%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL005-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:33:00 PM UTC 2026
% Result : Unsatisfiable 1.79s 0.67s
% Output : Proof 2.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL005-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 27 22:49:31 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.79/0.67 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.79/0.67
% 1.79/0.67 % SZS status Unsatisfiable
% 1.79/0.67
% 2.20/0.73 % SZS output start Proof
% 2.20/0.73 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 2.20/0.73 Axiom 2 (composition_identity_6): composition(X, one) = X.
% 2.20/0.73 Axiom 3 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 2.20/0.73 Axiom 4 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 2.20/0.73 Axiom 5 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 2.20/0.73 Axiom 6 (def_zero_13): zero = meet(X, complement(X)).
% 2.20/0.73 Axiom 7 (def_top_12): top = join(X, complement(X)).
% 2.20/0.73 Axiom 8 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 2.20/0.73 Axiom 9 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 2.20/0.73 Axiom 10 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 2.20/0.73 Axiom 11 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 2.20/0.73 Axiom 12 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 2.20/0.73
% 2.20/0.73 Lemma 13: complement(top) = zero.
% 2.20/0.73 Proof:
% 2.20/0.73 complement(top)
% 2.20/0.73 = { by axiom 7 (def_top_12) }
% 2.20/0.73 complement(join(complement(X), complement(complement(X))))
% 2.20/0.73 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 2.20/0.73 meet(X, complement(X))
% 2.20/0.73 = { by axiom 6 (def_zero_13) R->L }
% 2.20/0.73 zero
% 2.20/0.73
% 2.20/0.73 Lemma 14: join(X, join(Y, complement(X))) = join(Y, top).
% 2.20/0.73 Proof:
% 2.20/0.73 join(X, join(Y, complement(X)))
% 2.20/0.73 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.73 join(X, join(complement(X), Y))
% 2.20/0.73 = { by axiom 9 (maddux2_join_associativity_2) }
% 2.20/0.73 join(join(X, complement(X)), Y)
% 2.20/0.73 = { by axiom 7 (def_top_12) R->L }
% 2.20/0.73 join(top, Y)
% 2.20/0.73 = { by axiom 3 (maddux1_join_commutativity_1) }
% 2.20/0.73 join(Y, top)
% 2.20/0.73
% 2.20/0.73 Lemma 15: composition(converse(one), X) = X.
% 2.20/0.73 Proof:
% 2.20/0.73 composition(converse(one), X)
% 2.20/0.73 = { by axiom 1 (converse_idempotence_8) R->L }
% 2.20/0.73 composition(converse(one), converse(converse(X)))
% 2.20/0.73 = { by axiom 4 (converse_multiplicativity_10) R->L }
% 2.20/0.73 converse(composition(converse(X), one))
% 2.20/0.73 = { by axiom 2 (composition_identity_6) }
% 2.20/0.73 converse(converse(X))
% 2.20/0.73 = { by axiom 1 (converse_idempotence_8) }
% 2.20/0.73 X
% 2.20/0.73
% 2.20/0.73 Lemma 16: join(complement(X), complement(X)) = complement(X).
% 2.20/0.73 Proof:
% 2.20/0.73 join(complement(X), complement(X))
% 2.20/0.73 = { by lemma 15 R->L }
% 2.20/0.73 join(complement(X), composition(converse(one), complement(X)))
% 2.20/0.73 = { by lemma 15 R->L }
% 2.20/0.73 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 2.20/0.73 = { by axiom 2 (composition_identity_6) R->L }
% 2.20/0.73 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 2.20/0.73 = { by axiom 8 (composition_associativity_5) R->L }
% 2.20/0.73 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 2.20/0.73 = { by lemma 15 }
% 2.20/0.74 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 2.20/0.74 = { by axiom 11 (converse_cancellativity_11) }
% 2.20/0.74 complement(X)
% 2.20/0.74
% 2.20/0.74 Lemma 17: join(top, complement(X)) = top.
% 2.20/0.74 Proof:
% 2.20/0.74 join(top, complement(X))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(complement(X), top)
% 2.20/0.74 = { by lemma 14 R->L }
% 2.20/0.74 join(X, join(complement(X), complement(X)))
% 2.20/0.74 = { by lemma 16 }
% 2.20/0.74 join(X, complement(X))
% 2.20/0.74 = { by axiom 7 (def_top_12) R->L }
% 2.20/0.74 top
% 2.20/0.74
% 2.20/0.74 Lemma 18: join(X, top) = top.
