TSTP Solution File: REL047-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL047-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:44:31 EDT 2023
% Result : Unsatisfiable 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL047-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 19:16:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.54 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.54
% 0.20/0.54 % SZS status Unsatisfiable
% 0.20/0.54
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.20/0.57 Axiom 2 (goals_14): join(sk1, sk2) = sk2.
% 0.20/0.57 Axiom 3 (goals_15): join(sk1, sk3) = sk3.
% 0.20/0.57 Axiom 4 (composition_identity_6): composition(X, one) = X.
% 0.20/0.57 Axiom 5 (converse_idempotence_8): converse(converse(X)) = X.
% 0.20/0.57 Axiom 6 (def_top_12): top = join(X, complement(X)).
% 0.20/0.57 Axiom 7 (def_zero_13): zero = meet(X, complement(X)).
% 0.20/0.57 Axiom 8 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.20/0.57 Axiom 9 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.57 Axiom 10 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.20/0.57 Axiom 11 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.20/0.57 Axiom 12 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.20/0.57 Axiom 13 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.20/0.57
% 0.20/0.57 Lemma 14: complement(top) = zero.
% 0.20/0.57 Proof:
% 0.20/0.57 complement(top)
% 0.20/0.57 = { by axiom 6 (def_top_12) }
% 0.20/0.57 complement(join(complement(X), complement(complement(X))))
% 0.20/0.57 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.57 meet(X, complement(X))
% 0.20/0.57 = { by axiom 7 (def_zero_13) R->L }
% 0.20/0.57 zero
% 0.20/0.57
% 0.20/0.57 Lemma 15: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.20/0.57 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.57 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.20/0.57 = { by axiom 13 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 16: join(zero, meet(X, X)) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 join(zero, meet(X, X))
% 0.20/0.57 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.57 join(zero, complement(join(complement(X), complement(X))))
% 0.20/0.57 = { by axiom 7 (def_zero_13) }
% 0.20/0.57 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.57 = { by lemma 15 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 17: composition(converse(one), X) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 composition(converse(one), X)
% 0.20/0.57 = { by axiom 5 (converse_idempotence_8) R->L }
% 0.20/0.57 composition(converse(one), converse(converse(X)))
% 0.20/0.57 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 0.20/0.57 converse(composition(converse(X), one))
% 0.20/0.57 = { by axiom 4 (composition_identity_6) }
% 0.20/0.57 converse(converse(X))
% 0.20/0.57 = { by axiom 5 (converse_idempotence_8) }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 18: join(complement(X), complement(X)) = complement(X).
% 0.20/0.57 Proof:
% 0.20/0.57 join(complement(X), complement(X))
% 0.20/0.57 = { by lemma 17 R->L }
% 0.20/0.57 join(complement(X), composition(converse(one), complement(X)))
% 0.20/0.57 = { by lemma 17 R->L }
% 0.20/0.57 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.20/0.57 = { by axiom 4 (composition_identity_6) R->L }
% 0.20/0.57 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.20/0.57 = { by axiom 10 (composition_associativity_5) R->L }
% 0.20/0.57 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.20/0.57 = { by lemma 17 }
% 0.20/0.57 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.57 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.20/0.57 = { by axiom 12 (converse_cancellativity_11) }
% 0.20/0.57 complement(X)
% 0.20/0.57
% 0.20/0.57 Lemma 19: join(zero, complement(complement(X))) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 join(zero, complement(complement(X)))
% 0.20/0.57 = { by axiom 7 (def_zero_13) }
% 0.20/0.57 join(meet(X, complement(X)), complement(complement(X)))
% 0.20/0.57 = { by lemma 18 R->L }
% 0.20/0.57 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.57 = { by lemma 15 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 20: join(X, zero) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 join(X, zero)
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.57 join(zero, X)
% 0.20/0.57 = { by lemma 16 R->L }
% 0.20/0.57 join(zero, join(zero, meet(X, X)))
% 0.20/0.57 = { by axiom 8 (maddux2_join_associativity_2) }
% 0.20/0.57 join(join(zero, zero), meet(X, X))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 join(join(zero, complement(top)), meet(X, X))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 join(join(complement(top), complement(top)), meet(X, X))
% 0.20/0.57 = { by lemma 18 }
% 0.20/0.57 join(complement(top), meet(X, X))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 join(zero, meet(X, X))
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.57 join(meet(X, X), zero)
% 0.20/0.57 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.57 join(complement(join(complement(X), complement(X))), zero)
% 0.20/0.57 = { by lemma 18 }
% 0.20/0.57 join(complement(complement(X)), zero)
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.57 join(zero, complement(complement(X)))
% 0.20/0.57 = { by lemma 19 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 21: join(zero, X) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 join(zero, X)
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.57 join(X, zero)
% 0.20/0.57 = { by lemma 20 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 22: join(X, join(Y, complement(X))) = join(Y, top).
