%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL026-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:33:16 PM UTC 2026
% Result : Unsatisfiable 14.84s 2.33s
% Output : Proof 15.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL026-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:58:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.84/2.33 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 14.84/2.33
% 14.84/2.33 % SZS status Unsatisfiable
% 14.84/2.33
% 15.56/2.41 % SZS output start Proof
% 15.56/2.41 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 15.56/2.41 Axiom 2 (composition_identity_6): composition(X, one) = X.
% 15.56/2.41 Axiom 3 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 15.56/2.41 Axiom 4 (goals_17): join(sk1, one) = one.
% 15.56/2.41 Axiom 5 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 15.56/2.41 Axiom 6 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 15.56/2.41 Axiom 7 (def_top_12): top = join(X, complement(X)).
% 15.56/2.41 Axiom 8 (def_zero_13): zero = meet(X, complement(X)).
% 15.56/2.41 Axiom 9 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 15.56/2.41 Axiom 10 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 15.56/2.41 Axiom 11 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 15.56/2.41 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 15.56/2.41 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 15.56/2.41 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 15.56/2.41
% 15.56/2.41 Lemma 15: complement(top) = zero.
% 15.56/2.41 Proof:
% 15.56/2.41 complement(top)
% 15.56/2.41 = { by axiom 7 (def_top_12) }
% 15.56/2.41 complement(join(complement(X), complement(complement(X))))
% 15.56/2.41 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 15.56/2.41 meet(X, complement(X))
% 15.56/2.41 = { by axiom 8 (def_zero_13) R->L }
% 15.56/2.41 zero
% 15.56/2.41
% 15.56/2.41 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 15.56/2.41 Proof:
% 15.56/2.41 join(X, join(Y, complement(X)))
% 15.56/2.41 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.41 join(X, join(complement(X), Y))
% 15.56/2.41 = { by axiom 10 (maddux2_join_associativity_2) }
% 15.56/2.41 join(join(X, complement(X)), Y)
% 15.56/2.41 = { by axiom 7 (def_top_12) R->L }
% 15.56/2.41 join(top, Y)
% 15.56/2.41 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.41 join(Y, top)
% 15.56/2.41
% 15.56/2.41 Lemma 17: composition(converse(one), X) = X.
% 15.56/2.41 Proof:
% 15.56/2.41 composition(converse(one), X)
% 15.56/2.41 = { by axiom 1 (converse_idempotence_8) R->L }
% 15.56/2.41 composition(converse(one), converse(converse(X)))
% 15.56/2.41 = { by axiom 5 (converse_multiplicativity_10) R->L }
% 15.56/2.41 converse(composition(converse(X), one))
% 15.56/2.41 = { by axiom 2 (composition_identity_6) }
% 15.56/2.41 converse(converse(X))
% 15.56/2.41 = { by axiom 1 (converse_idempotence_8) }
% 15.56/2.41 X
% 15.56/2.41
% 15.56/2.41 Lemma 18: composition(one, X) = X.
% 15.56/2.41 Proof:
% 15.56/2.41 composition(one, X)
% 15.56/2.41 = { by lemma 17 R->L }
% 15.56/2.41 composition(converse(one), composition(one, X))
% 15.56/2.41 = { by axiom 9 (composition_associativity_5) }
% 15.56/2.41 composition(composition(converse(one), one), X)
% 15.56/2.41 = { by axiom 2 (composition_identity_6) }
% 15.56/2.41 composition(converse(one), X)
% 15.56/2.41 = { by lemma 17 }
% 15.56/2.41 X
% 15.56/2.41
% 15.56/2.41 Lemma 19: join(complement(X), complement(X)) = complement(X).
% 15.56/2.41 Proof:
% 15.56/2.41 join(complement(X), complement(X))
% 15.56/2.41 = { by lemma 17 R->L }
% 15.56/2.41 join(complement(X), composition(converse(one), complement(X)))
% 15.56/2.41 = { by lemma 18 R->L }
% 15.56/2.41 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 15.56/2.41 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.41 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 15.56/2.41 = { by axiom 13 (converse_cancellativity_11) }
% 15.56/2.41 complement(X)
% 15.56/2.41
% 15.56/2.41 Lemma 20: join(top, complement(X)) = top.
% 15.56/2.41 Proof:
% 15.56/2.41 join(top, complement(X))
% 15.56/2.41 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.41 join(complement(X), top)
% 15.56/2.41 = { by lemma 16 R->L }
% 15.56/2.41 join(X, join(complement(X), complement(X)))
% 15.56/2.41 = { by lemma 19 }
% 15.56/2.41 join(X, complement(X))
% 15.56/2.41 = { by axiom 7 (def_top_12) R->L }
% 15.56/2.41 top
% 15.56/2.41
% 15.56/2.41 Lemma 21: join(X, top) = top.
