TSTP Solution File: REL019-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL019-1 : 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 : n019.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 13:43:59 EDT 2023
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL019-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 22:22:13 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.51 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.51
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51
% 0.20/0.54 % SZS output start Proof
% 0.20/0.54 Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.20/0.54 Axiom 2 (composition_identity_6): composition(X, one) = X.
% 0.20/0.54 Axiom 3 (goals_14): composition(sk1, top) = sk1.
% 0.20/0.54 Axiom 4 (goals_15): composition(sk2, top) = sk2.
% 0.20/0.54 Axiom 5 (converse_idempotence_8): converse(converse(X)) = X.
% 0.20/0.54 Axiom 6 (def_top_12): top = join(X, complement(X)).
% 0.20/0.54 Axiom 7 (def_zero_13): zero = meet(X, complement(X)).
% 0.20/0.54 Axiom 8 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.20/0.54 Axiom 9 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.20/0.54 Axiom 10 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.54 Axiom 11 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.20/0.54 Axiom 12 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.20/0.54 Axiom 13 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.20/0.54 Axiom 14 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.20/0.54 Axiom 15 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.20/0.54
% 0.20/0.54 Lemma 16: complement(top) = zero.
% 0.20/0.54 Proof:
% 0.20/0.54 complement(top)
% 0.20/0.54 = { by axiom 6 (def_top_12) }
% 0.20/0.54 complement(join(complement(X), complement(complement(X))))
% 0.20/0.54 = { by axiom 12 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.54 meet(X, complement(X))
% 0.20/0.54 = { by axiom 7 (def_zero_13) R->L }
% 0.20/0.54 zero
% 0.20/0.54
% 0.20/0.54 Lemma 17: join(X, join(Y, complement(X))) = join(Y, top).
% 0.20/0.54 Proof:
% 0.20/0.54 join(X, join(Y, complement(X)))
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.54 join(X, join(complement(X), Y))
% 0.20/0.54 = { by axiom 9 (maddux2_join_associativity_2) }
% 0.20/0.54 join(join(X, complement(X)), Y)
% 0.20/0.54 = { by axiom 6 (def_top_12) R->L }
% 0.20/0.54 join(top, Y)
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.54 join(Y, top)
% 0.20/0.54
% 0.20/0.54 Lemma 18: composition(converse(one), X) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 composition(converse(one), X)
% 0.20/0.54 = { by axiom 5 (converse_idempotence_8) R->L }
% 0.20/0.54 composition(converse(one), converse(converse(X)))
% 0.20/0.54 = { by axiom 10 (converse_multiplicativity_10) R->L }
% 0.20/0.54 converse(composition(converse(X), one))
% 0.20/0.54 = { by axiom 2 (composition_identity_6) }
% 0.20/0.54 converse(converse(X))
% 0.20/0.54 = { by axiom 5 (converse_idempotence_8) }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 19: composition(one, X) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 composition(one, X)
% 0.20/0.54 = { by lemma 18 R->L }
% 0.20/0.54 composition(converse(one), composition(one, X))
% 0.20/0.54 = { by axiom 11 (composition_associativity_5) }
% 0.20/0.54 composition(composition(converse(one), one), X)
% 0.20/0.54 = { by axiom 2 (composition_identity_6) }
% 0.20/0.54 composition(converse(one), X)
% 0.20/0.54 = { by lemma 18 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 0.20/0.54 Proof:
% 0.20/0.54 join(complement(X), complement(X))
% 0.20/0.54 = { by lemma 18 R->L }
% 0.20/0.54 join(complement(X), composition(converse(one), complement(X)))
% 0.20/0.54 = { by lemma 19 R->L }
% 0.20/0.54 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.54 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.20/0.54 = { by axiom 14 (converse_cancellativity_11) }
% 0.20/0.54 complement(X)
% 0.20/0.54
% 0.20/0.54 Lemma 21: join(top, complement(X)) = top.
