complement(X))))), converse(composition(meet(sk1, one), X))))))
% 6.90/1.41 = { by lemma 63 }
% 6.90/1.41 meet(X, join(complement(X), converse(join(composition(converse(complement(X)), converse(meet(sk1, one))), converse(composition(meet(sk1, one), X))))))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.41 meet(X, join(complement(X), converse(join(converse(composition(meet(sk1, one), X)), composition(converse(complement(X)), converse(meet(sk1, one)))))))
% 6.90/1.41 = { by axiom 9 (converse_multiplicativity_10) }
% 6.90/1.41 meet(X, join(complement(X), converse(join(composition(converse(X), converse(meet(sk1, one))), composition(converse(complement(X)), converse(meet(sk1, one)))))))
% 6.90/1.41 = { by axiom 12 (composition_distributivity_7) R->L }
% 6.90/1.41 meet(X, join(complement(X), converse(composition(join(converse(X), converse(complement(X))), converse(meet(sk1, one))))))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.41 meet(X, join(complement(X), converse(composition(join(converse(complement(X)), converse(X)), converse(meet(sk1, one))))))
% 6.90/1.41 = { by lemma 31 R->L }
% 6.90/1.41 meet(X, join(complement(X), converse(composition(converse(join(X, converse(converse(complement(X))))), converse(meet(sk1, one))))))
% 6.90/1.41 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 6.90/1.41 meet(X, join(complement(X), converse(converse(composition(meet(sk1, one), join(X, converse(converse(complement(X)))))))))
% 6.90/1.41 = { by axiom 1 (converse_idempotence_8) }
% 6.90/1.41 meet(X, join(complement(X), composition(meet(sk1, one), join(X, converse(converse(complement(X)))))))
% 6.90/1.41 = { by axiom 1 (converse_idempotence_8) }
% 6.90/1.41 meet(X, join(complement(X), composition(meet(sk1, one), join(X, complement(X)))))
% 6.90/1.41 = { by axiom 6 (def_top_12) R->L }
% 6.90/1.41 meet(X, join(complement(X), composition(meet(sk1, one), top)))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.41 meet(X, join(composition(meet(sk1, one), top), complement(X)))
% 6.90/1.41 = { by lemma 62 }
% 6.90/1.41 meet(X, composition(meet(sk1, one), top))
% 6.90/1.41 = { by lemma 64 R->L }
% 6.90/1.41 meet(X, join(meet(composition(sk1, top), composition(meet(sk1, one), top)), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 43 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), zero), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 15 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(top)), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 28 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(sk1, top), join(complement(composition(sk1, top)), join(composition(complement(composition(sk1, top)), composition(sk1, top)), composition(meet(sk1, one), top)))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(sk1, top), join(join(composition(complement(composition(sk1, top)), composition(sk1, top)), composition(meet(sk1, one), top)), complement(composition(sk1, top)))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(sk1, top), join(composition(complement(composition(sk1, top)), composition(sk1, top)), join(composition(meet(sk1, one), top), complement(composition(sk1, top))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(sk1, top), join(composition(complement(composition(sk1, top)), composition(sk1, top)), join(complement(composition(sk1, top)), composition(meet(sk1, one), top)))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 66 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(sk1, top), join(composition(complement(composition(sk1, top)), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by axiom 8 (maddux2_join_associativity_2) }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(join(composition(sk1, top), composition(complement(composition(sk1, top)), composition(sk1, top))), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 65 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(join(composition(sk1, top), composition(composition(complement(composition(sk1, top)), top), composition(sk1, top))), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 48 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(composition(complement(composition(sk1, top)), top), one), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by axiom 2 (maddux1_join_commutativity_1) }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(one, composition(complement(composition(sk1, top)), top)), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 65 }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(one, complement(composition(sk1, top))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 54 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(meet(composition(sk1, top), complement(one))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 53 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(complement(composition(sk1, top)), complement(complement(one))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 52 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(composition(sk1, top), complement(one)))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by axiom 4 (goals_14) }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, complement(one)))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 57 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, complement(join(one, meet(one, sk1)))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 46 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, complement(join(one, meet(meet(one, sk1), meet(one, sk1))))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 35 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, complement(join(one, complement(complement(meet(one, sk1)))))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 54 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, complement(complement(meet(complement(meet(one, sk1)), complement(one))))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 35 }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, meet(meet(complement(meet(one, sk1)), complement(one)), meet(complement(meet(one, sk1)), complement(one)))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 46 }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, meet(complement(meet(one, sk1)), complement(one))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.41 = { by lemma 36 R->L }