% 15.56/2.41 Proof:
% 15.56/2.41 join(X, top)
% 15.56/2.41 = { by lemma 20 R->L }
% 15.56/2.41 join(X, join(top, complement(X)))
% 15.56/2.41 = { by lemma 16 }
% 15.56/2.41 join(top, top)
% 15.56/2.41 = { by axiom 7 (def_top_12) }
% 15.56/2.41 join(top, join(zero, complement(zero)))
% 15.56/2.41 = { by axiom 10 (maddux2_join_associativity_2) }
% 15.56/2.41 join(join(top, zero), complement(zero))
% 15.56/2.41 = { by lemma 15 R->L }
% 15.56/2.41 join(join(top, complement(top)), complement(zero))
% 15.56/2.41 = { by axiom 7 (def_top_12) R->L }
% 15.56/2.41 join(top, complement(zero))
% 15.56/2.41 = { by lemma 20 }
% 15.56/2.41 top
% 15.56/2.41
% 15.56/2.41 Lemma 22: join(top, X) = top.
% 15.56/2.41 Proof:
% 15.56/2.41 join(top, X)
% 15.56/2.41 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.41 join(X, top)
% 15.56/2.41 = { by lemma 21 }
% 15.56/2.42 top
% 15.56/2.42
% 15.56/2.42 Lemma 23: converse(top) = top.
% 15.56/2.42 Proof:
% 15.56/2.42 converse(top)
% 15.56/2.42 = { by axiom 7 (def_top_12) }
% 15.56/2.42 converse(join(converse(top), complement(converse(top))))
% 15.56/2.42 = { by axiom 6 (converse_additivity_9) }
% 15.56/2.42 join(converse(converse(top)), converse(complement(converse(top))))
% 15.56/2.42 = { by axiom 1 (converse_idempotence_8) }
% 15.56/2.42 join(top, converse(complement(converse(top))))
% 15.56/2.42 = { by lemma 22 }
% 15.56/2.42 top
% 15.56/2.42
% 15.56/2.42 Lemma 24: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 join(meet(X, Y), complement(join(complement(X), Y)))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.42 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 15.56/2.42 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 25: meet(Y, X) = meet(X, Y).
% 15.56/2.42 Proof:
% 15.56/2.42 meet(Y, X)
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.42 complement(join(complement(Y), complement(X)))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 complement(join(complement(X), complement(Y)))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 15.56/2.42 meet(X, Y)
% 15.56/2.42
% 15.56/2.42 Lemma 26: complement(complement(X)) = meet(X, X).
% 15.56/2.42 Proof:
% 15.56/2.42 complement(complement(X))
% 15.56/2.42 = { by lemma 19 R->L }
% 15.56/2.42 complement(join(complement(X), complement(X)))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 15.56/2.42 meet(X, X)
% 15.56/2.42
% 15.56/2.42 Lemma 27: complement(join(zero, complement(X))) = meet(X, top).
% 15.56/2.42 Proof:
% 15.56/2.42 complement(join(zero, complement(X)))
% 15.56/2.42 = { by lemma 15 R->L }
% 15.56/2.42 complement(join(complement(top), complement(X)))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 15.56/2.42 meet(top, X)
% 15.56/2.42 = { by lemma 25 R->L }
% 15.56/2.42 meet(X, top)
% 15.56/2.42
% 15.56/2.42 Lemma 28: join(zero, meet(X, X)) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 join(zero, meet(X, X))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.42 join(zero, complement(join(complement(X), complement(X))))
% 15.56/2.42 = { by axiom 8 (def_zero_13) }
% 15.56/2.42 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 15.56/2.42 = { by lemma 24 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 29: meet(top, complement(X)) = complement(X).
