%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL026-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:33:15 PM UTC 2026
% Result : Unsatisfiable 16.52s 2.57s
% Output : Proof 17.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL026-2 : 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 : n001.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
% 0.10/0.36 % DateTime : Sun Sep 27 22:59:01 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.52/2.57 Command-line arguments: --no-flatten-goal
% 16.52/2.57
% 16.52/2.57 % SZS status Unsatisfiable
% 16.52/2.57
% 17.28/2.65 % SZS output start Proof
% 17.28/2.65 Axiom 1 (def_zero_13): zero = meet(X, complement(X)).
% 17.28/2.65 Axiom 2 (converse_idempotence_8): converse(converse(X)) = X.
% 17.28/2.65 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 17.28/2.65 Axiom 4 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 17.28/2.65 Axiom 5 (def_top_12): top = join(X, complement(X)).
% 17.28/2.65 Axiom 6 (goals_14): join(sk1, one) = one.
% 17.28/2.65 Axiom 7 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 17.28/2.65 Axiom 8 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 17.28/2.65 Axiom 9 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 17.28/2.65 Axiom 10 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 17.28/2.65 Axiom 11 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 17.28/2.65 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 17.28/2.65 Axiom 13 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 17.28/2.65 Axiom 14 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 17.28/2.65
% 17.28/2.65 Lemma 15: complement(top) = zero.
% 17.28/2.65 Proof:
% 17.28/2.65 complement(top)
% 17.28/2.65 = { by axiom 5 (def_top_12) }
% 17.28/2.65 complement(join(complement(X), complement(complement(X))))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) R->L }
% 17.28/2.65 meet(X, complement(X))
% 17.28/2.65 = { by axiom 1 (def_zero_13) R->L }
% 17.28/2.65 zero
% 17.28/2.65
% 17.28/2.65 Lemma 16: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 join(meet(X, Y), complement(join(complement(X), Y)))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) }
% 17.28/2.65 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 17.28/2.65 = { by axiom 13 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 17: join(meet(X, Y), meet(X, complement(Y))) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 join(meet(X, Y), meet(X, complement(Y)))
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.65 join(meet(X, complement(Y)), meet(X, Y))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) }
% 17.28/2.65 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 17.28/2.65 = { by lemma 16 }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 18: meet(Y, X) = meet(X, Y).
% 17.28/2.65 Proof:
% 17.28/2.65 meet(Y, X)
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) }
% 17.28/2.65 complement(join(complement(Y), complement(X)))
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.65 complement(join(complement(X), complement(Y)))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) R->L }
% 17.28/2.65 meet(X, Y)
% 17.28/2.65
% 17.28/2.65 Lemma 19: complement(join(zero, complement(X))) = meet(X, top).
% 17.28/2.65 Proof:
% 17.28/2.65 complement(join(zero, complement(X)))
% 17.28/2.65 = { by lemma 15 R->L }
% 17.28/2.65 complement(join(complement(top), complement(X)))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) R->L }
% 17.28/2.65 meet(top, X)
% 17.28/2.65 = { by lemma 18 R->L }
% 17.28/2.65 meet(X, top)
% 17.28/2.65
% 17.28/2.65 Lemma 20: composition(converse(one), X) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 composition(converse(one), X)
% 17.28/2.65 = { by axiom 2 (converse_idempotence_8) R->L }
% 17.28/2.65 composition(converse(one), converse(converse(X)))
% 17.28/2.65 = { by axiom 8 (converse_multiplicativity_10) R->L }
% 17.28/2.65 converse(composition(converse(X), one))
% 17.28/2.65 = { by axiom 3 (composition_identity_6) }
% 17.28/2.65 converse(converse(X))
% 17.28/2.65 = { by axiom 2 (converse_idempotence_8) }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 21: composition(one, X) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 composition(one, X)
% 17.28/2.65 = { by lemma 20 R->L }
% 17.28/2.65 composition(converse(one), composition(one, X))
% 17.28/2.65 = { by axiom 9 (composition_associativity_5) }
% 17.28/2.65 composition(composition(converse(one), one), X)
% 17.28/2.65 = { by axiom 3 (composition_identity_6) }
% 17.28/2.65 composition(converse(one), X)
% 17.28/2.65 = { by lemma 20 }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 22: join(complement(X), complement(X)) = complement(X).