% 0.20/0.57 Proof:
% 0.20/0.57 join(X, join(Y, complement(X)))
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.57 join(X, join(complement(X), Y))
% 0.20/0.57 = { by axiom 8 (maddux2_join_associativity_2) }
% 0.20/0.57 join(join(X, complement(X)), Y)
% 0.20/0.57 = { by axiom 6 (def_top_12) R->L }
% 0.20/0.57 join(top, Y)
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.57 join(Y, top)
% 0.20/0.57
% 0.20/0.57 Lemma 23: join(sk2, join(sk1, X)) = join(X, sk2).
% 0.20/0.57 Proof:
% 0.20/0.57 join(sk2, join(sk1, X))
% 0.20/0.57 = { by axiom 8 (maddux2_join_associativity_2) }
% 0.20/0.57 join(join(sk2, sk1), X)
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.57 join(join(sk1, sk2), X)
% 0.20/0.57 = { by axiom 2 (goals_14) }
% 0.20/0.57 join(sk2, X)
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.57 join(X, sk2)
% 0.20/0.57
% 0.20/0.57 Lemma 24: join(sk1, top) = top.
% 0.20/0.57 Proof:
% 0.20/0.57 join(sk1, top)
% 0.20/0.57 = { by lemma 22 R->L }
% 0.20/0.57 join(sk2, join(sk1, complement(sk2)))
% 0.20/0.57 = { by lemma 23 }
% 0.20/0.57 join(complement(sk2), sk2)
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.57 join(sk2, complement(sk2))
% 0.20/0.57 = { by axiom 6 (def_top_12) R->L }
% 0.20/0.57 top
% 0.20/0.57
% 0.20/0.57 Lemma 25: complement(complement(X)) = X.
% 0.20/0.57 Proof:
% 0.20/0.57 complement(complement(X))
% 0.20/0.57 = { by lemma 21 R->L }
% 0.20/0.57 join(zero, complement(complement(X)))
% 0.20/0.57 = { by lemma 19 }
% 0.20/0.57 X
% 0.20/0.57
% 0.20/0.57 Lemma 26: meet(Y, X) = meet(X, Y).
% 0.20/0.57 Proof:
% 0.20/0.57 meet(Y, X)
% 0.20/0.57 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.57 complement(join(complement(Y), complement(X)))
% 0.20/0.57 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.57 complement(join(complement(X), complement(Y)))
% 0.20/0.57 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.57 meet(X, Y)
% 0.20/0.57
% 0.20/0.57 Lemma 27: complement(join(zero, complement(X))) = meet(X, top).
% 0.20/0.57 Proof:
% 0.20/0.57 complement(join(zero, complement(X)))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 complement(join(complement(top), complement(X)))
% 0.20/0.57 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.57 meet(top, X)
% 0.20/0.57 = { by lemma 26 R->L }
% 0.20/0.57 meet(X, top)
% 0.20/0.57
% 0.20/0.57 Lemma 28: meet(X, top) = X.
% 0.20/0.57 Proof:
% 0.20/0.58 meet(X, top)
% 0.20/0.58 = { by lemma 27 R->L }
% 0.20/0.58 complement(join(zero, complement(X)))
% 0.20/0.58 = { by lemma 21 }
% 0.20/0.58 complement(complement(X))
% 0.20/0.58 = { by lemma 25 }
% 0.20/0.58 X
% 0.20/0.58
% 0.20/0.58 Lemma 29: join(top, complement(X)) = top.