% 15.56/2.42 Proof:
% 15.56/2.42 meet(top, complement(X))
% 15.56/2.42 = { by lemma 25 }
% 15.56/2.42 meet(complement(X), top)
% 15.56/2.42 = { by lemma 27 R->L }
% 15.56/2.42 complement(join(zero, complement(complement(X))))
% 15.56/2.42 = { by lemma 26 }
% 15.56/2.42 complement(join(zero, meet(X, X)))
% 15.56/2.42 = { by lemma 28 }
% 15.56/2.42 complement(X)
% 15.56/2.42
% 15.56/2.42 Lemma 30: meet(X, X) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 meet(X, X)
% 15.56/2.42 = { by lemma 24 R->L }
% 15.56/2.42 join(meet(meet(X, X), top), complement(join(complement(meet(X, X)), top)))
% 15.56/2.42 = { by lemma 21 }
% 15.56/2.42 join(meet(meet(X, X), top), complement(top))
% 15.56/2.42 = { by lemma 15 }
% 15.56/2.42 join(meet(meet(X, X), top), zero)
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 join(zero, meet(meet(X, X), top))
% 15.56/2.42 = { by lemma 25 R->L }
% 15.56/2.42 join(zero, meet(top, meet(X, X)))
% 15.56/2.42 = { by lemma 26 R->L }
% 15.56/2.42 join(zero, meet(top, complement(complement(X))))
% 15.56/2.42 = { by lemma 29 }
% 15.56/2.42 join(zero, complement(complement(X)))
% 15.56/2.42 = { by lemma 26 }
% 15.56/2.42 join(zero, meet(X, X))
% 15.56/2.42 = { by lemma 28 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 31: join(X, zero) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 join(X, zero)
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(zero, X)
% 15.56/2.42 = { by lemma 30 R->L }
% 15.56/2.42 join(zero, meet(X, X))
% 15.56/2.42 = { by lemma 28 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 32: join(zero, X) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 join(zero, X)
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(X, zero)
% 15.56/2.42 = { by lemma 31 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 33: complement(complement(X)) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 complement(complement(X))
% 15.56/2.42 = { by lemma 26 }
% 15.56/2.42 meet(X, X)
% 15.56/2.42 = { by lemma 30 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 34: meet(X, top) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 meet(X, top)
% 15.56/2.42 = { by lemma 25 }
% 15.56/2.42 meet(top, X)
% 15.56/2.42 = { by lemma 30 R->L }
% 15.56/2.42 meet(top, meet(X, X))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.42 meet(top, complement(join(complement(X), complement(X))))
% 15.56/2.42 = { by lemma 29 }
% 15.56/2.42 complement(join(complement(X), complement(X)))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 15.56/2.42 meet(X, X)
% 15.56/2.42 = { by lemma 30 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 35: join(X, meet(X, Y)) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 join(X, meet(X, Y))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(meet(X, Y), X)
% 15.56/2.42 = { by lemma 24 R->L }
% 15.56/2.42 join(meet(X, Y), join(meet(X, Y), complement(join(complement(X), Y))))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(meet(X, Y), join(complement(join(complement(X), Y)), meet(X, Y)))
% 15.56/2.42 = { by lemma 33 R->L }
% 15.56/2.42 join(meet(X, Y), join(complement(join(complement(X), Y)), complement(complement(meet(X, Y)))))
% 15.56/2.42 = { by lemma 30 R->L }
% 15.56/2.42 join(meet(meet(X, Y), meet(X, Y)), join(complement(join(complement(X), Y)), complement(complement(meet(X, Y)))))
% 15.56/2.42 = { by lemma 26 R->L }
% 15.56/2.42 join(complement(complement(meet(X, Y))), join(complement(join(complement(X), Y)), complement(complement(meet(X, Y)))))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(complement(complement(meet(X, Y))), join(complement(complement(meet(X, Y))), complement(join(complement(X), Y))))
% 15.56/2.42 = { by axiom 10 (maddux2_join_associativity_2) }
% 15.56/2.42 join(join(complement(complement(meet(X, Y))), complement(complement(meet(X, Y)))), complement(join(complement(X), Y)))
% 15.56/2.42 = { by lemma 19 }
% 15.56/2.42 join(complement(complement(meet(X, Y))), complement(join(complement(X), Y)))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 join(complement(join(complement(X), Y)), complement(complement(meet(X, Y))))
% 15.56/2.42 = { by lemma 33 }
% 15.56/2.42 join(complement(join(complement(X), Y)), meet(X, Y))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 join(meet(X, Y), complement(join(complement(X), Y)))
% 15.56/2.42 = { by lemma 24 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 36: join(X, composition(sk1, X)) = X.
% 15.56/2.42 Proof:
% 15.56/2.42 join(X, composition(sk1, X))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(composition(sk1, X), X)
% 15.56/2.42 = { by lemma 17 R->L }
% 15.56/2.42 join(composition(sk1, X), composition(converse(one), X))
% 15.56/2.42 = { by axiom 12 (composition_distributivity_7) R->L }
% 15.56/2.42 composition(join(sk1, converse(one)), X)