% 17.28/2.65 Proof:
% 17.28/2.65 join(complement(X), complement(X))
% 17.28/2.65 = { by lemma 20 R->L }
% 17.28/2.65 join(complement(X), composition(converse(one), complement(X)))
% 17.28/2.65 = { by lemma 21 R->L }
% 17.28/2.65 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.65 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 17.28/2.65 = { by axiom 14 (converse_cancellativity_11) }
% 17.28/2.65 complement(X)
% 17.28/2.65
% 17.28/2.65 Lemma 23: join(zero, complement(complement(X))) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 join(zero, complement(complement(X)))
% 17.28/2.65 = { by axiom 1 (def_zero_13) }
% 17.28/2.65 join(meet(X, complement(X)), complement(complement(X)))
% 17.28/2.65 = { by lemma 22 R->L }
% 17.28/2.65 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 17.28/2.65 = { by lemma 16 }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 24: meet(top, complement(X)) = complement(X).
% 17.28/2.65 Proof:
% 17.28/2.65 meet(top, complement(X))
% 17.28/2.65 = { by lemma 18 }
% 17.28/2.65 meet(complement(X), top)
% 17.28/2.65 = { by lemma 19 R->L }
% 17.28/2.65 complement(join(zero, complement(complement(X))))
% 17.28/2.65 = { by lemma 23 }
% 17.28/2.65 complement(X)
% 17.28/2.65
% 17.28/2.65 Lemma 25: complement(zero) = top.
% 17.28/2.65 Proof:
% 17.28/2.65 complement(zero)
% 17.28/2.65 = { by lemma 17 R->L }
% 17.28/2.65 join(meet(complement(zero), top), meet(complement(zero), complement(top)))
% 17.28/2.65 = { by lemma 15 }
% 17.28/2.65 join(meet(complement(zero), top), meet(complement(zero), zero))
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.65 join(meet(complement(zero), zero), meet(complement(zero), top))
% 17.28/2.65 = { by lemma 18 R->L }
% 17.28/2.65 join(meet(zero, complement(zero)), meet(complement(zero), top))
% 17.28/2.65 = { by axiom 1 (def_zero_13) R->L }
% 17.28/2.65 join(zero, meet(complement(zero), top))
% 17.28/2.65 = { by lemma 18 R->L }
% 17.28/2.65 join(zero, meet(top, complement(zero)))
% 17.28/2.65 = { by lemma 24 }
% 17.28/2.65 join(zero, complement(zero))
% 17.28/2.65 = { by axiom 5 (def_top_12) R->L }
% 17.28/2.65 top
% 17.28/2.65
% 17.28/2.65 Lemma 26: join(X, join(Y, complement(X))) = join(Y, top).
% 17.28/2.65 Proof:
% 17.28/2.65 join(X, join(Y, complement(X)))
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.65 join(X, join(complement(X), Y))
% 17.28/2.65 = { by axiom 11 (maddux2_join_associativity_2) }
% 17.28/2.65 join(join(X, complement(X)), Y)
% 17.28/2.65 = { by axiom 5 (def_top_12) R->L }
% 17.28/2.65 join(top, Y)
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.65 join(Y, top)
% 17.28/2.65
% 17.28/2.65 Lemma 27: join(top, complement(X)) = top.
