TSTP Solution File: REL042-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL042-1 : 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 : n031.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 13:44:27 EDT 2023
% Result : Unsatisfiable 32.76s 4.60s
% Output : Proof 32.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL042-1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 20:12:22 EDT 2023
% 0.14/0.34 % CPUTime :
% 32.76/4.60 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 32.76/4.60
% 32.76/4.60 % SZS status Unsatisfiable
% 32.76/4.60
% 32.76/4.62 % SZS output start Proof
% 32.76/4.63 Axiom 1 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 32.76/4.63 Axiom 2 (composition_identity_6): composition(X, one) = X.
% 32.76/4.63 Axiom 3 (converse_idempotence_8): converse(converse(X)) = X.
% 32.76/4.63 Axiom 4 (def_top_12): top = join(X, complement(X)).
% 32.76/4.63 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 32.76/4.63 Axiom 6 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 32.76/4.63 Axiom 7 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 32.76/4.63 Axiom 8 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 32.76/4.63 Axiom 9 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 32.76/4.63 Axiom 10 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 32.76/4.63 Axiom 11 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 32.76/4.63 Axiom 12 (goals_14): meet(composition(sk1, X), composition(sk1, complement(X))) = zero.
% 32.76/4.63 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 32.76/4.63 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 32.76/4.63
% 32.76/4.63 Lemma 15: complement(top) = zero.
% 32.76/4.63 Proof:
% 32.76/4.63 complement(top)
% 32.76/4.63 = { by axiom 4 (def_top_12) }
% 32.76/4.63 complement(join(complement(X), complement(complement(X))))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 32.76/4.63 meet(X, complement(X))
% 32.76/4.63 = { by axiom 5 (def_zero_13) R->L }
% 32.76/4.63 zero
% 32.76/4.63
% 32.76/4.63 Lemma 16: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 join(meet(X, Y), complement(join(complement(X), Y)))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 32.76/4.63 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 17: join(zero, meet(X, X)) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 join(zero, meet(X, X))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 join(zero, complement(join(complement(X), complement(X))))
% 32.76/4.63 = { by axiom 5 (def_zero_13) }
% 32.76/4.63 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 32.76/4.63 = { by lemma 16 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 18: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 32.76/4.63 Proof:
% 32.76/4.63 converse(composition(converse(X), Y))
% 32.76/4.63 = { by axiom 8 (converse_multiplicativity_10) }
% 32.76/4.63 composition(converse(Y), converse(converse(X)))
% 32.76/4.63 = { by axiom 3 (converse_idempotence_8) }
% 32.76/4.63 composition(converse(Y), X)
% 32.76/4.63
% 32.76/4.63 Lemma 19: composition(converse(one), X) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 composition(converse(one), X)
% 32.76/4.63 = { by lemma 18 R->L }
% 32.76/4.63 converse(composition(converse(X), one))
% 32.76/4.63 = { by axiom 2 (composition_identity_6) }
% 32.76/4.63 converse(converse(X))
% 32.76/4.63 = { by axiom 3 (converse_idempotence_8) }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 20: composition(one, X) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 composition(one, X)
% 32.76/4.63 = { by lemma 19 R->L }
% 32.76/4.63 composition(converse(one), composition(one, X))
% 32.76/4.63 = { by axiom 9 (composition_associativity_5) }
% 32.76/4.63 composition(composition(converse(one), one), X)
% 32.76/4.63 = { by axiom 2 (composition_identity_6) }
% 32.76/4.63 composition(converse(one), X)
% 32.76/4.63 = { by lemma 19 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 21: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 32.76/4.63 Proof:
% 32.76/4.63 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 32.76/4.63 = { by axiom 13 (converse_cancellativity_11) }
% 32.76/4.63 complement(X)
% 32.76/4.63
% 32.76/4.63 Lemma 22: join(complement(X), complement(X)) = complement(X).