% 0.20/0.58 Proof:
% 0.20/0.58 join(top, complement(X))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.58 join(complement(X), top)
% 0.20/0.58 = { by lemma 22 R->L }
% 0.20/0.58 join(X, join(complement(X), complement(X)))
% 0.20/0.58 = { by lemma 18 }
% 0.20/0.58 join(X, complement(X))
% 0.20/0.58 = { by axiom 6 (def_top_12) R->L }
% 0.20/0.58 top
% 0.20/0.58
% 0.20/0.58 Lemma 30: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 0.20/0.58 Proof:
% 0.20/0.58 meet(X, join(complement(Y), complement(Z)))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.58 meet(X, join(complement(Z), complement(Y)))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 meet(join(complement(Z), complement(Y)), X)
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.58 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.58 complement(join(meet(Z, Y), complement(X)))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.58 complement(join(complement(X), meet(Z, Y)))
% 0.20/0.58 = { by lemma 26 R->L }
% 0.20/0.58 complement(join(complement(X), meet(Y, Z)))
% 0.20/0.58
% 0.20/0.58 Lemma 31: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 0.20/0.58 Proof:
% 0.20/0.58 complement(join(X, complement(Y)))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.58 complement(join(complement(Y), X))
% 0.20/0.58 = { by lemma 28 R->L }
% 0.20/0.58 complement(join(complement(Y), meet(X, top)))
% 0.20/0.58 = { by lemma 26 R->L }
% 0.20/0.58 complement(join(complement(Y), meet(top, X)))
% 0.20/0.58 = { by lemma 30 R->L }
% 0.20/0.58 meet(Y, join(complement(top), complement(X)))
% 0.20/0.58 = { by lemma 14 }
% 0.20/0.58 meet(Y, join(zero, complement(X)))
% 0.20/0.58 = { by lemma 21 }
% 0.20/0.58 meet(Y, complement(X))
% 0.20/0.58
% 0.20/0.58 Lemma 32: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 0.20/0.58 Proof:
% 0.20/0.58 complement(meet(complement(X), Y))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 complement(meet(Y, complement(X)))
% 0.20/0.58 = { by lemma 21 R->L }
% 0.20/0.58 complement(join(zero, meet(Y, complement(X))))
% 0.20/0.58 = { by lemma 31 R->L }
% 0.20/0.58 complement(join(zero, complement(join(X, complement(Y)))))
% 0.20/0.58 = { by lemma 27 }
% 0.20/0.58 meet(join(X, complement(Y)), top)
% 0.20/0.58 = { by lemma 28 }
% 0.20/0.58 join(X, complement(Y))
% 0.20/0.58
% 0.20/0.58 Lemma 33: meet(X, join(X, complement(Y))) = X.
% 0.20/0.58 Proof:
% 0.20/0.58 meet(X, join(X, complement(Y)))
% 0.20/0.58 = { by lemma 20 R->L }
% 0.20/0.58 join(meet(X, join(X, complement(Y))), zero)
% 0.20/0.58 = { by lemma 14 R->L }
% 0.20/0.58 join(meet(X, join(X, complement(Y))), complement(top))
% 0.20/0.58 = { by lemma 32 R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(top))
% 0.20/0.58 = { by lemma 24 R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(sk1, top)))
% 0.20/0.58 = { by lemma 29 R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(sk1, join(top, complement(sk1)))))
% 0.20/0.58 = { by lemma 22 }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(top, top)))
% 0.20/0.58 = { by lemma 22 R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(Y), join(top, complement(complement(Y))))))
% 0.20/0.58 = { by lemma 29 }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(Y), top)))
% 0.20/0.58 = { by lemma 22 R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(complement(Y), complement(complement(X))))))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(complement(complement(X)), complement(Y)))))
% 0.20/0.58 = { by lemma 16 R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(zero, meet(join(complement(complement(X)), complement(Y)), join(complement(complement(X)), complement(Y)))))))
% 0.20/0.58 = { by lemma 30 }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(zero, complement(join(complement(join(complement(complement(X)), complement(Y))), meet(complement(X), Y)))))))
% 0.20/0.58 = { by lemma 21 }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(complement(join(complement(complement(X)), complement(Y))), meet(complement(X), Y))))))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(complement(X), Y), meet(complement(X), Y))))))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), meet(complement(X), Y))))))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), meet(Y, complement(X)))))))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), complement(join(complement(Y), complement(complement(X)))))))))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(complement(join(complement(Y), complement(complement(X)))), complement(join(complement(Y), complement(complement(X)))))))))
% 0.20/0.58 = { by lemma 18 }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(complement(join(complement(Y), complement(complement(X))))))))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(Y, complement(X))))))
% 0.20/0.58 = { by lemma 26 R->L }
% 0.20/0.58 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(complement(X), Y)))))
% 0.20/0.58 = { by lemma 15 }
% 0.20/0.58 X
% 0.20/0.58
% 0.20/0.58 Lemma 34: join(X, meet(X, Y)) = X.
