TSTP Solution File: REL024-2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL024-2 : 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 : n014.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 13:44:05 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL024-2 : 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
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 19:53:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.64 Command-line arguments: --no-flatten-goal
% 0.20/0.64
% 0.20/0.64 % SZS status Unsatisfiable
% 0.20/0.64
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 0.20/0.66 Axiom 2 (converse_idempotence_8): converse(converse(X)) = X.
% 0.20/0.66 Axiom 3 (composition_identity_6): composition(X, one) = X.
% 0.20/0.66 Axiom 4 (def_top_12): top = join(X, complement(X)).
% 0.20/0.66 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 0.20/0.66 Axiom 6 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.20/0.66 Axiom 7 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.20/0.66 Axiom 8 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.66 Axiom 9 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.20/0.66 Axiom 10 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.20/0.66 Axiom 11 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.20/0.66 Axiom 12 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.20/0.66 Axiom 13 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.20/0.66
% 0.20/0.66 Lemma 14: complement(top) = zero.
% 0.20/0.66 Proof:
% 0.20/0.66 complement(top)
% 0.20/0.66 = { by axiom 4 (def_top_12) }
% 0.20/0.66 complement(join(complement(X), complement(complement(X))))
% 0.20/0.66 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.66 meet(X, complement(X))
% 0.20/0.66 = { by axiom 5 (def_zero_13) R->L }
% 0.20/0.66 zero
% 0.20/0.66
% 0.20/0.66 Lemma 15: join(X, join(Y, complement(X))) = join(Y, top).
% 0.20/0.66 Proof:
% 0.20/0.66 join(X, join(Y, complement(X)))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(X, join(complement(X), Y))
% 0.20/0.66 = { by axiom 7 (maddux2_join_associativity_2) }
% 0.20/0.66 join(join(X, complement(X)), Y)
% 0.20/0.66 = { by axiom 4 (def_top_12) R->L }
% 0.20/0.66 join(top, Y)
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.66 join(Y, top)
% 0.20/0.66
% 0.20/0.66 Lemma 16: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 0.20/0.66 Proof:
% 0.20/0.66 converse(composition(converse(X), Y))
% 0.20/0.66 = { by axiom 8 (converse_multiplicativity_10) }
% 0.20/0.66 composition(converse(Y), converse(converse(X)))
% 0.20/0.66 = { by axiom 2 (converse_idempotence_8) }
% 0.20/0.66 composition(converse(Y), X)
% 0.20/0.66
% 0.20/0.66 Lemma 17: composition(converse(one), X) = X.
% 0.20/0.66 Proof:
% 0.20/0.66 composition(converse(one), X)
% 0.20/0.66 = { by lemma 16 R->L }
% 0.20/0.66 converse(composition(converse(X), one))
% 0.20/0.66 = { by axiom 3 (composition_identity_6) }
% 0.20/0.66 converse(converse(X))
% 0.20/0.66 = { by axiom 2 (converse_idempotence_8) }
% 0.20/0.66 X
% 0.20/0.66
% 0.20/0.66 Lemma 18: join(complement(X), complement(X)) = complement(X).
% 0.20/0.66 Proof:
% 0.20/0.66 join(complement(X), complement(X))
% 0.20/0.66 = { by lemma 17 R->L }
% 0.20/0.66 join(complement(X), composition(converse(one), complement(X)))
% 0.20/0.66 = { by lemma 17 R->L }
% 0.20/0.66 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.20/0.66 = { by axiom 3 (composition_identity_6) R->L }
% 0.20/0.66 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.20/0.66 = { by axiom 9 (composition_associativity_5) R->L }
% 0.20/0.66 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.20/0.66 = { by lemma 17 }
% 0.20/0.66 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.20/0.66 = { by axiom 12 (converse_cancellativity_11) }
% 0.20/0.66 complement(X)
% 0.20/0.66
% 0.20/0.66 Lemma 19: join(top, complement(X)) = top.