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 composition(join(converse(one), sk1), X)
% 15.56/2.42 = { by axiom 2 (composition_identity_6) R->L }
% 15.56/2.42 composition(join(composition(converse(one), one), sk1), X)
% 15.56/2.42 = { by lemma 17 }
% 15.56/2.42 composition(join(one, sk1), X)
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 composition(join(sk1, one), X)
% 15.56/2.42 = { by axiom 4 (goals_17) }
% 15.56/2.42 composition(one, X)
% 15.56/2.42 = { by lemma 18 }
% 15.56/2.42 X
% 15.56/2.42
% 15.56/2.42 Lemma 37: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 15.56/2.42 Proof:
% 15.56/2.42 join(Y, join(X, Z))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(join(X, Z), Y)
% 15.56/2.42 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 15.56/2.42 join(X, join(Z, Y))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 join(X, join(Y, Z))
% 15.56/2.42
% 15.56/2.42 Lemma 38: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 15.56/2.42 Proof:
% 15.56/2.42 join(Z, join(X, Y))
% 15.56/2.42 = { by lemma 37 }
% 15.56/2.42 join(X, join(Z, Y))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 join(X, join(Y, Z))
% 15.56/2.42
% 15.56/2.42 Lemma 39: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 15.56/2.42 Proof:
% 15.56/2.42 join(complement(X), complement(Y))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 join(complement(Y), complement(X))
% 15.56/2.42 = { by lemma 34 R->L }
% 15.56/2.42 meet(join(complement(Y), complement(X)), top)
% 15.56/2.42 = { by lemma 25 R->L }
% 15.56/2.42 meet(top, join(complement(Y), complement(X)))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.42 meet(top, join(complement(X), complement(Y)))
% 15.56/2.42 = { by lemma 25 }
% 15.56/2.42 meet(join(complement(X), complement(Y)), top)
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.42 complement(join(complement(join(complement(X), complement(Y))), complement(top)))
% 15.56/2.42 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 15.56/2.42 complement(join(meet(X, Y), complement(top)))
% 15.56/2.42 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.42 complement(join(complement(top), meet(X, Y)))
% 15.56/2.42 = { by lemma 25 R->L }
% 15.56/2.42 complement(join(complement(top), meet(Y, X)))
% 15.56/2.42 = { by lemma 15 }
% 15.56/2.42 complement(join(zero, meet(Y, X)))
% 15.56/2.42 = { by lemma 32 }
% 15.56/2.42 complement(meet(Y, X))
% 15.56/2.42 = { by lemma 25 R->L }
% 15.56/2.42 complement(meet(X, Y))
% 15.56/2.42
% 15.56/2.42 Lemma 40: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 15.56/2.42 Proof:
% 15.56/2.42 complement(meet(X, complement(Y)))
% 15.56/2.42 = { by lemma 25 }
% 15.56/2.42 complement(meet(complement(Y), X))
% 15.56/2.42 = { by lemma 32 R->L }
% 15.56/2.42 complement(meet(join(zero, complement(Y)), X))
% 15.56/2.42 = { by lemma 39 R->L }
% 15.56/2.42 join(complement(join(zero, complement(Y))), complement(X))
% 15.56/2.42 = { by lemma 27 }
% 15.56/2.42 join(meet(Y, top), complement(X))
% 15.56/2.42 = { by lemma 34 }
% 15.56/2.42 join(Y, complement(X))
% 15.56/2.42
% 15.56/2.42 Lemma 41: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 15.56/2.42 Proof:
% 15.56/2.42 complement(join(X, complement(Y)))
% 15.56/2.42 = { by lemma 32 R->L }
% 15.56/2.42 complement(join(zero, join(X, complement(Y))))
% 15.56/2.42 = { by lemma 40 R->L }
% 15.56/2.42 complement(join(zero, complement(meet(Y, complement(X)))))
% 15.56/2.42 = { by lemma 27 }
% 15.56/2.42 meet(meet(Y, complement(X)), top)
% 15.56/2.42 = { by lemma 34 }
% 15.56/2.42 meet(Y, complement(X))
% 15.56/2.42
% 15.56/2.42 Lemma 42: join(X, complement(meet(X, Y))) = top.
% 15.56/2.42 Proof:
% 15.56/2.42 join(X, complement(meet(X, Y)))
% 15.56/2.42 = { by lemma 25 }
% 15.56/2.42 join(X, complement(meet(Y, X)))
% 15.56/2.42 = { by lemma 39 R->L }
% 15.56/2.42 join(X, join(complement(Y), complement(X)))
% 15.56/2.42 = { by lemma 16 }
% 15.56/2.42 join(complement(Y), top)
% 15.56/2.42 = { by lemma 21 }
% 15.56/2.42 top
% 15.56/2.42
% 15.56/2.42 Lemma 43: meet(X, join(X, complement(Y))) = X.
% 15.56/2.43 Proof:
% 15.56/2.43 meet(X, join(X, complement(Y)))
% 15.56/2.43 = { by lemma 31 R->L }
% 15.56/2.43 join(meet(X, join(X, complement(Y))), zero)
% 15.56/2.43 = { by lemma 15 R->L }
% 15.56/2.43 join(meet(X, join(X, complement(Y))), complement(top))
% 15.56/2.43 = { by lemma 40 R->L }
% 15.56/2.43 join(meet(X, complement(meet(Y, complement(X)))), complement(top))
% 15.56/2.43 = { by lemma 25 R->L }
% 15.56/2.43 join(meet(X, complement(meet(complement(X), Y))), complement(top))
% 15.56/2.43 = { by lemma 42 R->L }
% 15.56/2.43 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(complement(X), Y)))))
% 15.56/2.43 = { by lemma 24 }
% 15.56/2.43 X
% 15.56/2.43
% 15.56/2.43 Lemma 44: meet(X, join(X, Y)) = X.