% 2.20/0.74 Proof:
% 2.20/0.74 join(X, top)
% 2.20/0.74 = { by lemma 17 R->L }
% 2.20/0.74 join(X, join(top, complement(X)))
% 2.20/0.74 = { by lemma 14 }
% 2.20/0.74 join(top, top)
% 2.20/0.74 = { by axiom 7 (def_top_12) }
% 2.20/0.74 join(top, join(zero, complement(zero)))
% 2.20/0.74 = { by axiom 9 (maddux2_join_associativity_2) }
% 2.20/0.74 join(join(top, zero), complement(zero))
% 2.20/0.74 = { by lemma 13 R->L }
% 2.20/0.74 join(join(top, complement(top)), complement(zero))
% 2.20/0.74 = { by axiom 7 (def_top_12) R->L }
% 2.20/0.74 join(top, complement(zero))
% 2.20/0.74 = { by lemma 17 }
% 2.20/0.74 top
% 2.20/0.74
% 2.20/0.74 Lemma 19: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 join(meet(X, Y), complement(join(complement(X), Y)))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 2.20/0.74 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 2.20/0.74 = { by axiom 12 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 20: meet(Y, X) = meet(X, Y).
% 2.20/0.74 Proof:
% 2.20/0.74 meet(Y, X)
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 2.20/0.74 complement(join(complement(Y), complement(X)))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 complement(join(complement(X), complement(Y)))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 2.20/0.74 meet(X, Y)
% 2.20/0.74
% 2.20/0.74 Lemma 21: complement(complement(X)) = meet(X, X).
% 2.20/0.74 Proof:
% 2.20/0.74 complement(complement(X))
% 2.20/0.74 = { by lemma 16 R->L }
% 2.20/0.74 complement(join(complement(X), complement(X)))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 2.20/0.74 meet(X, X)
% 2.20/0.74
% 2.20/0.74 Lemma 22: complement(join(zero, complement(X))) = meet(X, top).
% 2.20/0.74 Proof:
% 2.20/0.74 complement(join(zero, complement(X)))
% 2.20/0.74 = { by lemma 13 R->L }
% 2.20/0.74 complement(join(complement(top), complement(X)))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 2.20/0.74 meet(top, X)
% 2.20/0.74 = { by lemma 20 R->L }
% 2.20/0.74 meet(X, top)
% 2.20/0.74
% 2.20/0.74 Lemma 23: join(zero, meet(X, X)) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 join(zero, meet(X, X))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 2.20/0.74 join(zero, complement(join(complement(X), complement(X))))
% 2.20/0.74 = { by axiom 6 (def_zero_13) }
% 2.20/0.74 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 2.20/0.74 = { by lemma 19 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 24: meet(top, complement(X)) = complement(X).
% 2.20/0.74 Proof:
% 2.20/0.74 meet(top, complement(X))
% 2.20/0.74 = { by lemma 20 }
% 2.20/0.74 meet(complement(X), top)
% 2.20/0.74 = { by lemma 22 R->L }
% 2.20/0.74 complement(join(zero, complement(complement(X))))
% 2.20/0.74 = { by lemma 21 }
% 2.20/0.74 complement(join(zero, meet(X, X)))
% 2.20/0.74 = { by lemma 23 }
% 2.20/0.74 complement(X)
% 2.20/0.74
% 2.20/0.74 Lemma 25: meet(X, X) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 meet(X, X)
% 2.20/0.74 = { by lemma 19 R->L }
% 2.20/0.74 join(meet(meet(X, X), top), complement(join(complement(meet(X, X)), top)))
% 2.20/0.74 = { by lemma 18 }
% 2.20/0.74 join(meet(meet(X, X), top), complement(top))
% 2.20/0.74 = { by lemma 13 }
% 2.20/0.74 join(meet(meet(X, X), top), zero)
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) }
% 2.20/0.74 join(zero, meet(meet(X, X), top))
% 2.20/0.74 = { by lemma 20 R->L }
% 2.20/0.74 join(zero, meet(top, meet(X, X)))
% 2.20/0.74 = { by lemma 21 R->L }
% 2.20/0.74 join(zero, meet(top, complement(complement(X))))
% 2.20/0.74 = { by lemma 24 }
% 2.20/0.74 join(zero, complement(complement(X)))
% 2.20/0.74 = { by lemma 21 }
% 2.20/0.74 join(zero, meet(X, X))
% 2.20/0.74 = { by lemma 23 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 26: join(X, zero) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 join(X, zero)
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(zero, X)
% 2.20/0.74 = { by lemma 25 R->L }
% 2.20/0.74 join(zero, meet(X, X))
% 2.20/0.74 = { by lemma 23 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 27: join(zero, X) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 join(zero, X)