% 32.76/4.63 Proof:
% 32.76/4.63 join(complement(X), complement(X))
% 32.76/4.63 = { by lemma 19 R->L }
% 32.76/4.63 join(complement(X), composition(converse(one), complement(X)))
% 32.76/4.63 = { by lemma 20 R->L }
% 32.76/4.63 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 32.76/4.63 = { by lemma 21 }
% 32.76/4.63 complement(X)
% 32.76/4.63
% 32.76/4.63 Lemma 23: join(zero, complement(complement(X))) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 join(zero, complement(complement(X)))
% 32.76/4.63 = { by axiom 5 (def_zero_13) }
% 32.76/4.63 join(meet(X, complement(X)), complement(complement(X)))
% 32.76/4.63 = { by lemma 22 R->L }
% 32.76/4.63 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 32.76/4.63 = { by lemma 16 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 24: join(X, zero) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 join(X, zero)
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 join(zero, X)
% 32.76/4.63 = { by lemma 17 R->L }
% 32.76/4.63 join(zero, join(zero, meet(X, X)))
% 32.76/4.63 = { by axiom 7 (maddux2_join_associativity_2) }
% 32.76/4.63 join(join(zero, zero), meet(X, X))
% 32.76/4.63 = { by lemma 15 R->L }
% 32.76/4.63 join(join(zero, complement(top)), meet(X, X))
% 32.76/4.63 = { by lemma 15 R->L }
% 32.76/4.63 join(join(complement(top), complement(top)), meet(X, X))
% 32.76/4.63 = { by lemma 22 }
% 32.76/4.63 join(complement(top), meet(X, X))
% 32.76/4.63 = { by lemma 15 }
% 32.76/4.63 join(zero, meet(X, X))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) }
% 32.76/4.63 join(meet(X, X), zero)
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 join(complement(join(complement(X), complement(X))), zero)
% 32.76/4.63 = { by lemma 22 }
% 32.76/4.63 join(complement(complement(X)), zero)
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) }
% 32.76/4.63 join(zero, complement(complement(X)))
% 32.76/4.63 = { by lemma 23 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 25: join(zero, X) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 join(zero, X)
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 join(X, zero)
% 32.76/4.63 = { by lemma 24 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 26: complement(complement(X)) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 complement(complement(X))
% 32.76/4.63 = { by lemma 25 R->L }
% 32.76/4.63 join(zero, complement(complement(X)))
% 32.76/4.63 = { by lemma 23 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 27: meet(Y, X) = meet(X, Y).
% 32.76/4.63 Proof:
% 32.76/4.63 meet(Y, X)
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 complement(join(complement(Y), complement(X)))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 complement(join(complement(X), complement(Y)))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 32.76/4.63 meet(X, Y)
% 32.76/4.63
% 32.76/4.63 Lemma 28: complement(join(zero, complement(X))) = meet(X, top).
% 32.76/4.63 Proof:
% 32.76/4.63 complement(join(zero, complement(X)))
% 32.76/4.63 = { by lemma 15 R->L }
% 32.76/4.63 complement(join(complement(top), complement(X)))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 32.76/4.63 meet(top, X)
% 32.76/4.63 = { by lemma 27 R->L }
% 32.76/4.63 meet(X, top)
% 32.76/4.63
% 32.76/4.63 Lemma 29: meet(X, top) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 meet(X, top)
% 32.76/4.63 = { by lemma 28 R->L }
% 32.76/4.63 complement(join(zero, complement(X)))
% 32.76/4.63 = { by lemma 25 }
% 32.76/4.63 complement(complement(X))
% 32.76/4.63 = { by lemma 26 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Lemma 30: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 32.76/4.63 Proof:
% 32.76/4.63 meet(X, join(complement(Y), complement(Z)))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 meet(X, join(complement(Z), complement(Y)))
% 32.76/4.63 = { by lemma 27 }
% 32.76/4.63 meet(join(complement(Z), complement(Y)), X)
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 32.76/4.63 complement(join(meet(Z, Y), complement(X)))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) }
% 32.76/4.63 complement(join(complement(X), meet(Z, Y)))