% 0.20/0.54 Proof:
% 0.20/0.54 join(top, complement(X))
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.54 join(complement(X), top)
% 0.20/0.54 = { by lemma 17 R->L }
% 0.20/0.54 join(X, join(complement(X), complement(X)))
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 join(X, complement(X))
% 0.20/0.54 = { by axiom 6 (def_top_12) R->L }
% 0.20/0.54 top
% 0.20/0.54
% 0.20/0.54 Lemma 22: join(top, X) = join(Y, top).
% 0.20/0.54 Proof:
% 0.20/0.54 join(top, X)
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.54 join(X, top)
% 0.20/0.54 = { by lemma 21 R->L }
% 0.20/0.54 join(X, join(top, complement(X)))
% 0.20/0.54 = { by lemma 17 }
% 0.20/0.54 join(top, top)
% 0.20/0.54 = { by lemma 17 R->L }
% 0.20/0.54 join(Y, join(top, complement(Y)))
% 0.20/0.54 = { by lemma 21 }
% 0.20/0.54 join(Y, top)
% 0.20/0.54
% 0.20/0.54 Lemma 23: join(X, top) = top.
% 0.20/0.54 Proof:
% 0.20/0.54 join(X, top)
% 0.20/0.54 = { by lemma 22 R->L }
% 0.20/0.54 join(top, complement(top))
% 0.20/0.54 = { by axiom 6 (def_top_12) R->L }
% 0.20/0.54 top
% 0.20/0.54
% 0.20/0.54 Lemma 24: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.20/0.54 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.54 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.20/0.54 = { by axiom 15 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 25: join(zero, meet(X, X)) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 join(zero, meet(X, X))
% 0.20/0.54 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.54 join(zero, complement(join(complement(X), complement(X))))
% 0.20/0.54 = { by axiom 7 (def_zero_13) }
% 0.20/0.54 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.54 = { by lemma 24 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 26: join(zero, complement(complement(X))) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 join(zero, complement(complement(X)))
% 0.20/0.54 = { by axiom 7 (def_zero_13) }
% 0.20/0.54 join(meet(X, complement(X)), complement(complement(X)))
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.54 = { by lemma 24 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 27: join(X, zero) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 join(X, zero)
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.54 join(zero, X)
% 0.20/0.54 = { by lemma 25 R->L }
% 0.20/0.54 join(zero, join(zero, meet(X, X)))
% 0.20/0.54 = { by axiom 9 (maddux2_join_associativity_2) }
% 0.20/0.54 join(join(zero, zero), meet(X, X))
% 0.20/0.54 = { by lemma 16 R->L }
% 0.20/0.54 join(join(zero, complement(top)), meet(X, X))
% 0.20/0.54 = { by lemma 16 R->L }
% 0.20/0.54 join(join(complement(top), complement(top)), meet(X, X))
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 join(complement(top), meet(X, X))
% 0.20/0.54 = { by lemma 16 }
% 0.20/0.54 join(zero, meet(X, X))
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.54 join(meet(X, X), zero)
% 0.20/0.54 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.54 join(complement(join(complement(X), complement(X))), zero)
% 0.20/0.54 = { by lemma 20 }
% 0.20/0.54 join(complement(complement(X)), zero)
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.54 join(zero, complement(complement(X)))
% 0.20/0.54 = { by lemma 26 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 28: join(zero, X) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 join(zero, X)
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.54 join(X, zero)
% 0.20/0.54 = { by lemma 27 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 29: complement(complement(X)) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 complement(complement(X))
% 0.20/0.54 = { by lemma 28 R->L }
% 0.20/0.54 join(zero, complement(complement(X)))
% 0.20/0.54 = { by lemma 26 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 30: meet(Y, X) = meet(X, Y).