% 17.28/2.65 Proof:
% 17.28/2.65 join(top, complement(X))
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.65 join(complement(X), top)
% 17.28/2.65 = { by lemma 26 R->L }
% 17.28/2.65 join(X, join(complement(X), complement(X)))
% 17.28/2.65 = { by lemma 22 }
% 17.28/2.65 join(X, complement(X))
% 17.28/2.65 = { by axiom 5 (def_top_12) R->L }
% 17.28/2.65 top
% 17.28/2.65
% 17.28/2.65 Lemma 28: join(zero, meet(X, top)) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 join(zero, meet(X, top))
% 17.28/2.65 = { by lemma 25 R->L }
% 17.28/2.65 join(zero, meet(X, complement(zero)))
% 17.28/2.65 = { by lemma 15 R->L }
% 17.28/2.65 join(complement(top), meet(X, complement(zero)))
% 17.28/2.65 = { by lemma 27 R->L }
% 17.28/2.65 join(complement(join(top, complement(X))), meet(X, complement(zero)))
% 17.28/2.65 = { by lemma 25 R->L }
% 17.28/2.65 join(complement(join(complement(zero), complement(X))), meet(X, complement(zero)))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) R->L }
% 17.28/2.65 join(meet(zero, X), meet(X, complement(zero)))
% 17.28/2.65 = { by lemma 18 R->L }
% 17.28/2.65 join(meet(X, zero), meet(X, complement(zero)))
% 17.28/2.65 = { by lemma 17 }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 29: join(zero, complement(X)) = complement(X).
% 17.28/2.65 Proof:
% 17.28/2.65 join(zero, complement(X))
% 17.28/2.65 = { by lemma 24 R->L }
% 17.28/2.65 join(zero, meet(top, complement(X)))
% 17.28/2.65 = { by lemma 18 }
% 17.28/2.65 join(zero, meet(complement(X), top))
% 17.28/2.65 = { by lemma 28 }
% 17.28/2.65 complement(X)
% 17.28/2.65
% 17.28/2.65 Lemma 30: meet(X, top) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 meet(X, top)
% 17.28/2.65 = { by lemma 19 R->L }
% 17.28/2.65 complement(join(zero, complement(X)))
% 17.28/2.65 = { by lemma 29 R->L }
% 17.28/2.65 join(zero, complement(join(zero, complement(X))))
% 17.28/2.65 = { by lemma 19 }
% 17.28/2.65 join(zero, meet(X, top))
% 17.28/2.65 = { by lemma 28 }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 31: join(X, X) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 join(X, X)
% 17.28/2.65 = { by lemma 30 R->L }
% 17.28/2.65 join(X, meet(X, top))
% 17.28/2.65 = { by lemma 30 R->L }
% 17.28/2.65 join(meet(X, top), meet(X, top))
% 17.28/2.65 = { by lemma 18 }
% 17.28/2.65 join(meet(top, X), meet(X, top))
% 17.28/2.65 = { by lemma 18 }
% 17.28/2.65 join(meet(top, X), meet(top, X))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) }
% 17.28/2.65 join(meet(top, X), complement(join(complement(top), complement(X))))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) }
% 17.28/2.65 join(complement(join(complement(top), complement(X))), complement(join(complement(top), complement(X))))
% 17.28/2.65 = { by lemma 22 }
% 17.28/2.65 complement(join(complement(top), complement(X)))
% 17.28/2.65 = { by axiom 7 (maddux4_definiton_of_meet_4) R->L }
% 17.28/2.65 meet(top, X)
% 17.28/2.65 = { by lemma 18 R->L }
% 17.28/2.65 meet(X, top)
% 17.28/2.65 = { by lemma 30 }
% 17.28/2.65 X
% 17.28/2.65
% 17.28/2.65 Lemma 32: join(X, top) = top.
% 17.28/2.65 Proof:
% 17.28/2.65 join(X, top)
% 17.28/2.65 = { by lemma 27 R->L }
% 17.28/2.65 join(X, join(top, complement(X)))
% 17.28/2.65 = { by lemma 26 }
% 17.28/2.65 join(top, top)
% 17.28/2.65 = { by lemma 26 R->L }
% 17.28/2.65 join(zero, join(top, complement(zero)))
% 17.28/2.65 = { by lemma 27 }
% 17.28/2.65 join(zero, top)
% 17.28/2.65 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.65 join(top, zero)
% 17.28/2.65 = { by lemma 15 R->L }
% 17.28/2.65 join(top, complement(top))
% 17.28/2.65 = { by axiom 5 (def_top_12) R->L }
% 17.28/2.65 top
% 17.28/2.65
% 17.28/2.65 Lemma 33: join(X, zero) = X.