% 0.20/0.66 Proof:
% 0.20/0.66 join(top, complement(X))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(complement(X), top)
% 0.20/0.66 = { by lemma 15 R->L }
% 0.20/0.66 join(X, join(complement(X), complement(X)))
% 0.20/0.66 = { by lemma 18 }
% 0.20/0.66 join(X, complement(X))
% 0.20/0.66 = { by axiom 4 (def_top_12) R->L }
% 0.20/0.66 top
% 0.20/0.66
% 0.20/0.66 Lemma 20: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.20/0.66 Proof:
% 0.20/0.66 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.20/0.66 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.66 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.20/0.66 = { by axiom 13 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 0.20/0.66 X
% 0.20/0.66
% 0.20/0.66 Lemma 21: join(zero, meet(X, X)) = X.
% 0.20/0.66 Proof:
% 0.20/0.66 join(zero, meet(X, X))
% 0.20/0.66 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.66 join(zero, complement(join(complement(X), complement(X))))
% 0.20/0.66 = { by axiom 5 (def_zero_13) }
% 0.20/0.66 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.66 = { by lemma 20 }
% 0.20/0.66 X
% 0.20/0.66
% 0.20/0.66 Lemma 22: join(zero, join(X, complement(complement(Y)))) = join(X, Y).
% 0.20/0.66 Proof:
% 0.20/0.66 join(zero, join(X, complement(complement(Y))))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(zero, join(complement(complement(Y)), X))
% 0.20/0.66 = { by lemma 18 R->L }
% 0.20/0.66 join(zero, join(complement(join(complement(Y), complement(Y))), X))
% 0.20/0.66 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.66 join(zero, join(meet(Y, Y), X))
% 0.20/0.66 = { by axiom 7 (maddux2_join_associativity_2) }
% 0.20/0.66 join(join(zero, meet(Y, Y)), X)
% 0.20/0.66 = { by lemma 21 }
% 0.20/0.66 join(Y, X)
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.66 join(X, Y)
% 0.20/0.66
% 0.20/0.66 Lemma 23: join(zero, complement(complement(X))) = X.
% 0.20/0.66 Proof:
% 0.20/0.66 join(zero, complement(complement(X)))
% 0.20/0.66 = { by axiom 5 (def_zero_13) }
% 0.20/0.66 join(meet(X, complement(X)), complement(complement(X)))
% 0.20/0.66 = { by lemma 18 R->L }
% 0.20/0.66 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.20/0.66 = { by lemma 20 }
% 0.20/0.66 X
% 0.20/0.66
% 0.20/0.66 Lemma 24: join(zero, complement(X)) = complement(X).
% 0.20/0.66 Proof:
% 0.20/0.66 join(zero, complement(X))
% 0.20/0.66 = { by lemma 23 R->L }
% 0.20/0.66 join(zero, join(zero, complement(complement(complement(X)))))
% 0.20/0.66 = { by lemma 18 R->L }
% 0.20/0.66 join(zero, join(zero, join(complement(complement(complement(X))), complement(complement(complement(X))))))
% 0.20/0.66 = { by lemma 22 }
% 0.20/0.66 join(zero, join(complement(complement(complement(X))), complement(X)))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.66 join(zero, join(complement(X), complement(complement(complement(X)))))
% 0.20/0.66 = { by lemma 22 }
% 0.20/0.66 join(complement(X), complement(X))
% 0.20/0.66 = { by lemma 18 }
% 0.20/0.66 complement(X)
% 0.20/0.66
% 0.20/0.66 Lemma 25: join(X, zero) = X.
% 0.20/0.66 Proof:
% 0.20/0.66 join(X, zero)
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(zero, X)
% 0.20/0.66 = { by lemma 22 R->L }
% 0.20/0.66 join(zero, join(zero, complement(complement(X))))
% 0.20/0.66 = { by lemma 24 }
% 0.20/0.66 join(zero, complement(complement(X)))
% 0.20/0.66 = { by lemma 23 }
% 0.20/0.66 X
% 0.20/0.66
% 0.20/0.66 Lemma 26: join(X, top) = top.