% 15.56/2.43 Proof:
% 15.56/2.43 meet(X, join(X, Y))
% 15.56/2.43 = { by lemma 34 R->L }
% 15.56/2.43 meet(X, join(X, meet(Y, top)))
% 15.56/2.43 = { by lemma 27 R->L }
% 15.56/2.43 meet(X, join(X, complement(join(zero, complement(Y)))))
% 15.56/2.43 = { by lemma 43 }
% 15.56/2.43 X
% 15.56/2.43
% 15.56/2.43 Lemma 45: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 15.56/2.43 Proof:
% 15.56/2.43 meet(Y, meet(X, Z))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 meet(Y, meet(Z, X))
% 15.56/2.43 = { by lemma 34 R->L }
% 15.56/2.43 meet(meet(Y, meet(Z, X)), top)
% 15.56/2.43 = { by lemma 27 R->L }
% 15.56/2.43 complement(join(zero, complement(meet(Y, meet(Z, X)))))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 complement(join(zero, complement(meet(Y, meet(X, Z)))))
% 15.56/2.43 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.43 complement(join(zero, complement(meet(Y, complement(join(complement(X), complement(Z)))))))
% 15.56/2.43 = { by lemma 40 }
% 15.56/2.43 complement(join(zero, join(join(complement(X), complement(Z)), complement(Y))))
% 15.56/2.43 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 15.56/2.43 complement(join(zero, join(complement(X), join(complement(Z), complement(Y)))))
% 15.56/2.43 = { by lemma 39 }
% 15.56/2.43 complement(join(zero, join(complement(X), complement(meet(Z, Y)))))
% 15.56/2.43 = { by lemma 39 }
% 15.56/2.43 complement(join(zero, complement(meet(X, meet(Z, Y)))))
% 15.56/2.43 = { by lemma 25 R->L }
% 15.56/2.43 complement(join(zero, complement(meet(X, meet(Y, Z)))))
% 15.56/2.43 = { by lemma 27 }
% 15.56/2.43 meet(meet(X, meet(Y, Z)), top)
% 15.56/2.43 = { by lemma 34 }
% 15.56/2.43 meet(X, meet(Y, Z))
% 15.56/2.43
% 15.56/2.43 Lemma 46: meet(X, complement(meet(X, Y))) = meet(X, complement(Y)).
% 15.56/2.43 Proof:
% 15.56/2.43 meet(X, complement(meet(X, Y)))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 meet(X, complement(meet(Y, X)))
% 15.56/2.43 = { by lemma 24 R->L }
% 15.56/2.43 join(meet(meet(X, complement(meet(Y, X))), complement(Y)), complement(join(complement(meet(X, complement(meet(Y, X)))), complement(Y))))
% 15.56/2.43 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 15.56/2.43 join(meet(meet(X, complement(meet(Y, X))), complement(Y)), meet(meet(X, complement(meet(Y, X))), Y))
% 15.56/2.43 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.43 join(meet(meet(X, complement(meet(Y, X))), Y), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 25 R->L }
% 15.56/2.43 join(meet(Y, meet(X, complement(meet(Y, X)))), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 join(meet(Y, meet(complement(meet(Y, X)), X)), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 45 }
% 15.56/2.43 join(meet(complement(meet(Y, X)), meet(Y, X)), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 43 R->L }
% 15.56/2.43 join(meet(complement(meet(Y, X)), meet(meet(Y, X), join(meet(Y, X), complement(join(complement(Y), X))))), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 24 }
% 15.56/2.43 join(meet(complement(meet(Y, X)), meet(meet(Y, X), Y)), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 join(meet(meet(meet(Y, X), Y), complement(meet(Y, X))), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 41 R->L }
% 15.56/2.43 join(complement(join(meet(Y, X), complement(meet(meet(Y, X), Y)))), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 42 }
% 15.56/2.43 join(complement(top), meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 15 }
% 15.56/2.43 join(zero, meet(meet(X, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 32 }
% 15.56/2.43 meet(meet(X, complement(meet(Y, X))), complement(Y))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 meet(complement(Y), meet(X, complement(meet(Y, X))))
% 15.56/2.43 = { by lemma 45 R->L }
% 15.56/2.43 meet(X, meet(complement(Y), complement(meet(Y, X))))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 meet(X, meet(complement(meet(Y, X)), complement(Y)))
% 15.56/2.43 = { by lemma 32 R->L }
% 15.56/2.43 meet(X, meet(join(zero, complement(meet(Y, X))), complement(Y)))
% 15.56/2.43 = { by lemma 41 R->L }
% 15.56/2.43 meet(X, complement(join(Y, complement(join(zero, complement(meet(Y, X)))))))
% 15.56/2.43 = { by lemma 27 }
% 15.56/2.43 meet(X, complement(join(Y, meet(meet(Y, X), top))))
% 15.56/2.43 = { by lemma 34 }
% 15.56/2.43 meet(X, complement(join(Y, meet(Y, X))))
% 15.56/2.43 = { by lemma 35 }
% 15.56/2.43 meet(X, complement(Y))
% 15.56/2.43
% 15.56/2.43 Lemma 47: meet(X, join(Y, complement(X))) = meet(X, Y).