% 32.76/4.63 = { by lemma 27 R->L }
% 32.76/4.63 complement(join(complement(X), meet(Y, Z)))
% 32.76/4.63
% 32.76/4.63 Lemma 31: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 32.76/4.63 Proof:
% 32.76/4.63 join(complement(X), complement(Y))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 join(complement(Y), complement(X))
% 32.76/4.63 = { by lemma 17 R->L }
% 32.76/4.63 join(zero, meet(join(complement(Y), complement(X)), join(complement(Y), complement(X))))
% 32.76/4.63 = { by lemma 30 }
% 32.76/4.63 join(zero, complement(join(complement(join(complement(Y), complement(X))), meet(Y, X))))
% 32.76/4.63 = { by lemma 25 }
% 32.76/4.63 complement(join(complement(join(complement(Y), complement(X))), meet(Y, X)))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 32.76/4.63 complement(join(meet(Y, X), meet(Y, X)))
% 32.76/4.63 = { by lemma 27 }
% 32.76/4.63 complement(join(meet(X, Y), meet(Y, X)))
% 32.76/4.63 = { by lemma 27 }
% 32.76/4.63 complement(join(meet(X, Y), meet(X, Y)))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 complement(join(meet(X, Y), complement(join(complement(X), complement(Y)))))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 complement(join(complement(join(complement(X), complement(Y))), complement(join(complement(X), complement(Y)))))
% 32.76/4.63 = { by lemma 22 }
% 32.76/4.63 complement(complement(join(complement(X), complement(Y))))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 32.76/4.63 complement(meet(X, Y))
% 32.76/4.63
% 32.76/4.63 Lemma 32: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 32.76/4.63 Proof:
% 32.76/4.63 complement(join(X, complement(Y)))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 complement(join(complement(Y), X))
% 32.76/4.63 = { by lemma 29 R->L }
% 32.76/4.63 complement(join(complement(Y), meet(X, top)))
% 32.76/4.63 = { by lemma 27 R->L }
% 32.76/4.63 complement(join(complement(Y), meet(top, X)))
% 32.76/4.63 = { by lemma 30 R->L }
% 32.76/4.63 meet(Y, join(complement(top), complement(X)))
% 32.76/4.63 = { by lemma 15 }
% 32.76/4.63 meet(Y, join(zero, complement(X)))
% 32.76/4.63 = { by lemma 25 }
% 32.76/4.63 meet(Y, complement(X))
% 32.76/4.63
% 32.76/4.63 Lemma 33: meet(complement(X), complement(Y)) = complement(join(X, Y)).
% 32.76/4.63 Proof:
% 32.76/4.63 meet(complement(X), complement(Y))
% 32.76/4.63 = { by lemma 27 }
% 32.76/4.63 meet(complement(Y), complement(X))
% 32.76/4.63 = { by lemma 25 R->L }
% 32.76/4.63 meet(join(zero, complement(Y)), complement(X))
% 32.76/4.63 = { by lemma 32 R->L }
% 32.76/4.63 complement(join(X, complement(join(zero, complement(Y)))))
% 32.76/4.63 = { by lemma 28 }
% 32.76/4.63 complement(join(X, meet(Y, top)))
% 32.76/4.63 = { by lemma 29 }
% 32.76/4.63 complement(join(X, Y))
% 32.76/4.63
% 32.76/4.63 Lemma 34: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 32.76/4.63 Proof:
% 32.76/4.63 converse(join(X, converse(Y)))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 converse(join(converse(Y), X))
% 32.76/4.63 = { by axiom 6 (converse_additivity_9) }
% 32.76/4.63 join(converse(converse(Y)), converse(X))
% 32.76/4.63 = { by axiom 3 (converse_idempotence_8) }
% 32.76/4.63 join(Y, converse(X))
% 32.76/4.63
% 32.76/4.63 Lemma 35: converse(composition(X, converse(Y))) = composition(Y, converse(X)).
% 32.76/4.63 Proof:
% 32.76/4.63 converse(composition(X, converse(Y)))
% 32.76/4.63 = { by axiom 8 (converse_multiplicativity_10) }
% 32.76/4.63 composition(converse(converse(Y)), converse(X))
% 32.76/4.63 = { by axiom 3 (converse_idempotence_8) }
% 32.76/4.63 composition(Y, converse(X))
% 32.76/4.63
% 32.76/4.63 Lemma 36: join(meet(X, Y), meet(X, complement(Y))) = X.
% 32.76/4.63 Proof:
% 32.76/4.63 join(meet(X, Y), meet(X, complement(Y)))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 join(meet(X, complement(Y)), meet(X, Y))
% 32.76/4.63 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 32.76/4.63 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 32.76/4.63 = { by lemma 16 }
% 32.76/4.63 X
% 32.76/4.63
% 32.76/4.63 Goal 1 (goals_15): join(composition(converse(sk1), sk1), one) = one.