% 0.20/0.66 Proof:
% 0.20/0.66 join(X, top)
% 0.20/0.66 = { by lemma 19 R->L }
% 0.20/0.66 join(X, join(top, complement(X)))
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 join(top, top)
% 0.20/0.66 = { by lemma 15 R->L }
% 0.20/0.66 join(join(zero, zero), join(top, complement(join(zero, zero))))
% 0.20/0.66 = { by lemma 19 }
% 0.20/0.66 join(join(zero, zero), top)
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(top, join(zero, zero))
% 0.20/0.66 = { by lemma 25 }
% 0.20/0.66 join(top, zero)
% 0.20/0.66 = { by lemma 25 }
% 0.20/0.66 top
% 0.20/0.66
% 0.20/0.66 Lemma 27: meet(Y, X) = meet(X, Y).
% 0.20/0.66 Proof:
% 0.20/0.66 meet(Y, X)
% 0.20/0.66 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.66 complement(join(complement(Y), complement(X)))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 complement(join(complement(X), complement(Y)))
% 0.20/0.66 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.66 meet(X, Y)
% 0.20/0.66
% 0.20/0.66 Lemma 28: complement(join(zero, complement(X))) = meet(X, top).
% 0.20/0.66 Proof:
% 0.20/0.66 complement(join(zero, complement(X)))
% 0.20/0.66 = { by lemma 14 R->L }
% 0.20/0.66 complement(join(complement(top), complement(X)))
% 0.20/0.66 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.66 meet(top, X)
% 0.20/0.66 = { by lemma 27 R->L }
% 0.20/0.66 meet(X, top)
% 0.20/0.66
% 0.20/0.66 Lemma 29: join(X, complement(zero)) = top.
% 0.20/0.66 Proof:
% 0.20/0.66 join(X, complement(zero))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(complement(zero), X)
% 0.20/0.66 = { by lemma 22 R->L }
% 0.20/0.66 join(zero, join(complement(zero), complement(complement(X))))
% 0.20/0.66 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.66 join(zero, join(complement(complement(X)), complement(zero)))
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 join(complement(complement(X)), top)
% 0.20/0.66 = { by lemma 26 }
% 0.20/0.67 top
% 0.20/0.67
% 0.20/0.67 Lemma 30: meet(X, top) = X.
% 0.20/0.67 Proof:
% 0.20/0.67 meet(X, top)
% 0.20/0.67 = { by lemma 28 R->L }
% 0.20/0.67 complement(join(zero, complement(X)))
% 0.20/0.67 = { by lemma 24 R->L }
% 0.20/0.67 join(zero, complement(join(zero, complement(X))))
% 0.20/0.67 = { by lemma 28 }
% 0.20/0.67 join(zero, meet(X, top))
% 0.20/0.67 = { by lemma 29 R->L }
% 0.20/0.67 join(zero, meet(X, join(complement(zero), complement(zero))))
% 0.20/0.67 = { by lemma 18 }
% 0.20/0.67 join(zero, meet(X, complement(zero)))
% 0.20/0.67 = { by lemma 14 R->L }
% 0.20/0.67 join(complement(top), meet(X, complement(zero)))
% 0.20/0.67 = { by lemma 29 R->L }
% 0.20/0.67 join(complement(join(complement(X), complement(zero))), meet(X, complement(zero)))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.67 join(meet(X, zero), meet(X, complement(zero)))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.67 join(meet(X, complement(zero)), meet(X, zero))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.67 join(meet(X, complement(zero)), complement(join(complement(X), complement(zero))))
% 0.20/0.67 = { by lemma 20 }
% 0.20/0.67 X
% 0.20/0.67
% 0.20/0.67 Lemma 31: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 0.20/0.67 Proof:
% 0.20/0.67 meet(X, join(complement(Y), complement(Z)))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.67 meet(X, join(complement(Z), complement(Y)))
% 0.20/0.67 = { by lemma 27 }
% 0.20/0.67 meet(join(complement(Z), complement(Y)), X)
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.67 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.67 complement(join(meet(Z, Y), complement(X)))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.67 complement(join(complement(X), meet(Z, Y)))
% 0.20/0.67 = { by lemma 27 R->L }
% 0.20/0.67 complement(join(complement(X), meet(Y, Z)))
% 0.20/0.67
% 0.20/0.67 Lemma 32: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 0.20/0.67 Proof:
% 0.20/0.67 complement(join(X, complement(Y)))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.67 complement(join(complement(Y), X))
% 0.20/0.67 = { by lemma 30 R->L }
% 0.20/0.67 complement(join(complement(Y), meet(X, top)))
% 0.20/0.67 = { by lemma 27 R->L }
% 0.20/0.67 complement(join(complement(Y), meet(top, X)))
% 0.20/0.67 = { by lemma 31 R->L }
% 0.20/0.67 meet(Y, join(complement(top), complement(X)))