% 15.56/2.43 Proof:
% 15.56/2.43 meet(X, join(Y, complement(X)))
% 15.56/2.43 = { by lemma 40 R->L }
% 15.56/2.43 meet(X, complement(meet(X, complement(Y))))
% 15.56/2.43 = { by lemma 46 }
% 15.56/2.43 meet(X, complement(complement(Y)))
% 15.56/2.43 = { by lemma 33 }
% 15.56/2.43 meet(X, Y)
% 15.56/2.43
% 15.56/2.43 Lemma 48: join(converse(composition(X, Y)), composition(Z, converse(X))) = composition(join(Z, converse(Y)), converse(X)).
% 15.56/2.43 Proof:
% 15.56/2.43 join(converse(composition(X, Y)), composition(Z, converse(X)))
% 15.56/2.43 = { by axiom 5 (converse_multiplicativity_10) }
% 15.56/2.43 join(composition(converse(Y), converse(X)), composition(Z, converse(X)))
% 15.56/2.43 = { by axiom 12 (composition_distributivity_7) R->L }
% 15.56/2.43 composition(join(converse(Y), Z), converse(X))
% 15.56/2.43 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.43 composition(join(Z, converse(Y)), converse(X))
% 15.56/2.43
% 15.56/2.43 Lemma 49: meet(X, join(meet(Y, X), composition(sk1, X))) = join(meet(Y, X), composition(sk1, X)).
% 15.56/2.43 Proof:
% 15.56/2.43 meet(X, join(meet(Y, X), composition(sk1, X)))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 meet(join(meet(Y, X), composition(sk1, X)), X)
% 15.56/2.43 = { by lemma 35 R->L }
% 15.56/2.43 meet(join(meet(Y, X), composition(sk1, X)), join(X, meet(X, Y)))
% 15.56/2.43 = { by lemma 25 }
% 15.56/2.43 meet(join(meet(Y, X), composition(sk1, X)), join(X, meet(Y, X)))
% 15.56/2.43 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.43 meet(join(meet(Y, X), composition(sk1, X)), join(meet(Y, X), X))
% 15.56/2.43 = { by lemma 36 R->L }
% 15.56/2.43 meet(join(meet(Y, X), composition(sk1, X)), join(meet(Y, X), join(X, composition(sk1, X))))
% 15.56/2.43 = { by lemma 37 R->L }
% 15.56/2.43 meet(join(meet(Y, X), composition(sk1, X)), join(X, join(meet(Y, X), composition(sk1, X))))
% 15.56/2.43 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.43 meet(join(meet(Y, X), composition(sk1, X)), join(join(meet(Y, X), composition(sk1, X)), X))
% 15.56/2.43 = { by lemma 44 }
% 15.56/2.43 join(meet(Y, X), composition(sk1, X))
% 15.56/2.43
% 15.56/2.43 Lemma 50: join(meet(composition(sk1, top), X), composition(sk1, X)) = meet(composition(sk1, top), X).
% 15.56/2.43 Proof:
% 15.56/2.43 join(meet(composition(sk1, top), X), composition(sk1, X))
% 15.56/2.43 = { by lemma 49 R->L }
% 15.56/2.43 meet(X, join(meet(composition(sk1, top), X), composition(sk1, X)))
% 15.56/2.43 = { by lemma 44 R->L }
% 15.56/2.43 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), join(join(meet(composition(sk1, top), X), composition(sk1, X)), composition(sk1, top))))
% 15.56/2.43 = { by axiom 1 (converse_idempotence_8) R->L }
% 15.56/2.43 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), join(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(composition(sk1, top))))))
% 15.56/2.43 = { by axiom 1 (converse_idempotence_8) R->L }
% 15.56/2.43 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), join(converse(converse(join(meet(composition(sk1, top), X), composition(sk1, X)))), converse(converse(composition(sk1, top))))))
% 15.56/2.43 = { by axiom 6 (converse_additivity_9) R->L }
% 15.56/2.43 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(join(converse(join(meet(composition(sk1, top), X), composition(sk1, X))), converse(composition(sk1, top))))))
% 15.56/2.43 = { by axiom 6 (converse_additivity_9) R->L }
% 15.56/2.43 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(join(join(meet(composition(sk1, top), X), composition(sk1, X)), composition(sk1, top))))))
% 15.56/2.43 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.43 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(join(composition(sk1, top), join(meet(composition(sk1, top), X), composition(sk1, X)))))))
% 15.56/2.44 = { by lemma 38 }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(join(meet(composition(sk1, top), X), join(composition(sk1, X), composition(sk1, top)))))))
% 15.56/2.44 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(join(meet(composition(sk1, top), X), join(composition(sk1, top), composition(sk1, X)))))))