% 0.20/0.54 Proof:
% 0.20/0.54 meet(Y, X)
% 0.20/0.54 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.54 complement(join(complement(Y), complement(X)))
% 0.20/0.54 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.54 complement(join(complement(X), complement(Y)))
% 0.20/0.54 = { by axiom 12 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.54 meet(X, Y)
% 0.20/0.54
% 0.20/0.54 Lemma 31: complement(join(zero, complement(X))) = meet(X, top).
% 0.20/0.54 Proof:
% 0.20/0.54 complement(join(zero, complement(X)))
% 0.20/0.54 = { by lemma 16 R->L }
% 0.20/0.54 complement(join(complement(top), complement(X)))
% 0.20/0.54 = { by axiom 12 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.54 meet(top, X)
% 0.20/0.54 = { by lemma 30 R->L }
% 0.20/0.54 meet(X, top)
% 0.20/0.54
% 0.20/0.54 Lemma 32: meet(X, top) = X.
% 0.20/0.54 Proof:
% 0.20/0.55 meet(X, top)
% 0.20/0.55 = { by lemma 31 R->L }
% 0.20/0.55 complement(join(zero, complement(X)))
% 0.20/0.55 = { by lemma 28 }
% 0.20/0.55 complement(complement(X))
% 0.20/0.55 = { by lemma 29 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 33: converse(composition(X, top)) = composition(top, converse(X)).
% 0.20/0.55 Proof:
% 0.20/0.55 converse(composition(X, top))
% 0.20/0.55 = { by axiom 10 (converse_multiplicativity_10) }
% 0.20/0.55 composition(converse(top), converse(X))
% 0.20/0.55 = { by lemma 23 R->L }
% 0.20/0.55 composition(converse(join(converse(top), top)), converse(X))
% 0.20/0.55 = { by axiom 8 (converse_additivity_9) }
% 0.20/0.55 composition(join(converse(converse(top)), converse(top)), converse(X))
% 0.20/0.55 = { by axiom 5 (converse_idempotence_8) }
% 0.20/0.55 composition(join(top, converse(top)), converse(X))
% 0.20/0.55 = { by lemma 22 }
% 0.20/0.55 composition(join(Y, top), converse(X))
% 0.20/0.55 = { by lemma 23 }
% 0.20/0.55 composition(top, converse(X))
% 0.20/0.55
% 0.20/0.55 Lemma 34: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 0.20/0.55 Proof:
% 0.20/0.55 meet(X, join(complement(Y), complement(Z)))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.55 meet(X, join(complement(Z), complement(Y)))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 meet(join(complement(Z), complement(Y)), X)
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.55 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.55 complement(join(meet(Z, Y), complement(X)))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.55 complement(join(complement(X), meet(Z, Y)))
% 0.20/0.55 = { by lemma 30 R->L }
% 0.20/0.55 complement(join(complement(X), meet(Y, Z)))
% 0.20/0.55
% 0.20/0.55 Lemma 35: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 0.20/0.55 Proof:
% 0.20/0.55 complement(join(X, complement(Y)))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.55 complement(join(complement(Y), X))
% 0.20/0.55 = { by lemma 32 R->L }
% 0.20/0.55 complement(join(complement(Y), meet(X, top)))
% 0.20/0.55 = { by lemma 30 R->L }
% 0.20/0.55 complement(join(complement(Y), meet(top, X)))
% 0.20/0.55 = { by lemma 34 R->L }
% 0.20/0.55 meet(Y, join(complement(top), complement(X)))
% 0.20/0.55 = { by lemma 16 }
% 0.20/0.55 meet(Y, join(zero, complement(X)))
% 0.20/0.55 = { by lemma 28 }
% 0.20/0.55 meet(Y, complement(X))
% 0.20/0.55
% 0.20/0.55 Lemma 36: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 0.20/0.55 Proof:
% 0.20/0.55 complement(meet(complement(X), Y))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 complement(meet(Y, complement(X)))
% 0.20/0.55 = { by lemma 28 R->L }
% 0.20/0.55 complement(join(zero, meet(Y, complement(X))))
% 0.20/0.55 = { by lemma 35 R->L }
% 0.20/0.55 complement(join(zero, complement(join(X, complement(Y)))))
% 0.20/0.55 = { by lemma 31 }
% 0.20/0.55 meet(join(X, complement(Y)), top)
% 0.20/0.55 = { by lemma 32 }
% 0.20/0.55 join(X, complement(Y))
% 0.20/0.55