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(X, zero)
% 2.20/0.74 = { by lemma 26 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 28: complement(complement(X)) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 complement(complement(X))
% 2.20/0.74 = { by lemma 21 }
% 2.20/0.74 meet(X, X)
% 2.20/0.74 = { by lemma 25 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 29: meet(X, top) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 meet(X, top)
% 2.20/0.74 = { by lemma 20 }
% 2.20/0.74 meet(top, X)
% 2.20/0.74 = { by lemma 25 R->L }
% 2.20/0.74 meet(top, meet(X, X))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 2.20/0.74 meet(top, complement(join(complement(X), complement(X))))
% 2.20/0.74 = { by lemma 24 }
% 2.20/0.74 complement(join(complement(X), complement(X)))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 2.20/0.74 meet(X, X)
% 2.20/0.74 = { by lemma 25 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 30: join(X, meet(X, Y)) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 join(X, meet(X, Y))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(meet(X, Y), X)
% 2.20/0.74 = { by lemma 19 R->L }
% 2.20/0.74 join(meet(X, Y), join(meet(X, Y), complement(join(complement(X), Y))))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(meet(X, Y), join(complement(join(complement(X), Y)), meet(X, Y)))
% 2.20/0.74 = { by lemma 28 R->L }
% 2.20/0.74 join(meet(X, Y), join(complement(join(complement(X), Y)), complement(complement(meet(X, Y)))))
% 2.20/0.74 = { by lemma 25 R->L }
% 2.20/0.74 join(meet(meet(X, Y), meet(X, Y)), join(complement(join(complement(X), Y)), complement(complement(meet(X, Y)))))
% 2.20/0.74 = { by lemma 21 R->L }
% 2.20/0.74 join(complement(complement(meet(X, Y))), join(complement(join(complement(X), Y)), complement(complement(meet(X, Y)))))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(complement(complement(meet(X, Y))), join(complement(complement(meet(X, Y))), complement(join(complement(X), Y))))
% 2.20/0.74 = { by axiom 9 (maddux2_join_associativity_2) }
% 2.20/0.74 join(join(complement(complement(meet(X, Y))), complement(complement(meet(X, Y)))), complement(join(complement(X), Y)))
% 2.20/0.74 = { by lemma 16 }
% 2.20/0.74 join(complement(complement(meet(X, Y))), complement(join(complement(X), Y)))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) }
% 2.20/0.74 join(complement(join(complement(X), Y)), complement(complement(meet(X, Y))))
% 2.20/0.74 = { by lemma 28 }
% 2.20/0.74 join(complement(join(complement(X), Y)), meet(X, Y))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) }
% 2.20/0.74 join(meet(X, Y), complement(join(complement(X), Y)))
% 2.20/0.74 = { by lemma 19 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 31: join(X, meet(Y, X)) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 join(X, meet(Y, X))
% 2.20/0.74 = { by lemma 20 }
% 2.20/0.74 join(X, meet(X, Y))
% 2.20/0.74 = { by lemma 30 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 32: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 2.20/0.74 Proof:
% 2.20/0.74 join(complement(X), complement(Y))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 join(complement(Y), complement(X))
% 2.20/0.74 = { by lemma 29 R->L }
% 2.20/0.74 meet(join(complement(Y), complement(X)), top)
% 2.20/0.74 = { by lemma 20 R->L }
% 2.20/0.74 meet(top, join(complement(Y), complement(X)))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 meet(top, join(complement(X), complement(Y)))
% 2.20/0.74 = { by lemma 20 }
% 2.20/0.74 meet(join(complement(X), complement(Y)), top)
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 2.20/0.74 complement(join(complement(join(complement(X), complement(Y))), complement(top)))
% 2.20/0.74 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 2.20/0.74 complement(join(meet(X, Y), complement(top)))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) }
% 2.20/0.74 complement(join(complement(top), meet(X, Y)))
% 2.20/0.74 = { by lemma 20 R->L }
% 2.20/0.74 complement(join(complement(top), meet(Y, X)))
% 2.20/0.74 = { by lemma 13 }
% 2.20/0.74 complement(join(zero, meet(Y, X)))
% 2.20/0.74 = { by lemma 27 }