% 15.56/2.44 = { by axiom 10 (maddux2_join_associativity_2) }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(join(join(meet(composition(sk1, top), X), composition(sk1, top)), composition(sk1, X))))))
% 15.56/2.44 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(join(join(composition(sk1, top), meet(composition(sk1, top), X)), composition(sk1, X))))))
% 15.56/2.44 = { by lemma 35 }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(join(composition(sk1, top), composition(sk1, X))))))
% 15.56/2.44 = { by axiom 6 (converse_additivity_9) }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(join(converse(composition(sk1, top)), converse(composition(sk1, X))))))
% 15.56/2.44 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(join(converse(composition(sk1, X)), converse(composition(sk1, top))))))
% 15.56/2.44 = { by axiom 5 (converse_multiplicativity_10) }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(join(converse(composition(sk1, X)), composition(converse(top), converse(sk1))))))
% 15.56/2.44 = { by lemma 48 }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(composition(join(converse(top), converse(X)), converse(sk1)))))
% 15.56/2.44 = { by lemma 23 }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(composition(join(top, converse(X)), converse(sk1)))))
% 15.56/2.44 = { by lemma 22 }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(composition(top, converse(sk1)))))
% 15.56/2.44 = { by lemma 23 R->L }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(composition(converse(top), converse(sk1)))))
% 15.56/2.44 = { by axiom 5 (converse_multiplicativity_10) R->L }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), converse(converse(composition(sk1, top)))))
% 15.56/2.44 = { by axiom 1 (converse_idempotence_8) }
% 15.56/2.44 meet(X, meet(join(meet(composition(sk1, top), X), composition(sk1, X)), composition(sk1, top)))
% 15.56/2.44 = { by lemma 45 }
% 15.56/2.44 meet(join(meet(composition(sk1, top), X), composition(sk1, X)), meet(X, composition(sk1, top)))
% 15.56/2.44 = { by lemma 25 }
% 15.56/2.44 meet(join(meet(composition(sk1, top), X), composition(sk1, X)), meet(composition(sk1, top), X))
% 15.56/2.44 = { by lemma 25 }
% 15.56/2.44 meet(meet(composition(sk1, top), X), join(meet(composition(sk1, top), X), composition(sk1, X)))
% 15.56/2.44 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.44 complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X)))))
% 15.56/2.44 = { by lemma 32 R->L }
% 15.56/2.44 join(zero, complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by lemma 15 R->L }
% 15.56/2.44 join(complement(top), complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by lemma 22 R->L }
% 15.56/2.44 join(complement(join(top, composition(sk1, X))), complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.44 join(complement(join(composition(sk1, X), top)), complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by lemma 16 R->L }
% 15.56/2.44 join(complement(join(meet(composition(sk1, top), X), join(composition(sk1, X), complement(meet(composition(sk1, top), X))))), complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by lemma 38 R->L }
% 15.56/2.44 join(complement(join(complement(meet(composition(sk1, top), X)), join(meet(composition(sk1, top), X), composition(sk1, X)))), complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.44 join(complement(join(join(meet(composition(sk1, top), X), composition(sk1, X)), complement(meet(composition(sk1, top), X)))), complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by lemma 41 }
% 15.56/2.44 join(meet(meet(composition(sk1, top), X), complement(join(meet(composition(sk1, top), X), composition(sk1, X)))), complement(join(complement(meet(composition(sk1, top), X)), complement(join(meet(composition(sk1, top), X), composition(sk1, X))))))
% 15.56/2.44 = { by lemma 24 }
% 15.56/2.44 meet(composition(sk1, top), X)
% 15.56/2.44
% 15.56/2.44 Goal 1 (goals_18): tuple(join(meet(composition(sk1, top), sk2), composition(sk1, sk2)), join(composition(sk1, sk2), meet(composition(sk1, top), sk2))) = tuple(composition(sk1, sk2), meet(composition(sk1, top), sk2)).