% 0.20/0.55 Lemma 37: meet(X, join(X, complement(Y))) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 meet(X, join(X, complement(Y)))
% 0.20/0.55 = { by lemma 27 R->L }
% 0.20/0.55 join(meet(X, join(X, complement(Y))), zero)
% 0.20/0.55 = { by lemma 16 R->L }
% 0.20/0.55 join(meet(X, join(X, complement(Y))), complement(top))
% 0.20/0.55 = { by lemma 36 R->L }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(top))
% 0.20/0.55 = { by lemma 23 R->L }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(Y), top)))
% 0.20/0.55 = { by lemma 17 R->L }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(complement(Y), complement(complement(X))))))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(complement(complement(X)), complement(Y)))))
% 0.20/0.55 = { by lemma 25 R->L }
% 0.20/0.55 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)))))))
% 0.20/0.55 = { by lemma 34 }
% 0.20/0.55 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)))))))
% 0.20/0.55 = { by lemma 28 }
% 0.20/0.55 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))))))
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(complement(X), Y), meet(complement(X), Y))))))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), meet(complement(X), Y))))))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(join(meet(Y, complement(X)), meet(Y, complement(X)))))))
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.55 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)))))))))
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.55 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)))))))))
% 0.20/0.55 = { by lemma 20 }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(complement(join(complement(Y), complement(complement(X))))))))
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(Y, complement(X))))))
% 0.20/0.55 = { by lemma 30 R->L }
% 0.20/0.55 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(complement(X), Y)))))
% 0.20/0.55 = { by lemma 24 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 38: join(X, meet(X, Y)) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 join(X, meet(X, Y))
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.55 join(X, complement(join(complement(X), complement(Y))))
% 0.20/0.55 = { by lemma 36 R->L }
% 0.20/0.55 complement(meet(complement(X), join(complement(X), complement(Y))))
% 0.20/0.55 = { by lemma 37 }
% 0.20/0.55 complement(complement(X))
% 0.20/0.55 = { by lemma 29 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 39: complement(join(complement(X), Y)) = meet(X, complement(Y)).
% 0.20/0.55 Proof:
% 0.20/0.55 complement(join(complement(X), Y))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.55 complement(join(Y, complement(X)))
% 0.20/0.55 = { by lemma 35 }
% 0.20/0.55 meet(X, complement(Y))
% 0.20/0.55
% 0.20/0.55 Lemma 40: meet(X, join(X, Y)) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 meet(X, join(X, Y))
% 0.20/0.55 = { by lemma 32 R->L }
% 0.20/0.55 meet(X, join(X, meet(Y, top)))
% 0.20/0.55 = { by lemma 31 R->L }
% 0.20/0.55 meet(X, join(X, complement(join(zero, complement(Y)))))
% 0.20/0.55 = { by lemma 37 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 41: meet(X, join(Y, X)) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 meet(X, join(Y, X))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.55 meet(X, join(X, Y))
% 0.20/0.55 = { by lemma 40 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 42: join(composition(Y, Z), composition(X, Z)) = composition(join(X, Y), Z).
% 0.20/0.55 Proof:
% 0.20/0.55 join(composition(Y, Z), composition(X, Z))
% 0.20/0.55 = { by axiom 13 (composition_distributivity_7) R->L }
% 0.20/0.55 composition(join(Y, X), Z)
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.55 composition(join(X, Y), Z)
% 0.20/0.55
% 0.20/0.55 Goal 1 (goals_16): composition(meet(sk1, sk2), top) = meet(sk1, sk2).