% 2.20/0.74 complement(meet(Y, X))
% 2.20/0.74 = { by lemma 20 R->L }
% 2.20/0.74 complement(meet(X, Y))
% 2.20/0.74
% 2.20/0.74 Lemma 33: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 2.20/0.74 Proof:
% 2.20/0.74 complement(meet(X, complement(Y)))
% 2.20/0.74 = { by lemma 20 }
% 2.20/0.74 complement(meet(complement(Y), X))
% 2.20/0.74 = { by lemma 27 R->L }
% 2.20/0.74 complement(meet(join(zero, complement(Y)), X))
% 2.20/0.74 = { by lemma 32 R->L }
% 2.20/0.74 join(complement(join(zero, complement(Y))), complement(X))
% 2.20/0.74 = { by lemma 22 }
% 2.20/0.74 join(meet(Y, top), complement(X))
% 2.20/0.74 = { by lemma 29 }
% 2.20/0.74 join(Y, complement(X))
% 2.20/0.74
% 2.20/0.74 Lemma 34: meet(X, join(X, Y)) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 meet(X, join(X, Y))
% 2.20/0.74 = { by lemma 29 R->L }
% 2.20/0.74 meet(X, join(X, meet(Y, top)))
% 2.20/0.74 = { by lemma 22 R->L }
% 2.20/0.74 meet(X, join(X, complement(join(zero, complement(Y)))))
% 2.20/0.74 = { by lemma 26 R->L }
% 2.20/0.74 join(meet(X, join(X, complement(join(zero, complement(Y))))), zero)
% 2.20/0.74 = { by lemma 13 R->L }
% 2.20/0.74 join(meet(X, join(X, complement(join(zero, complement(Y))))), complement(top))
% 2.20/0.74 = { by lemma 33 R->L }
% 2.20/0.74 join(meet(X, complement(meet(join(zero, complement(Y)), complement(X)))), complement(top))
% 2.20/0.74 = { by lemma 20 R->L }
% 2.20/0.74 join(meet(X, complement(meet(complement(X), join(zero, complement(Y))))), complement(top))
% 2.20/0.74 = { by lemma 18 R->L }
% 2.20/0.74 join(meet(X, complement(meet(complement(X), join(zero, complement(Y))))), complement(join(complement(join(zero, complement(Y))), top)))
% 2.20/0.74 = { by lemma 14 R->L }
% 2.20/0.74 join(meet(X, complement(meet(complement(X), join(zero, complement(Y))))), complement(join(complement(X), join(complement(join(zero, complement(Y))), complement(complement(X))))))
% 2.20/0.74 = { by lemma 32 }
% 2.20/0.74 join(meet(X, complement(meet(complement(X), join(zero, complement(Y))))), complement(join(complement(X), complement(meet(join(zero, complement(Y)), complement(X))))))
% 2.20/0.74 = { by lemma 20 R->L }
% 2.20/0.74 join(meet(X, complement(meet(complement(X), join(zero, complement(Y))))), complement(join(complement(X), complement(meet(complement(X), join(zero, complement(Y)))))))
% 2.20/0.74 = { by lemma 19 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.74 Lemma 35: meet(X, join(Y, X)) = X.
% 2.20/0.74 Proof:
% 2.20/0.74 meet(X, join(Y, X))
% 2.20/0.74 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.74 meet(X, join(X, Y))
% 2.20/0.74 = { by lemma 34 }
% 2.20/0.74 X
% 2.20/0.74
% 2.20/0.75 Lemma 36: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 2.20/0.75 Proof:
% 2.20/0.75 meet(Y, meet(X, Z))
% 2.20/0.75 = { by lemma 20 }
% 2.20/0.75 meet(Y, meet(Z, X))
% 2.20/0.75 = { by lemma 29 R->L }
% 2.20/0.75 meet(meet(Y, meet(Z, X)), top)
% 2.20/0.75 = { by lemma 22 R->L }
% 2.20/0.75 complement(join(zero, complement(meet(Y, meet(Z, X)))))
% 2.20/0.75 = { by lemma 20 }
% 2.20/0.75 complement(join(zero, complement(meet(Y, meet(X, Z)))))
% 2.20/0.75 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 2.20/0.75 complement(join(zero, complement(meet(Y, complement(join(complement(X), complement(Z)))))))
% 2.20/0.75 = { by lemma 33 }
% 2.20/0.75 complement(join(zero, join(join(complement(X), complement(Z)), complement(Y))))
% 2.20/0.75 = { by axiom 9 (maddux2_join_associativity_2) R->L }
% 2.20/0.75 complement(join(zero, join(complement(X), join(complement(Z), complement(Y)))))
% 2.20/0.75 = { by lemma 32 }
% 2.20/0.75 complement(join(zero, join(complement(X), complement(meet(Z, Y)))))
% 2.20/0.75 = { by lemma 32 }
% 2.20/0.75 complement(join(zero, complement(meet(X, meet(Z, Y)))))
% 2.20/0.75 = { by lemma 20 R->L }
% 2.20/0.75 complement(join(zero, complement(meet(X, meet(Y, Z)))))
% 2.20/0.75 = { by lemma 22 }
% 2.20/0.75 meet(meet(X, meet(Y, Z)), top)
% 2.20/0.75 = { by lemma 29 }
% 2.20/0.75 meet(X, meet(Y, Z))
% 2.20/0.75
% 2.20/0.75 Lemma 37: join(meet(converse(X), converse(Y)), converse(meet(X, Y))) = meet(converse(X), converse(Y)).