% 0.20/0.67 = { by lemma 14 }
% 0.20/0.67 meet(Y, join(zero, complement(X)))
% 0.20/0.67 = { by lemma 24 }
% 0.20/0.67 meet(Y, complement(X))
% 0.20/0.67
% 0.20/0.67 Lemma 33: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 0.20/0.67 Proof:
% 0.20/0.67 complement(meet(X, complement(Y)))
% 0.20/0.67 = { by lemma 25 R->L }
% 0.20/0.67 complement(join(meet(X, complement(Y)), zero))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.67 complement(join(zero, meet(X, complement(Y))))
% 0.20/0.67 = { by lemma 32 R->L }
% 0.20/0.67 complement(join(zero, complement(join(Y, complement(X)))))
% 0.20/0.67 = { by lemma 28 }
% 0.20/0.67 meet(join(Y, complement(X)), top)
% 0.20/0.67 = { by lemma 30 }
% 0.20/0.67 join(Y, complement(X))
% 0.20/0.67
% 0.20/0.67 Goal 1 (goals_17): join(composition(meet(sk1, converse(sk2)), meet(sk2, sk3)), composition(meet(sk1, converse(sk2)), sk3)) = composition(meet(sk1, converse(sk2)), sk3).
% 0.20/0.67 Proof:
% 0.20/0.67 join(composition(meet(sk1, converse(sk2)), meet(sk2, sk3)), composition(meet(sk1, converse(sk2)), sk3))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.67 join(composition(meet(sk1, converse(sk2)), sk3), composition(meet(sk1, converse(sk2)), meet(sk2, sk3)))
% 0.20/0.67 = { by lemma 27 R->L }
% 0.20/0.67 join(composition(meet(sk1, converse(sk2)), sk3), composition(meet(sk1, converse(sk2)), meet(sk3, sk2)))
% 0.20/0.67 = { by axiom 2 (converse_idempotence_8) R->L }
% 0.20/0.67 join(composition(meet(sk1, converse(sk2)), sk3), composition(converse(converse(meet(sk1, converse(sk2)))), meet(sk3, sk2)))
% 0.20/0.67 = { by axiom 2 (converse_idempotence_8) R->L }
% 0.20/0.67 join(converse(converse(composition(meet(sk1, converse(sk2)), sk3))), composition(converse(converse(meet(sk1, converse(sk2)))), meet(sk3, sk2)))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.67 join(composition(converse(converse(meet(sk1, converse(sk2)))), meet(sk3, sk2)), converse(converse(composition(meet(sk1, converse(sk2)), sk3))))
% 0.20/0.67 = { by lemma 16 R->L }
% 0.20/0.67 join(converse(composition(converse(meet(sk3, sk2)), converse(meet(sk1, converse(sk2))))), converse(converse(composition(meet(sk1, converse(sk2)), sk3))))
% 0.20/0.67 = { by axiom 6 (converse_additivity_9) R->L }
% 0.20/0.67 converse(join(composition(converse(meet(sk3, sk2)), converse(meet(sk1, converse(sk2)))), converse(composition(meet(sk1, converse(sk2)), sk3))))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.67 converse(join(converse(composition(meet(sk1, converse(sk2)), sk3)), composition(converse(meet(sk3, sk2)), converse(meet(sk1, converse(sk2))))))
% 0.20/0.67 = { by axiom 8 (converse_multiplicativity_10) }
% 0.20/0.67 converse(join(composition(converse(sk3), converse(meet(sk1, converse(sk2)))), composition(converse(meet(sk3, sk2)), converse(meet(sk1, converse(sk2))))))
% 0.20/0.67 = { by axiom 11 (composition_distributivity_7) R->L }
% 0.20/0.67 converse(composition(join(converse(sk3), converse(meet(sk3, sk2))), converse(meet(sk1, converse(sk2)))))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.67 converse(composition(join(converse(meet(sk3, sk2)), converse(sk3)), converse(meet(sk1, converse(sk2)))))
% 0.20/0.67 = { by axiom 2 (converse_idempotence_8) R->L }
% 0.20/0.67 converse(composition(join(converse(converse(converse(meet(sk3, sk2)))), converse(sk3)), converse(meet(sk1, converse(sk2)))))
% 0.20/0.67 = { by axiom 6 (converse_additivity_9) R->L }
% 0.20/0.67 converse(composition(converse(join(converse(converse(meet(sk3, sk2))), sk3)), converse(meet(sk1, converse(sk2)))))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.67 converse(composition(converse(join(sk3, converse(converse(meet(sk3, sk2))))), converse(meet(sk1, converse(sk2)))))
% 0.20/0.67 = { by axiom 8 (converse_multiplicativity_10) R->L }
% 0.20/0.67 converse(converse(composition(meet(sk1, converse(sk2)), join(sk3, converse(converse(meet(sk3, sk2)))))))
% 0.20/0.67 = { by axiom 2 (converse_idempotence_8) }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), join(sk3, converse(converse(meet(sk3, sk2)))))
% 0.20/0.67 = { by axiom 2 (converse_idempotence_8) }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), join(sk3, meet(sk3, sk2)))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), join(sk3, complement(join(complement(sk3), complement(sk2)))))