% 17.28/2.65 Proof:
% 17.28/2.65 join(X, zero)
% 17.28/2.65 = { by lemma 15 R->L }
% 17.28/2.65 join(X, complement(top))
% 17.28/2.65 = { by lemma 32 R->L }
% 17.28/2.65 join(X, complement(join(complement(X), top)))
% 17.28/2.65 = { by lemma 30 R->L }
% 17.28/2.65 join(meet(X, top), complement(join(complement(X), top)))
% 17.28/2.65 = { by lemma 16 }
% 17.28/2.66 X
% 17.28/2.66
% 17.28/2.66 Lemma 34: join(one, sk1) = one.
% 17.28/2.66 Proof:
% 17.28/2.66 join(one, sk1)
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.66 join(sk1, one)
% 17.28/2.66 = { by axiom 6 (goals_14) }
% 17.28/2.66 one
% 17.28/2.66
% 17.28/2.66 Lemma 35: join(meet(X, Y), complement(join(Y, complement(X)))) = X.
% 17.28/2.66 Proof:
% 17.28/2.66 join(meet(X, Y), complement(join(Y, complement(X))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.66 join(meet(X, Y), complement(join(complement(X), Y)))
% 17.28/2.66 = { by lemma 16 }
% 17.28/2.66 X
% 17.28/2.66
% 17.28/2.66 Lemma 36: meet(X, join(complement(X), Y)) = meet(X, Y).
% 17.28/2.66 Proof:
% 17.28/2.66 meet(X, join(complement(X), Y))
% 17.28/2.66 = { by axiom 7 (maddux4_definiton_of_meet_4) }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), Y))))
% 17.28/2.66 = { by lemma 16 R->L }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(meet(Y, complement(X)), complement(join(complement(Y), complement(X))))))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(complement(join(complement(Y), complement(X))), meet(Y, complement(X)))))))
% 17.28/2.66 = { by lemma 22 R->L }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(join(complement(join(complement(Y), complement(X))), complement(join(complement(Y), complement(X)))), meet(Y, complement(X)))))))
% 17.28/2.66 = { by axiom 11 (maddux2_join_associativity_2) R->L }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(complement(join(complement(Y), complement(X))), join(complement(join(complement(Y), complement(X))), meet(Y, complement(X))))))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(complement(join(complement(Y), complement(X))), join(meet(Y, complement(X)), complement(join(complement(Y), complement(X)))))))))
% 17.28/2.66 = { by lemma 16 }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(complement(join(complement(Y), complement(X))), Y)))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(Y, complement(join(complement(Y), complement(X))))))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.66 complement(join(complement(X), complement(join(complement(X), join(Y, complement(join(complement(X), complement(Y))))))))
% 17.28/2.66 = { by axiom 11 (maddux2_join_associativity_2) }
% 17.28/2.66 complement(join(complement(X), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 30 R->L }
% 17.28/2.66 complement(join(meet(complement(X), top), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 19 R->L }
% 17.28/2.66 complement(join(complement(join(zero, complement(complement(X)))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 16 R->L }
% 17.28/2.66 complement(join(complement(join(meet(join(zero, complement(complement(X))), Y), complement(join(complement(join(zero, complement(complement(X)))), Y)))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by axiom 7 (maddux4_definiton_of_meet_4) }
% 17.28/2.66 complement(join(complement(join(complement(join(complement(join(zero, complement(complement(X)))), complement(Y))), complement(join(complement(join(zero, complement(complement(X)))), Y)))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by axiom 7 (maddux4_definiton_of_meet_4) R->L }
% 17.28/2.66 complement(join(meet(join(complement(join(zero, complement(complement(X)))), complement(Y)), join(complement(join(zero, complement(complement(X)))), Y)), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 18 R->L }