% 6.90/1.41 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, meet(complement(one), complement(meet(one, sk1)))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.42 = { by lemma 60 R->L }
% 6.90/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(meet(sk1, complement(meet(one, sk1))), complement(one)))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 6.90/1.42 = { by lemma 45 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, join(zero, meet(meet(sk1, complement(meet(one, sk1))), complement(one))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 61 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, join(meet(one, meet(sk1, complement(meet(one, sk1)))), meet(meet(sk1, complement(meet(one, sk1))), complement(one))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 64 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, complement(meet(one, sk1))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 36 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(sk1, complement(meet(sk1, one))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 4 (goals_14) R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(join(zero, meet(composition(sk1, top), complement(meet(sk1, one))))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 52 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(complement(composition(sk1, top)), complement(complement(meet(sk1, one)))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 53 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(complement(meet(composition(sk1, top), complement(meet(sk1, one)))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 54 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 10 (composition_associativity_5) }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(composition(join(meet(sk1, one), complement(composition(sk1, top))), sk1), top), composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 12 (composition_distributivity_7) R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(composition(join(composition(join(meet(sk1, one), complement(composition(sk1, top))), sk1), join(meet(sk1, one), complement(composition(sk1, top)))), top))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 2 (maddux1_join_commutativity_1) }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(composition(join(join(meet(sk1, one), complement(composition(sk1, top))), composition(join(meet(sk1, one), complement(composition(sk1, top))), sk1)), top))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 4 (goals_14) R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(composition(join(join(meet(sk1, one), complement(composition(sk1, top))), composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top))), top))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 12 (composition_distributivity_7) }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(meet(sk1, one), complement(composition(sk1, top))), top), composition(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 10 (composition_associativity_5) R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(meet(sk1, one), complement(composition(sk1, top))), top), composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(composition(sk1, top), top))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 30 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(meet(sk1, one), complement(composition(sk1, top))), top), composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(composition(sk1, top), complement(zero)))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 10 (composition_associativity_5) }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(meet(sk1, one), complement(composition(sk1, top))), top), composition(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)), complement(zero))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 1 (converse_idempotence_8) R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(composition(join(meet(sk1, one), complement(composition(sk1, top))), top), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(zero))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 41 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(zero))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 50 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(top, zero)))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 44 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(join(top, converse(composition(sk1, top))), zero)))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 12 (composition_distributivity_7) }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(join(composition(top, zero), composition(converse(composition(sk1, top)), zero))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 