% 32.76/4.63 Proof:
% 32.76/4.63 join(composition(converse(sk1), sk1), one)
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) }
% 32.76/4.63 join(one, composition(converse(sk1), sk1))
% 32.76/4.63 = { by lemma 26 R->L }
% 32.76/4.63 join(complement(complement(one)), composition(converse(sk1), sk1))
% 32.76/4.63 = { by lemma 24 R->L }
% 32.76/4.63 join(complement(complement(one)), join(composition(converse(sk1), sk1), zero))
% 32.76/4.63 = { by lemma 15 R->L }
% 32.76/4.63 join(complement(complement(one)), join(composition(converse(sk1), sk1), complement(top)))
% 32.76/4.63 = { by lemma 21 R->L }
% 32.76/4.63 join(complement(complement(one)), join(composition(converse(sk1), sk1), join(complement(top), composition(converse(sk1), complement(composition(sk1, top))))))
% 32.76/4.63 = { by lemma 15 }
% 32.76/4.63 join(complement(complement(one)), join(composition(converse(sk1), sk1), join(zero, composition(converse(sk1), complement(composition(sk1, top))))))
% 32.76/4.63 = { by lemma 25 }
% 32.76/4.63 join(complement(complement(one)), join(composition(converse(sk1), sk1), composition(converse(sk1), complement(composition(sk1, top)))))
% 32.76/4.63 = { by axiom 3 (converse_idempotence_8) R->L }
% 32.76/4.63 join(complement(complement(one)), join(composition(converse(sk1), sk1), composition(converse(sk1), converse(converse(complement(composition(sk1, top)))))))
% 32.76/4.63 = { by axiom 8 (converse_multiplicativity_10) R->L }
% 32.76/4.63 join(complement(complement(one)), join(composition(converse(sk1), sk1), converse(composition(converse(complement(composition(sk1, top))), sk1))))
% 32.76/4.63 = { by lemma 18 R->L }
% 32.76/4.63 join(complement(complement(one)), join(converse(composition(converse(sk1), sk1)), converse(composition(converse(complement(composition(sk1, top))), sk1))))
% 32.76/4.63 = { by axiom 6 (converse_additivity_9) R->L }
% 32.76/4.63 join(complement(complement(one)), converse(join(composition(converse(sk1), sk1), composition(converse(complement(composition(sk1, top))), sk1))))
% 32.76/4.63 = { by axiom 11 (composition_distributivity_7) R->L }
% 32.76/4.63 join(complement(complement(one)), converse(composition(join(converse(sk1), converse(complement(composition(sk1, top)))), sk1)))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) }
% 32.76/4.63 join(complement(complement(one)), converse(composition(join(converse(complement(composition(sk1, top))), converse(sk1)), sk1)))
% 32.76/4.63 = { by axiom 8 (converse_multiplicativity_10) }
% 32.76/4.63 join(complement(complement(one)), composition(converse(sk1), converse(join(converse(complement(composition(sk1, top))), converse(sk1)))))
% 32.76/4.63 = { by lemma 34 }
% 32.76/4.63 join(complement(complement(one)), composition(converse(sk1), join(sk1, converse(converse(complement(composition(sk1, top)))))))
% 32.76/4.63 = { by axiom 3 (converse_idempotence_8) }
% 32.76/4.63 join(complement(complement(one)), composition(converse(sk1), join(sk1, complement(composition(sk1, top)))))
% 32.76/4.63 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.63 join(complement(complement(one)), composition(converse(sk1), join(complement(composition(sk1, top)), sk1)))
% 32.76/4.63 = { by axiom 4 (def_top_12) }
% 32.76/4.63 join(complement(complement(one)), composition(converse(sk1), join(complement(composition(sk1, join(one, complement(one)))), sk1)))
% 32.76/4.63 = { by axiom 3 (converse_idempotence_8) R->L }
% 32.76/4.63 join(complement(complement(one)), composition(converse(sk1), join(complement(composition(sk1, join(one, converse(converse(complement(one)))))), sk1)))
% 32.76/4.63 = { by lemma 19 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(composition(sk1, join(composition(converse(one), one), converse(converse(complement(one)))))), sk1)))
% 32.76/4.64 = { by axiom 2 (composition_identity_6) }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(composition(sk1, join(converse(one), converse(converse(complement(one)))))), sk1)))
% 32.76/4.64 = { by axiom 6 (converse_additivity_9) R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(composition(sk1, converse(join(one, converse(complement(one)))))), sk1)))
% 32.76/4.64 = { by axiom 1 (maddux1_join_commutativity_1) }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(composition(sk1, converse(join(converse(complement(one)), one)))), sk1)))