% 17.28/2.66 complement(join(meet(join(complement(join(zero, complement(complement(X)))), Y), join(complement(join(zero, complement(complement(X)))), complement(Y))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.66 complement(join(meet(join(Y, complement(join(zero, complement(complement(X))))), join(complement(join(zero, complement(complement(X)))), complement(Y))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.66 complement(join(meet(join(Y, complement(join(zero, complement(complement(X))))), join(complement(Y), complement(join(zero, complement(complement(X)))))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 19 }
% 17.28/2.66 complement(join(meet(join(Y, meet(complement(X), top)), join(complement(Y), complement(join(zero, complement(complement(X)))))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 30 }
% 17.28/2.66 complement(join(meet(join(Y, complement(X)), join(complement(Y), complement(join(zero, complement(complement(X)))))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 19 }
% 17.28/2.66 complement(join(meet(join(Y, complement(X)), join(complement(Y), meet(complement(X), top))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 30 }
% 17.28/2.66 complement(join(meet(join(Y, complement(X)), join(complement(Y), complement(X))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.66 complement(join(meet(join(complement(X), Y), join(complement(Y), complement(X))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.66 complement(join(meet(join(complement(X), Y), join(complement(X), complement(Y))), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 18 }
% 17.28/2.66 complement(join(meet(join(complement(X), complement(Y)), join(complement(X), Y)), complement(join(join(complement(X), Y), complement(join(complement(X), complement(Y)))))))
% 17.28/2.66 = { by lemma 35 }
% 17.28/2.66 complement(join(complement(X), complement(Y)))
% 17.28/2.66 = { by axiom 7 (maddux4_definiton_of_meet_4) R->L }
% 17.28/2.66 meet(X, Y)
% 17.28/2.66
% 17.28/2.66 Lemma 37: meet(X, composition(sk1, top)) = composition(sk1, X).
% 17.28/2.66 Proof:
% 17.28/2.66 meet(X, composition(sk1, top))
% 17.28/2.66 = { by lemma 36 R->L }
% 17.28/2.66 meet(X, join(complement(X), composition(sk1, top)))
% 17.28/2.66 = { by axiom 5 (def_top_12) }
% 17.28/2.66 meet(X, join(complement(X), composition(sk1, join(complement(X), complement(complement(X))))))
% 17.28/2.66 = { by axiom 2 (converse_idempotence_8) R->L }
% 17.28/2.66 meet(X, join(complement(X), composition(sk1, join(complement(X), converse(converse(complement(complement(X))))))))
% 17.28/2.66 = { by axiom 2 (converse_idempotence_8) R->L }
% 17.28/2.66 meet(X, join(complement(X), converse(converse(composition(sk1, join(complement(X), converse(converse(complement(complement(X))))))))))
% 17.28/2.66 = { by axiom 8 (converse_multiplicativity_10) }
% 17.28/2.66 meet(X, join(complement(X), converse(composition(converse(join(complement(X), converse(converse(complement(complement(X)))))), converse(sk1)))))
% 17.28/2.66 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.66 meet(X, join(complement(X), converse(composition(converse(join(converse(converse(complement(complement(X)))), complement(X))), converse(sk1)))))
% 17.28/2.66 = { by axiom 10 (converse_additivity_9) }
% 17.28/2.66 meet(X, join(complement(X), converse(composition(join(converse(converse(converse(complement(complement(X))))), converse(complement(X))), converse(sk1)))))
% 17.28/2.67 = { by axiom 2 (converse_idempotence_8) }
% 17.28/2.67 meet(X, join(complement(X), converse(composition(join(converse(complement(complement(X))), converse(complement(X))), converse(sk1)))))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.67 meet(X, join(complement(X), converse(composition(join(converse(complement(X)), converse(complement(complement(X)))), converse(sk1)))))
% 17.28/2.67 = { by axiom 12 (composition_distributivity_7) }
% 17.28/2.67 meet(X, join(complement(X), converse(join(composition(converse(complement(X)), converse(sk1)), composition(converse(complement(complement(X))), converse(sk1))))))
% 17.28/2.67 = { by axiom 8 (converse_multiplicativity_10) R->L }