50 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(join(zero, composition(converse(composition(sk1, top)), zero))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 45 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(converse(composition(sk1, top)), zero)))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 15 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(converse(composition(sk1, top)), complement(top))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 19 R->L }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(converse(composition(sk1, top)), join(complement(top), composition(converse(join(meet(sk1, one), complement(composition(sk1, top)))), complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 15 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(converse(composition(sk1, top)), join(zero, composition(converse(join(meet(sk1, one), complement(composition(sk1, top)))), complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by lemma 45 }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(converse(composition(sk1, top)), composition(converse(join(meet(sk1, one), complement(composition(sk1, top)))), complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.42 = { by axiom 10 (composition_associativity_5) }
% 7.89/1.42 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(composition(converse(composition(sk1, top)), converse(join(meet(sk1, one), complement(composition(sk1, top))))), complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.43 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 7.89/1.43 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), composition(converse(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top)))), complement(composition(converse(composition(join(meet(sk1, one), complement(composition(sk1, top))), composition(sk1, top))), complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top)))))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.43 = { by lemma 19 }
% 7.89/1.43 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(complement(complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.43 = { by lemma 41 }
% 7.89/1.43 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(composition(join(meet(sk1, one), complement(composition(sk1, top))), top))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.43 = { by lemma 66 }
% 7.89/1.43 meet(X, join(join(meet(composition(sk1, top), composition(meet(sk1, one), top)), complement(join(complement(composition(sk1, top)), composition(meet(sk1, one), top)))), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.43 = { by lemma 21 }
% 7.89/1.43 meet(X, join(composition(sk1, top), meet(composition(meet(sk1, one), top), complement(composition(sk1, top)))))
% 7.89/1.43 = { by lemma 36 }
% 7.89/1.43 meet(X, join(composition(sk1, top), meet(complement(composition(sk1, top)), composition(meet(sk1, one), top))))
% 7.89/1.43 = { by lemma 59 R->L }
% 7.89/1.43 meet(X, join(meet(composition(sk1, top), join(composition(sk1, top), composition(meet(sk1, one), top))), meet(complement(composition(sk1, top)), composition(meet(sk1, one), top))))
% 7.89/1.43 = { by axiom 2 (maddux1_join_commutativity_1) }
% 7.89/1.43 meet(X, join(meet(composition(sk1, top), join(composition(meet(sk1, one), top), composition(sk1, top))), meet(complement(composition(sk1, top)), composition(meet(sk1, one), top))))
% 7.89/1.43 = { by lemma 41 R->L }
% 7.89/1.43 meet(X, join(meet(composition(sk1, top), join(composition(meet(sk1, one), top), complement(complement(composition(sk1, top))))), meet(complement(composition(sk1, top)), composition(meet(sk1, one), top))))
% 7.89/1.43 = { by lemma 62 R->L }
% 7.89/1.43 meet(X, join(meet(composition(sk1, top), join(composition(meet(sk1, one), top), complement(complement(composition(sk1, top))))), meet(complement(composition(sk1, top)), join(composition(meet(sk1, one), top), complement(complement(composition(sk1, top)))))))
% 7.89/1.43 = { by lemma 36 }
% 7.89/1.43 meet(X, join(meet(composition(sk1, top), join(composition(meet(sk1, one), top), complement(complement(composition(sk1, top))))), meet(join(composition(meet(sk1, one), top), complement(complement(composition(sk1, top)))), complement(composition(sk1, top)))))
% 7.89/1.43 = { by lemma 64 }
% 7.89/1.43 meet(X, join(composition(meet(sk1, one), top), complement(complement(composition(sk1, top)))))
% 7.89/1.43 = { by lemma 41 }
% 7.89/1.43 meet(X, join(composition(meet(sk1, one), top), composition(sk1, top)))
% 7.89/1.43 = { by axiom 2 (maddux1_join_commutativity_1) }
% 7.89/1.43 meet(X, join(composition(sk1, top), composition(meet(sk1, one), top)))
% 7.89/1.43 = { by axiom 12 (composition_distributivity_7) R->L }
% 7.89/1.43 meet(X, composition(join(sk1, meet(sk1, one)), top))
% 7.89/1.43 = { by lemma 57 }
% 7.89/1.43 meet(X, composition(sk1, top))
% 7.89/1.43 = { by lemma 36 R->L }
% 7.89/1.43 meet(composition(sk1, top), X)
% 7.89/1.43 = { by axiom 4 (goals_14) }
% 7.89/1.43 meet(sk1, X)
% 7.89/1.43
% 7.89/1.43 Goal 1 (goals_15): join(meet(sk1, sk2), composition(meet(sk1, one), sk2)) = composition(meet(sk1, one), sk2).
% 7.89/1.43 Proof:
% 7.89/1.43 join(meet(sk1, sk2), composition(meet(sk1, one), sk2))
% 7.89/1.43 = { by lemma 67 }
% 7.89/1.43 join(meet(sk1, sk2), meet(sk1, sk2))
% 7.89/1.43 = { by lemma 42 }
% 7.89/1.43 meet(sk1, sk2)
% 7.89/1.43 = { by lemma 67 R->L }
% 7.89/1.43 composition(meet(sk1, one), sk2)
% 7.89/1.43 % SZS output end Proof
% 7.89/1.43
% 7.89/1.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------