% 0.20/0.55 Proof:
% 0.20/0.55 composition(meet(sk1, sk2), top)
% 0.20/0.55 = { by lemma 41 R->L }
% 0.20/0.55 meet(composition(meet(sk1, sk2), top), join(sk1, composition(meet(sk1, sk2), top)))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.55 meet(composition(meet(sk1, sk2), top), join(composition(meet(sk1, sk2), top), sk1))
% 0.20/0.55 = { by axiom 3 (goals_14) R->L }
% 0.20/0.55 meet(composition(meet(sk1, sk2), top), join(composition(meet(sk1, sk2), top), composition(sk1, top)))
% 0.20/0.55 = { by lemma 42 }
% 0.20/0.55 meet(composition(meet(sk1, sk2), top), composition(join(sk1, meet(sk1, sk2)), top))
% 0.20/0.55 = { by lemma 38 }
% 0.20/0.55 meet(composition(meet(sk1, sk2), top), composition(sk1, top))
% 0.20/0.55 = { by axiom 3 (goals_14) }
% 0.20/0.55 meet(composition(meet(sk1, sk2), top), sk1)
% 0.20/0.55 = { by lemma 30 R->L }
% 0.20/0.55 meet(sk1, composition(meet(sk1, sk2), top))
% 0.20/0.55 = { by lemma 41 R->L }
% 0.20/0.55 meet(sk1, meet(composition(meet(sk1, sk2), top), join(sk2, composition(meet(sk1, sk2), top))))
% 0.20/0.55 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.55 meet(sk1, meet(composition(meet(sk1, sk2), top), join(composition(meet(sk1, sk2), top), sk2)))
% 0.20/0.55 = { by axiom 4 (goals_15) R->L }
% 0.20/0.55 meet(sk1, meet(composition(meet(sk1, sk2), top), join(composition(meet(sk1, sk2), top), composition(sk2, top))))
% 0.20/0.55 = { by lemma 42 }
% 0.20/0.55 meet(sk1, meet(composition(meet(sk1, sk2), top), composition(join(sk2, meet(sk1, sk2)), top)))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 meet(sk1, meet(composition(meet(sk1, sk2), top), composition(join(sk2, meet(sk2, sk1)), top)))
% 0.20/0.55 = { by lemma 38 }
% 0.20/0.55 meet(sk1, meet(composition(meet(sk1, sk2), top), composition(sk2, top)))
% 0.20/0.55 = { by axiom 4 (goals_15) }
% 0.20/0.55 meet(sk1, meet(composition(meet(sk1, sk2), top), sk2))
% 0.20/0.55 = { by lemma 30 R->L }
% 0.20/0.55 meet(sk1, meet(sk2, composition(meet(sk1, sk2), top)))
% 0.20/0.55 = { by lemma 32 R->L }
% 0.20/0.55 meet(meet(sk1, top), meet(sk2, composition(meet(sk1, sk2), top)))
% 0.20/0.55 = { by lemma 31 R->L }
% 0.20/0.55 meet(complement(join(zero, complement(sk1))), meet(sk2, composition(meet(sk1, sk2), top)))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 meet(complement(join(zero, complement(sk1))), meet(composition(meet(sk1, sk2), top), sk2))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 meet(meet(composition(meet(sk1, sk2), top), sk2), complement(join(zero, complement(sk1))))
% 0.20/0.55 = { by axiom 12 (maddux4_definiton_of_meet_4) }
% 0.20/0.55 meet(complement(join(complement(composition(meet(sk1, sk2), top)), complement(sk2))), complement(join(zero, complement(sk1))))
% 0.20/0.55 = { by lemma 30 }
% 0.20/0.55 meet(complement(join(zero, complement(sk1))), complement(join(complement(composition(meet(sk1, sk2), top)), complement(sk2))))