% 17.28/2.67 meet(X, join(complement(X), converse(join(converse(composition(sk1, complement(X))), composition(converse(complement(complement(X))), converse(sk1))))))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.67 meet(X, join(complement(X), converse(join(composition(converse(complement(complement(X))), converse(sk1)), converse(composition(sk1, complement(X)))))))
% 17.28/2.67 = { by axiom 2 (converse_idempotence_8) R->L }
% 17.28/2.67 meet(X, join(complement(X), converse(join(composition(converse(converse(converse(complement(complement(X))))), converse(sk1)), converse(composition(sk1, complement(X)))))))
% 17.28/2.67 = { by axiom 8 (converse_multiplicativity_10) R->L }
% 17.28/2.67 meet(X, join(complement(X), converse(join(converse(composition(sk1, converse(converse(complement(complement(X)))))), converse(composition(sk1, complement(X)))))))
% 17.28/2.67 = { by axiom 10 (converse_additivity_9) R->L }
% 17.28/2.67 meet(X, join(complement(X), converse(converse(join(composition(sk1, converse(converse(complement(complement(X))))), composition(sk1, complement(X)))))))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.67 meet(X, join(complement(X), converse(converse(join(composition(sk1, complement(X)), composition(sk1, converse(converse(complement(complement(X))))))))))
% 17.28/2.67 = { by axiom 2 (converse_idempotence_8) }
% 17.28/2.67 meet(X, join(complement(X), join(composition(sk1, complement(X)), composition(sk1, converse(converse(complement(complement(X))))))))
% 17.28/2.67 = { by axiom 2 (converse_idempotence_8) }
% 17.28/2.67 meet(X, join(complement(X), join(composition(sk1, complement(X)), composition(sk1, complement(complement(X))))))
% 17.28/2.67 = { by axiom 11 (maddux2_join_associativity_2) }
% 17.28/2.67 meet(X, join(join(complement(X), composition(sk1, complement(X))), composition(sk1, complement(complement(X)))))
% 17.28/2.67 = { by lemma 21 R->L }
% 17.28/2.67 meet(X, join(join(composition(one, complement(X)), composition(sk1, complement(X))), composition(sk1, complement(complement(X)))))
% 17.28/2.67 = { by axiom 12 (composition_distributivity_7) R->L }
% 17.28/2.67 meet(X, join(composition(join(one, sk1), complement(X)), composition(sk1, complement(complement(X)))))
% 17.28/2.67 = { by lemma 34 }
% 17.28/2.67 meet(X, join(composition(one, complement(X)), composition(sk1, complement(complement(X)))))
% 17.28/2.67 = { by lemma 21 }
% 17.28/2.67 meet(X, join(complement(X), composition(sk1, complement(complement(X)))))
% 17.28/2.67 = { by lemma 36 }
% 17.28/2.67 meet(X, composition(sk1, complement(complement(X))))
% 17.28/2.67 = { by lemma 29 R->L }
% 17.28/2.67 meet(X, composition(sk1, join(zero, complement(complement(X)))))
% 17.28/2.67 = { by lemma 23 }
% 17.28/2.67 meet(X, composition(sk1, X))
% 17.28/2.67 = { by lemma 18 }
% 17.28/2.67 meet(composition(sk1, X), X)
% 17.28/2.67 = { by lemma 33 R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), zero)
% 17.28/2.67 = { by lemma 15 R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(top))
% 17.28/2.67 = { by lemma 32 R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(composition(meet(one, complement(sk1)), X), top)))
% 17.28/2.67 = { by lemma 26 R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(composition(sk1, X), join(composition(meet(one, complement(sk1)), X), complement(composition(sk1, X))))))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(composition(sk1, X), join(complement(composition(sk1, X)), composition(meet(one, complement(sk1)), X)))))
% 17.28/2.67 = { by axiom 11 (maddux2_join_associativity_2) }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(join(composition(sk1, X), complement(composition(sk1, X))), composition(meet(one, complement(sk1)), X))))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(composition(meet(one, complement(sk1)), X), join(composition(sk1, X), complement(composition(sk1, X))))))
% 17.28/2.67 = { by axiom 11 (maddux2_join_associativity_2) }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(join(composition(meet(one, complement(sk1)), X), composition(sk1, X)), complement(composition(sk1, X)))))