% 0.20/0.67 = { by lemma 33 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(meet(join(complement(sk3), complement(sk2)), complement(sk3))))
% 0.20/0.67 = { by lemma 27 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(meet(complement(sk3), join(complement(sk3), complement(sk2)))))
% 0.20/0.67 = { by lemma 33 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(meet(complement(sk3), complement(meet(sk2, complement(complement(sk3)))))))
% 0.20/0.67 = { by lemma 32 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(complement(join(meet(sk2, complement(complement(sk3))), complement(complement(sk3))))))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3)))))))
% 0.20/0.67 = { by lemma 24 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(zero, complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 14 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(top), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 26 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(sk2), top)), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 15 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), join(complement(sk2), complement(complement(complement(sk3)))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), join(complement(complement(complement(sk3))), complement(sk2)))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 21 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), join(zero, meet(join(complement(complement(complement(sk3))), complement(sk2)), join(complement(complement(complement(sk3))), complement(sk2)))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 31 }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), join(zero, complement(join(complement(join(complement(complement(complement(sk3))), complement(sk2))), meet(complement(complement(sk3)), sk2)))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 24 }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(join(complement(join(complement(complement(complement(sk3))), complement(sk2))), meet(complement(complement(sk3)), sk2))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(join(meet(complement(complement(sk3)), sk2), meet(complement(complement(sk3)), sk2))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 27 }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(join(meet(sk2, complement(complement(sk3))), meet(complement(complement(sk3)), sk2))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 27 }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(join(meet(sk2, complement(complement(sk3))), meet(sk2, complement(complement(sk3))))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(join(meet(sk2, complement(complement(sk3))), complement(join(complement(sk2), complement(complement(complement(sk3))))))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(join(complement(join(complement(sk2), complement(complement(complement(sk3))))), complement(join(complement(sk2), complement(complement(complement(sk3))))))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 18 }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(complement(join(complement(sk2), complement(complement(complement(sk3)))))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(meet(sk2, complement(complement(sk3)))))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 27 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(complement(join(complement(complement(sk3)), complement(meet(complement(complement(sk3)), sk2)))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(meet(complement(sk3), meet(complement(complement(sk3)), sk2)), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 27 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(join(meet(complement(sk3), meet(sk2, complement(complement(sk3)))), complement(join(complement(complement(sk3)), meet(sk2, complement(complement(sk3))))))))
% 0.20/0.67 = { by lemma 20 }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), complement(complement(sk3)))
% 0.20/0.67 = { by lemma 24 R->L }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), join(zero, complement(complement(sk3))))
% 0.20/0.67 = { by lemma 23 }
% 0.20/0.67 composition(meet(sk1, converse(sk2)), sk3)
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67
% 0.20/0.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------