% 0.20/0.55 = { by lemma 28 R->L }
% 0.20/0.55 meet(join(zero, complement(join(zero, complement(sk1)))), complement(join(complement(composition(meet(sk1, sk2), top)), complement(sk2))))
% 0.20/0.55 = { by lemma 35 R->L }
% 0.20/0.55 complement(join(join(complement(composition(meet(sk1, sk2), top)), complement(sk2)), complement(join(zero, complement(join(zero, complement(sk1)))))))
% 0.20/0.55 = { by lemma 31 }
% 0.20/0.55 complement(join(join(complement(composition(meet(sk1, sk2), top)), complement(sk2)), meet(join(zero, complement(sk1)), top)))
% 0.20/0.55 = { by lemma 32 }
% 0.20/0.55 complement(join(join(complement(composition(meet(sk1, sk2), top)), complement(sk2)), join(zero, complement(sk1))))
% 0.20/0.55 = { by axiom 9 (maddux2_join_associativity_2) R->L }
% 0.20/0.56 complement(join(complement(composition(meet(sk1, sk2), top)), join(complement(sk2), join(zero, complement(sk1)))))
% 0.20/0.56 = { by lemma 39 }
% 0.20/0.56 meet(composition(meet(sk1, sk2), top), complement(join(complement(sk2), join(zero, complement(sk1)))))
% 0.20/0.56 = { by lemma 39 }
% 0.20/0.56 meet(composition(meet(sk1, sk2), top), meet(sk2, complement(join(zero, complement(sk1)))))
% 0.20/0.56 = { by lemma 31 }
% 0.20/0.56 meet(composition(meet(sk1, sk2), top), meet(sk2, meet(sk1, top)))
% 0.20/0.56 = { by lemma 32 }
% 0.20/0.56 meet(composition(meet(sk1, sk2), top), meet(sk2, sk1))
% 0.20/0.56 = { by lemma 30 R->L }
% 0.20/0.56 meet(composition(meet(sk1, sk2), top), meet(sk1, sk2))
% 0.20/0.56 = { by lemma 30 R->L }
% 0.20/0.56 meet(meet(sk1, sk2), composition(meet(sk1, sk2), top))
% 0.20/0.56 = { by axiom 5 (converse_idempotence_8) R->L }
% 0.20/0.56 meet(meet(sk1, sk2), converse(converse(composition(meet(sk1, sk2), top))))
% 0.20/0.56 = { by lemma 33 }
% 0.20/0.56 meet(meet(sk1, sk2), converse(composition(top, converse(meet(sk1, sk2)))))
% 0.20/0.56 = { by lemma 23 R->L }
% 0.20/0.56 meet(meet(sk1, sk2), converse(composition(join(one, top), converse(meet(sk1, sk2)))))
% 0.20/0.56 = { by axiom 13 (composition_distributivity_7) }
% 0.20/0.56 meet(meet(sk1, sk2), converse(join(composition(one, converse(meet(sk1, sk2))), composition(top, converse(meet(sk1, sk2))))))
% 0.20/0.56 = { by lemma 19 }
% 0.20/0.56 meet(meet(sk1, sk2), converse(join(converse(meet(sk1, sk2)), composition(top, converse(meet(sk1, sk2))))))
% 0.20/0.56 = { by lemma 33 R->L }
% 0.20/0.56 meet(meet(sk1, sk2), converse(join(converse(meet(sk1, sk2)), converse(composition(meet(sk1, sk2), top)))))
% 0.20/0.56 = { by axiom 8 (converse_additivity_9) R->L }
% 0.20/0.56 meet(meet(sk1, sk2), converse(converse(join(meet(sk1, sk2), composition(meet(sk1, sk2), top)))))
% 0.20/0.56 = { by axiom 5 (converse_idempotence_8) }
% 0.20/0.56 meet(meet(sk1, sk2), join(meet(sk1, sk2), composition(meet(sk1, sk2), top)))
% 0.20/0.56 = { by lemma 40 }
% 0.20/0.56 meet(sk1, sk2)
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------