% 17.28/2.67 = { by axiom 12 (composition_distributivity_7) R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(composition(join(meet(one, complement(sk1)), sk1), X), complement(composition(sk1, X)))))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(meet(one, complement(sk1)), sk1), X))))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(sk1, meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by lemma 35 R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(join(meet(sk1, one), complement(join(one, complement(sk1)))), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by lemma 34 R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(join(meet(sk1, one), complement(join(join(one, sk1), complement(sk1)))), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by axiom 11 (maddux2_join_associativity_2) R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(join(meet(sk1, one), complement(join(one, join(sk1, complement(sk1))))), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by axiom 5 (def_top_12) R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(join(meet(sk1, one), complement(join(one, top))), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by lemma 32 }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(join(meet(sk1, one), complement(top)), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by lemma 15 }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(join(meet(sk1, one), zero), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by lemma 33 }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(meet(sk1, one), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by lemma 18 R->L }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(join(meet(one, sk1), meet(one, complement(sk1))), X))))
% 17.28/2.67 = { by lemma 17 }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), composition(one, X))))
% 17.28/2.67 = { by lemma 21 }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(complement(composition(sk1, X)), X)))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.67 join(meet(composition(sk1, X), X), complement(join(X, complement(composition(sk1, X)))))
% 17.28/2.67 = { by lemma 35 }
% 17.28/2.67 composition(sk1, X)
% 17.28/2.67
% 17.28/2.67 Goal 1 (goals_15): 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)).
% 17.28/2.67 Proof:
% 17.28/2.67 tuple(join(meet(composition(sk1, top), sk2), composition(sk1, sk2)), join(composition(sk1, sk2), meet(composition(sk1, top), sk2)))
% 17.28/2.67 = { by axiom 4 (maddux1_join_commutativity_1) }
% 17.28/2.67 tuple(join(composition(sk1, sk2), meet(composition(sk1, top), sk2)), join(composition(sk1, sk2), meet(composition(sk1, top), sk2)))
% 17.28/2.67 = { by lemma 18 R->L }
% 17.28/2.67 tuple(join(composition(sk1, sk2), meet(sk2, composition(sk1, top))), join(composition(sk1, sk2), meet(composition(sk1, top), sk2)))
% 17.28/2.67 = { by lemma 18 R->L }
% 17.28/2.67 tuple(join(composition(sk1, sk2), meet(sk2, composition(sk1, top))), join(composition(sk1, sk2), meet(sk2, composition(sk1, top))))
% 17.28/2.67 = { by lemma 37 }
% 17.28/2.67 tuple(join(composition(sk1, sk2), composition(sk1, sk2)), join(composition(sk1, sk2), meet(sk2, composition(sk1, top))))
% 17.28/2.67 = { by lemma 37 }
% 17.28/2.67 tuple(join(composition(sk1, sk2), composition(sk1, sk2)), join(composition(sk1, sk2), composition(sk1, sk2)))
% 17.28/2.67 = { by lemma 31 }
% 17.28/2.67 tuple(composition(sk1, sk2), join(composition(sk1, sk2), composition(sk1, sk2)))
% 17.28/2.67 = { by lemma 31 }
% 17.28/2.67 tuple(composition(sk1, sk2), composition(sk1, sk2))
% 17.28/2.67 = { by lemma 37 R->L }
% 17.28/2.67 tuple(composition(sk1, sk2), meet(sk2, composition(sk1, top)))
% 17.28/2.67 = { by lemma 18 }
% 17.28/2.67 tuple(composition(sk1, sk2), meet(composition(sk1, top), sk2))
% 17.28/2.67 % SZS output end Proof
% 17.28/2.67
% 17.28/2.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------