% 2.20/0.75 Proof:
% 2.20/0.75 join(meet(converse(X), converse(Y)), converse(meet(X, Y)))
% 2.20/0.75 = { by lemma 34 R->L }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(meet(X, Y)), join(converse(meet(X, Y)), converse(X))))
% 2.20/0.75 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(meet(X, Y)), join(converse(X), converse(meet(X, Y)))))
% 2.20/0.75 = { by axiom 5 (converse_additivity_9) R->L }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(meet(X, Y)), converse(join(X, meet(X, Y)))))
% 2.20/0.75 = { by lemma 30 }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(meet(X, Y)), converse(X)))
% 2.20/0.75 = { by lemma 20 }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(X), converse(meet(X, Y))))
% 2.20/0.75 = { by lemma 34 R->L }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(X), meet(converse(meet(X, Y)), join(converse(meet(X, Y)), converse(Y)))))
% 2.20/0.75 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(X), meet(converse(meet(X, Y)), join(converse(Y), converse(meet(X, Y))))))
% 2.20/0.75 = { by axiom 5 (converse_additivity_9) R->L }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(X), meet(converse(meet(X, Y)), converse(join(Y, meet(X, Y))))))
% 2.20/0.75 = { by lemma 31 }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(X), meet(converse(meet(X, Y)), converse(Y))))
% 2.20/0.75 = { by lemma 36 }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(converse(meet(X, Y)), meet(converse(X), converse(Y))))
% 2.20/0.75 = { by lemma 20 R->L }
% 2.20/0.75 join(meet(converse(X), converse(Y)), meet(meet(converse(X), converse(Y)), converse(meet(X, Y))))
% 2.20/0.75 = { by lemma 30 }
% 2.20/0.75 meet(converse(X), converse(Y))
% 2.20/0.75
% 2.20/0.75 Goal 1 (goals_17): tuple(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))), join(converse(meet(sk1, sk2)), meet(converse(sk1), converse(sk2)))) = tuple(converse(meet(sk1, sk2)), meet(converse(sk1), converse(sk2))).