% 32.76/4.64 = { by lemma 35 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(converse(composition(join(converse(complement(one)), one), converse(sk1)))), sk1)))
% 32.76/4.64 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(converse(composition(join(one, converse(complement(one))), converse(sk1)))), sk1)))
% 32.76/4.64 = { by axiom 11 (composition_distributivity_7) }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(converse(join(composition(one, converse(sk1)), composition(converse(complement(one)), converse(sk1))))), sk1)))
% 32.76/4.64 = { by lemma 20 }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(converse(join(converse(sk1), composition(converse(complement(one)), converse(sk1))))), sk1)))
% 32.76/4.64 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(converse(join(composition(converse(complement(one)), converse(sk1)), converse(sk1)))), sk1)))
% 32.76/4.64 = { by lemma 34 }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, converse(composition(converse(complement(one)), converse(sk1))))), sk1)))
% 32.76/4.64 = { by lemma 35 }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, converse(converse(complement(one)))))), sk1)))
% 32.76/4.64 = { by axiom 3 (converse_idempotence_8) }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, complement(one)))), sk1)))
% 32.76/4.64 = { by lemma 36 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, complement(one)))), join(meet(sk1, composition(sk1, complement(one))), meet(sk1, complement(composition(sk1, complement(one))))))))
% 32.76/4.64 = { by axiom 2 (composition_identity_6) R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, complement(one)))), join(meet(composition(sk1, one), composition(sk1, complement(one))), meet(sk1, complement(composition(sk1, complement(one))))))))
% 32.76/4.64 = { by axiom 12 (goals_14) }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, complement(one)))), join(zero, meet(sk1, complement(composition(sk1, complement(one))))))))
% 32.76/4.64 = { by lemma 25 }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, complement(one)))), meet(sk1, complement(composition(sk1, complement(one)))))))
% 32.76/4.64 = { by axiom 1 (maddux1_join_commutativity_1) R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(meet(sk1, complement(composition(sk1, complement(one)))), complement(join(sk1, composition(sk1, complement(one)))))))
% 32.76/4.64 = { by lemma 32 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(composition(sk1, complement(one)), complement(sk1))), complement(join(sk1, composition(sk1, complement(one)))))))
% 32.76/4.64 = { by lemma 31 }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), complement(meet(join(composition(sk1, complement(one)), complement(sk1)), join(sk1, composition(sk1, complement(one)))))))
% 32.76/4.64 = { by lemma 27 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), complement(meet(join(sk1, composition(sk1, complement(one))), join(composition(sk1, complement(one)), complement(sk1))))))
% 32.76/4.64 = { by lemma 31 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, complement(one)))), complement(join(composition(sk1, complement(one)), complement(sk1))))))
% 32.76/4.64 = { by lemma 33 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(complement(join(sk1, composition(sk1, complement(one)))), meet(complement(composition(sk1, complement(one))), complement(complement(sk1))))))
% 32.76/4.64 = { by lemma 33 R->L }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(meet(complement(sk1), complement(composition(sk1, complement(one)))), meet(complement(composition(sk1, complement(one))), complement(complement(sk1))))))
% 32.76/4.64 = { by lemma 27 }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), join(meet(complement(composition(sk1, complement(one))), complement(sk1)), meet(complement(composition(sk1, complement(one))), complement(complement(sk1))))))
% 32.76/4.64 = { by lemma 36 }
% 32.76/4.64 join(complement(complement(one)), composition(converse(sk1), complement(composition(sk1, complement(one)))))
% 32.76/4.64 = { by lemma 21 }
% 32.76/4.64 complement(complement(one))
% 32.76/4.64 = { by lemma 26 }
% 32.76/4.64 one
% 32.76/4.64 % SZS output end Proof
% 32.76/4.64
% 32.76/4.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------