% 0.20/0.58 Proof:
% 0.20/0.58 join(X, meet(X, Y))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.58 join(X, complement(join(complement(X), complement(Y))))
% 0.20/0.58 = { by lemma 32 R->L }
% 0.20/0.58 complement(meet(complement(X), join(complement(X), complement(Y))))
% 0.20/0.58 = { by lemma 33 }
% 0.20/0.58 complement(complement(X))
% 0.20/0.58 = { by lemma 25 }
% 0.20/0.58 X
% 0.20/0.58
% 0.20/0.58 Lemma 35: complement(join(complement(X), Y)) = meet(X, complement(Y)).
% 0.20/0.58 Proof:
% 0.20/0.58 complement(join(complement(X), Y))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.58 complement(join(Y, complement(X)))
% 0.20/0.58 = { by lemma 31 }
% 0.20/0.58 meet(X, complement(Y))
% 0.20/0.58
% 0.20/0.58 Lemma 36: meet(X, join(Y, X)) = X.
% 0.20/0.58 Proof:
% 0.20/0.58 meet(X, join(Y, X))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.58 meet(X, join(X, Y))
% 0.20/0.58 = { by lemma 28 R->L }
% 0.20/0.58 meet(X, join(X, meet(Y, top)))
% 0.20/0.58 = { by lemma 27 R->L }
% 0.20/0.58 meet(X, join(X, complement(join(zero, complement(Y)))))
% 0.20/0.58 = { by lemma 33 }
% 0.20/0.58 X
% 0.20/0.58
% 0.20/0.58 Goal 1 (goals_16): join(sk1, meet(sk2, sk3)) = meet(sk2, sk3).
% 0.20/0.58 Proof:
% 0.20/0.58 join(sk1, meet(sk2, sk3))
% 0.20/0.58 = { by lemma 36 R->L }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), join(sk2, join(sk1, meet(sk2, sk3))))
% 0.20/0.58 = { by lemma 23 }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), join(meet(sk2, sk3), sk2))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), join(sk2, meet(sk2, sk3)))
% 0.20/0.58 = { by lemma 34 }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), sk2)
% 0.20/0.58 = { by lemma 26 R->L }
% 0.20/0.58 meet(sk2, join(sk1, meet(sk2, sk3)))
% 0.20/0.58 = { by lemma 36 R->L }
% 0.20/0.58 meet(sk2, meet(join(sk1, meet(sk2, sk3)), join(sk3, join(sk1, meet(sk2, sk3)))))
% 0.20/0.58 = { by axiom 8 (maddux2_join_associativity_2) }
% 0.20/0.58 meet(sk2, meet(join(sk1, meet(sk2, sk3)), join(join(sk3, sk1), meet(sk2, sk3))))
% 0.20/0.58 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.58 meet(sk2, meet(join(sk1, meet(sk2, sk3)), join(join(sk1, sk3), meet(sk2, sk3))))
% 0.20/0.58 = { by axiom 3 (goals_15) }
% 0.20/0.58 meet(sk2, meet(join(sk1, meet(sk2, sk3)), join(sk3, meet(sk2, sk3))))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 meet(sk2, meet(join(sk1, meet(sk2, sk3)), join(sk3, meet(sk3, sk2))))
% 0.20/0.58 = { by lemma 34 }
% 0.20/0.58 meet(sk2, meet(join(sk1, meet(sk2, sk3)), sk3))
% 0.20/0.58 = { by lemma 26 R->L }
% 0.20/0.58 meet(sk2, meet(sk3, join(sk1, meet(sk2, sk3))))
% 0.20/0.58 = { by lemma 28 R->L }
% 0.20/0.58 meet(meet(sk2, top), meet(sk3, join(sk1, meet(sk2, sk3))))
% 0.20/0.58 = { by lemma 27 R->L }
% 0.20/0.58 meet(complement(join(zero, complement(sk2))), meet(sk3, join(sk1, meet(sk2, sk3))))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 meet(complement(join(zero, complement(sk2))), meet(join(sk1, meet(sk2, sk3)), sk3))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 meet(meet(join(sk1, meet(sk2, sk3)), sk3), complement(join(zero, complement(sk2))))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.58 meet(complement(join(complement(join(sk1, meet(sk2, sk3))), complement(sk3))), complement(join(zero, complement(sk2))))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 meet(complement(join(zero, complement(sk2))), complement(join(complement(join(sk1, meet(sk2, sk3))), complement(sk3))))