% 15.56/2.44 Proof:
% 15.56/2.44 tuple(join(meet(composition(sk1, top), sk2), composition(sk1, sk2)), join(composition(sk1, sk2), meet(composition(sk1, top), sk2)))
% 15.56/2.44 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.44 tuple(join(meet(composition(sk1, top), sk2), composition(sk1, sk2)), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by lemma 49 R->L }
% 15.56/2.44 tuple(meet(sk2, join(meet(composition(sk1, top), sk2), composition(sk1, sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by lemma 47 R->L }
% 15.56/2.44 tuple(meet(sk2, join(join(meet(composition(sk1, top), sk2), composition(sk1, sk2)), complement(sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by lemma 50 }
% 15.56/2.44 tuple(meet(sk2, join(meet(composition(sk1, top), sk2), complement(sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by lemma 40 R->L }
% 15.56/2.44 tuple(meet(sk2, complement(meet(sk2, complement(meet(composition(sk1, top), sk2))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by lemma 25 R->L }
% 15.56/2.44 tuple(meet(sk2, complement(meet(sk2, complement(meet(sk2, composition(sk1, top)))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by lemma 46 }
% 15.56/2.44 tuple(meet(sk2, complement(meet(sk2, complement(composition(sk1, top))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by lemma 40 }
% 15.56/2.44 tuple(meet(sk2, join(composition(sk1, top), complement(sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.44 tuple(meet(sk2, join(complement(sk2), composition(sk1, top))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by axiom 7 (def_top_12) }
% 15.56/2.44 tuple(meet(sk2, join(complement(sk2), composition(sk1, join(sk2, complement(sk2))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.44 = { by axiom 1 (converse_idempotence_8) R->L }
% 15.56/2.44 tuple(meet(sk2, join(complement(sk2), composition(sk1, join(sk2, converse(converse(complement(sk2))))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), composition(sk1, join(converse(converse(complement(sk2))), sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 1 (converse_idempotence_8) R->L }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), composition(sk1, join(converse(converse(complement(sk2))), converse(converse(sk2)))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 6 (converse_additivity_9) R->L }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), composition(sk1, converse(join(converse(complement(sk2)), converse(sk2)))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 1 (converse_idempotence_8) R->L }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), composition(converse(converse(sk1)), converse(join(converse(complement(sk2)), converse(sk2)))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 5 (converse_multiplicativity_10) R->L }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), converse(composition(join(converse(complement(sk2)), converse(sk2)), converse(sk1))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 48 R->L }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), converse(join(converse(composition(sk1, sk2)), composition(converse(complement(sk2)), converse(sk1)))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 6 (converse_additivity_9) }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), join(converse(converse(composition(sk1, sk2))), converse(composition(converse(complement(sk2)), converse(sk1)))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 1 (converse_idempotence_8) }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), join(composition(sk1, sk2), converse(composition(converse(complement(sk2)), converse(sk1)))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 5 (converse_multiplicativity_10) }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), join(composition(sk1, sk2), composition(converse(converse(sk1)), converse(converse(complement(sk2))))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 1 (converse_idempotence_8) }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), join(composition(sk1, sk2), composition(sk1, converse(converse(complement(sk2))))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 1 (converse_idempotence_8) }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), join(composition(sk1, sk2), composition(sk1, complement(sk2))))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), join(composition(sk1, complement(sk2)), composition(sk1, sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 10 (maddux2_join_associativity_2) }
% 15.56/2.45 tuple(meet(sk2, join(join(complement(sk2), composition(sk1, complement(sk2))), composition(sk1, sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 18 R->L }
% 15.56/2.45 tuple(meet(sk2, join(join(composition(one, complement(sk2)), composition(sk1, complement(sk2))), composition(sk1, sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 12 (composition_distributivity_7) R->L }
% 15.56/2.45 tuple(meet(sk2, join(composition(join(one, sk1), complement(sk2)), composition(sk1, sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.45 tuple(meet(sk2, join(composition(join(sk1, one), complement(sk2)), composition(sk1, sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 4 (goals_17) }
% 15.56/2.45 tuple(meet(sk2, join(composition(one, complement(sk2)), composition(sk1, sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 18 }
% 15.56/2.45 tuple(meet(sk2, join(complement(sk2), composition(sk1, sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 3 (maddux1_join_commutativity_1) }
% 15.56/2.45 tuple(meet(sk2, join(composition(sk1, sk2), complement(sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 47 }
% 15.56/2.45 tuple(meet(sk2, composition(sk1, sk2)), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 25 }
% 15.56/2.45 tuple(meet(composition(sk1, sk2), sk2), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 15.56/2.45 tuple(complement(join(complement(composition(sk1, sk2)), complement(sk2))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 32 R->L }
% 15.56/2.45 tuple(join(zero, complement(join(complement(composition(sk1, sk2)), complement(sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 15 R->L }
% 15.56/2.45 tuple(join(complement(top), complement(join(complement(composition(sk1, sk2)), complement(sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 21 R->L }
% 15.56/2.45 tuple(join(complement(join(sk2, top)), complement(join(complement(composition(sk1, sk2)), complement(sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 7 (def_top_12) }
% 15.56/2.45 tuple(join(complement(join(sk2, join(composition(sk1, sk2), complement(composition(sk1, sk2))))), complement(join(complement(composition(sk1, sk2)), complement(sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by axiom 10 (maddux2_join_associativity_2) }
% 15.56/2.45 tuple(join(complement(join(join(sk2, composition(sk1, sk2)), complement(composition(sk1, sk2)))), complement(join(complement(composition(sk1, sk2)), complement(sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 36 }
% 15.56/2.45 tuple(join(complement(join(sk2, complement(composition(sk1, sk2)))), complement(join(complement(composition(sk1, sk2)), complement(sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 41 }
% 15.56/2.45 tuple(join(meet(composition(sk1, sk2), complement(sk2)), complement(join(complement(composition(sk1, sk2)), complement(sk2)))), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 24 }
% 15.56/2.45 tuple(composition(sk1, sk2), join(meet(composition(sk1, top), sk2), composition(sk1, sk2)))
% 15.56/2.45 = { by lemma 50 }
% 15.56/2.45 tuple(composition(sk1, sk2), meet(composition(sk1, top), sk2))
% 15.56/2.45 % SZS output end Proof
% 15.56/2.45
% 15.56/2.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------