% 2.20/0.75 Proof:
% 2.20/0.75 tuple(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))), join(converse(meet(sk1, sk2)), meet(converse(sk1), converse(sk2))))
% 2.20/0.75 = { by axiom 3 (maddux1_join_commutativity_1) }
% 2.20/0.75 tuple(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))), join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))
% 2.20/0.75 = { by lemma 37 }
% 2.20/0.75 tuple(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 1 (converse_idempotence_8) R->L }
% 2.20/0.75 tuple(converse(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 37 }
% 2.20/0.75 tuple(converse(converse(meet(converse(sk1), converse(sk2)))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 35 R->L }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), join(sk1, converse(meet(converse(sk1), converse(sk2)))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), join(converse(meet(converse(sk1), converse(sk2))), sk1))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 1 (converse_idempotence_8) R->L }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), join(converse(meet(converse(sk1), converse(sk2))), converse(converse(sk1))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 5 (converse_additivity_9) R->L }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), converse(join(meet(converse(sk1), converse(sk2)), converse(sk1))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), converse(join(converse(sk1), meet(converse(sk1), converse(sk2)))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 30 }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), converse(converse(sk1)))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 1 (converse_idempotence_8) }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), sk1)), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 20 R->L }
% 2.20/0.75 tuple(converse(meet(sk1, converse(meet(converse(sk1), converse(sk2))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 35 R->L }
% 2.20/0.75 tuple(converse(meet(sk1, meet(converse(meet(converse(sk1), converse(sk2))), join(sk2, converse(meet(converse(sk1), converse(sk2))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.75 tuple(converse(meet(sk1, meet(converse(meet(converse(sk1), converse(sk2))), join(converse(meet(converse(sk1), converse(sk2))), sk2)))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 1 (converse_idempotence_8) R->L }
% 2.20/0.75 tuple(converse(meet(sk1, meet(converse(meet(converse(sk1), converse(sk2))), join(converse(meet(converse(sk1), converse(sk2))), converse(converse(sk2)))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 5 (converse_additivity_9) R->L }
% 2.20/0.75 tuple(converse(meet(sk1, meet(converse(meet(converse(sk1), converse(sk2))), converse(join(meet(converse(sk1), converse(sk2)), converse(sk2)))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 2.20/0.75 tuple(converse(meet(sk1, meet(converse(meet(converse(sk1), converse(sk2))), converse(join(converse(sk2), meet(converse(sk1), converse(sk2))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 31 }
% 2.20/0.75 tuple(converse(meet(sk1, meet(converse(meet(converse(sk1), converse(sk2))), converse(converse(sk2))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 1 (converse_idempotence_8) }
% 2.20/0.75 tuple(converse(meet(sk1, meet(converse(meet(converse(sk1), converse(sk2))), sk2))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 36 }
% 2.20/0.75 tuple(converse(meet(converse(meet(converse(sk1), converse(sk2))), meet(sk1, sk2))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 37 R->L }
% 2.20/0.75 tuple(converse(meet(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))), meet(sk1, sk2))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 20 R->L }
% 2.20/0.75 tuple(converse(meet(meet(sk1, sk2), converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 2.20/0.75 tuple(converse(complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 27 R->L }
% 2.20/0.75 tuple(converse(join(zero, complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 13 R->L }
% 2.20/0.75 tuple(converse(join(complement(top), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 18 R->L }
% 2.20/0.75 tuple(converse(join(complement(join(converse(meet(converse(sk1), converse(sk2))), top)), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 1 (converse_idempotence_8) R->L }
% 2.20/0.75 tuple(converse(join(complement(join(converse(meet(converse(sk1), converse(sk2))), converse(converse(top)))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 5 (converse_additivity_9) R->L }
% 2.20/0.75 tuple(converse(join(complement(converse(join(meet(converse(sk1), converse(sk2)), converse(top)))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 7 (def_top_12) }
% 2.20/0.75 tuple(converse(join(complement(converse(join(meet(converse(sk1), converse(sk2)), converse(join(meet(sk1, sk2), complement(meet(sk1, sk2))))))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 5 (converse_additivity_9) }
% 2.20/0.75 tuple(converse(join(complement(converse(join(meet(converse(sk1), converse(sk2)), join(converse(meet(sk1, sk2)), converse(complement(meet(sk1, sk2))))))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 9 (maddux2_join_associativity_2) }
% 2.20/0.75 tuple(converse(join(complement(converse(join(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))), converse(complement(meet(sk1, sk2)))))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 5 (converse_additivity_9) }
% 2.20/0.75 tuple(converse(join(complement(join(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))), converse(converse(complement(meet(sk1, sk2)))))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by axiom 1 (converse_idempotence_8) }
% 2.20/0.75 tuple(converse(join(complement(join(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))), complement(meet(sk1, sk2)))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 27 R->L }
% 2.20/0.75 tuple(converse(join(complement(join(zero, join(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))), complement(meet(sk1, sk2))))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 33 R->L }
% 2.20/0.75 tuple(converse(join(complement(join(zero, complement(meet(meet(sk1, sk2), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 22 }
% 2.20/0.75 tuple(converse(join(meet(meet(meet(sk1, sk2), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))))), top), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 29 }
% 2.20/0.75 tuple(converse(join(meet(meet(sk1, sk2), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2)))))), complement(join(complement(meet(sk1, sk2)), complement(converse(join(meet(converse(sk1), converse(sk2)), converse(meet(sk1, sk2))))))))), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 = { by lemma 19 }
% 2.20/0.75 tuple(converse(meet(sk1, sk2)), meet(converse(sk1), converse(sk2)))
% 2.20/0.75 % SZS output end Proof
% 2.20/0.75
% 2.20/0.75 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------