% 0.20/0.58 = { by lemma 21 R->L }
% 0.20/0.58 meet(join(zero, complement(join(zero, complement(sk2)))), complement(join(complement(join(sk1, meet(sk2, sk3))), complement(sk3))))
% 0.20/0.58 = { by lemma 31 R->L }
% 0.20/0.58 complement(join(join(complement(join(sk1, meet(sk2, sk3))), complement(sk3)), complement(join(zero, complement(join(zero, complement(sk2)))))))
% 0.20/0.58 = { by lemma 27 }
% 0.20/0.58 complement(join(join(complement(join(sk1, meet(sk2, sk3))), complement(sk3)), meet(join(zero, complement(sk2)), top)))
% 0.20/0.58 = { by lemma 28 }
% 0.20/0.58 complement(join(join(complement(join(sk1, meet(sk2, sk3))), complement(sk3)), join(zero, complement(sk2))))
% 0.20/0.58 = { by axiom 8 (maddux2_join_associativity_2) R->L }
% 0.20/0.58 complement(join(complement(join(sk1, meet(sk2, sk3))), join(complement(sk3), join(zero, complement(sk2)))))
% 0.20/0.58 = { by lemma 35 }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), complement(join(complement(sk3), join(zero, complement(sk2)))))
% 0.20/0.58 = { by lemma 35 }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), meet(sk3, complement(join(zero, complement(sk2)))))
% 0.20/0.58 = { by lemma 27 }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), meet(sk3, meet(sk2, top)))
% 0.20/0.58 = { by lemma 28 }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), meet(sk3, sk2))
% 0.20/0.58 = { by lemma 26 R->L }
% 0.20/0.58 meet(join(sk1, meet(sk2, sk3)), meet(sk2, sk3))
% 0.20/0.58 = { by lemma 26 }
% 0.20/0.58 meet(meet(sk2, sk3), join(sk1, meet(sk2, sk3)))
% 0.20/0.58 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 0.20/0.58 complement(join(complement(meet(sk2, sk3)), complement(join(sk1, meet(sk2, sk3)))))
% 0.20/0.58 = { by lemma 21 R->L }
% 0.20/0.58 join(zero, complement(join(complement(meet(sk2, sk3)), complement(join(sk1, meet(sk2, sk3))))))
% 0.20/0.58 = { by lemma 14 R->L }
% 0.20/0.58 join(complement(top), complement(join(complement(meet(sk2, sk3)), complement(join(sk1, meet(sk2, sk3))))))
% 0.20/0.58 = { by lemma 24 R->L }
% 0.20/0.58 join(complement(join(sk1, top)), complement(join(complement(meet(sk2, sk3)), complement(join(sk1, meet(sk2, sk3))))))
% 0.20/0.58 = { by axiom 6 (def_top_12) }
% 0.20/0.58 join(complement(join(sk1, join(meet(sk2, sk3), complement(meet(sk2, sk3))))), complement(join(complement(meet(sk2, sk3)), complement(join(sk1, meet(sk2, sk3))))))
% 0.20/0.58 = { by axiom 8 (maddux2_join_associativity_2) }
% 0.20/0.58 join(complement(join(join(sk1, meet(sk2, sk3)), complement(meet(sk2, sk3)))), complement(join(complement(meet(sk2, sk3)), complement(join(sk1, meet(sk2, sk3))))))
% 0.20/0.58 = { by lemma 31 }
% 0.20/0.58 join(meet(meet(sk2, sk3), complement(join(sk1, meet(sk2, sk3)))), complement(join(complement(meet(sk2, sk3)), complement(join(sk1, meet(sk2, sk3))))))
% 0.20/0.58 = { by lemma 15 }
% 0.20/0.58 meet(sk2, sk3)
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58
% 0.20/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------