TSTP Solution File: REL027-3 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL027-3 : 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 : n005.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 13:44:09 EDT 2023
% Result : Unsatisfiable 19.12s 2.89s
% Output : Proof 19.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL027-3 : 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
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Fri Aug 25 19:03:08 EDT 2023
% 0.19/0.34 % CPUTime :
% 19.12/2.89 Command-line arguments: --no-flatten-goal
% 19.12/2.89
% 19.12/2.89 % SZS status Unsatisfiable
% 19.12/2.89
% 19.84/2.91 % SZS output start Proof
% 19.84/2.91 Axiom 1 (converse_idempotence_8): converse(converse(X)) = X.
% 19.84/2.91 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 19.84/2.91 Axiom 3 (goals_17): join(sk1, one) = one.
% 19.84/2.91 Axiom 4 (composition_identity_6): composition(X, one) = X.
% 19.84/2.91 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 19.84/2.91 Axiom 6 (def_top_12): top = join(X, complement(X)).
% 19.84/2.91 Axiom 7 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 19.84/2.91 Axiom 8 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 19.84/2.91 Axiom 9 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 19.84/2.91 Axiom 10 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 19.84/2.91 Axiom 11 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 19.84/2.91 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 19.84/2.91 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 19.84/2.91 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 19.84/2.91
% 19.84/2.91 Lemma 15: complement(top) = zero.
% 19.84/2.91 Proof:
% 19.84/2.91 complement(top)
% 19.84/2.91 = { by axiom 6 (def_top_12) }
% 19.84/2.91 complement(join(complement(X), complement(complement(X))))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 19.84/2.91 meet(X, complement(X))
% 19.84/2.91 = { by axiom 5 (def_zero_13) R->L }
% 19.84/2.91 zero
% 19.84/2.91
% 19.84/2.91 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 19.84/2.91 Proof:
% 19.84/2.91 join(X, join(Y, complement(X)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(X, join(complement(X), Y))
% 19.84/2.91 = { by axiom 8 (maddux2_join_associativity_2) }
% 19.84/2.91 join(join(X, complement(X)), Y)
% 19.84/2.91 = { by axiom 6 (def_top_12) R->L }
% 19.84/2.91 join(top, Y)
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) }
% 19.84/2.91 join(Y, top)
% 19.84/2.91
% 19.84/2.91 Lemma 17: composition(converse(one), X) = X.
% 19.84/2.91 Proof:
% 19.84/2.91 composition(converse(one), X)
% 19.84/2.91 = { by axiom 1 (converse_idempotence_8) R->L }
% 19.84/2.91 composition(converse(one), converse(converse(X)))
% 19.84/2.91 = { by axiom 9 (converse_multiplicativity_10) R->L }
% 19.84/2.91 converse(composition(converse(X), one))
% 19.84/2.91 = { by axiom 4 (composition_identity_6) }
% 19.84/2.91 converse(converse(X))
% 19.84/2.91 = { by axiom 1 (converse_idempotence_8) }
% 19.84/2.91 X
% 19.84/2.91
% 19.84/2.91 Lemma 18: composition(one, X) = X.
% 19.84/2.91 Proof:
% 19.84/2.91 composition(one, X)
% 19.84/2.91 = { by lemma 17 R->L }
% 19.84/2.91 composition(converse(one), composition(one, X))
% 19.84/2.91 = { by axiom 10 (composition_associativity_5) }
% 19.84/2.91 composition(composition(converse(one), one), X)
% 19.84/2.91 = { by axiom 4 (composition_identity_6) }
% 19.84/2.91 composition(converse(one), X)
% 19.84/2.91 = { by lemma 17 }
% 19.84/2.91 X
% 19.84/2.91
% 19.84/2.91 Lemma 19: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 19.84/2.91 Proof:
% 19.84/2.91 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 19.84/2.91 = { by axiom 13 (converse_cancellativity_11) }
% 19.84/2.91 complement(X)
% 19.84/2.91
% 19.84/2.91 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 19.84/2.91 Proof:
% 19.84/2.91 join(complement(X), complement(X))
% 19.84/2.91 = { by lemma 17 R->L }
% 19.84/2.91 join(complement(X), composition(converse(one), complement(X)))
% 19.84/2.91 = { by lemma 18 R->L }
% 19.84/2.91 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 19.84/2.91 = { by lemma 19 }
% 19.84/2.91 complement(X)
% 19.84/2.91
% 19.84/2.91 Lemma 21: join(top, complement(X)) = top.
% 19.84/2.91 Proof:
% 19.84/2.91 join(top, complement(X))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(complement(X), top)
% 19.84/2.91 = { by lemma 16 R->L }
% 19.84/2.91 join(X, join(complement(X), complement(X)))
% 19.84/2.91 = { by lemma 20 }
% 19.84/2.91 join(X, complement(X))
% 19.84/2.91 = { by axiom 6 (def_top_12) R->L }
% 19.84/2.91 top
% 19.84/2.91
% 19.84/2.91 Lemma 22: join(Y, top) = join(X, top).
% 19.84/2.91 Proof:
% 19.84/2.91 join(Y, top)
% 19.84/2.91 = { by lemma 21 R->L }
% 19.84/2.91 join(Y, join(top, complement(Y)))
% 19.84/2.91 = { by lemma 16 }
% 19.84/2.91 join(top, top)
% 19.84/2.91 = { by lemma 16 R->L }
% 19.84/2.91 join(X, join(top, complement(X)))
% 19.84/2.91 = { by lemma 21 }
% 19.84/2.91 join(X, top)
% 19.84/2.91
% 19.84/2.91 Lemma 23: join(X, top) = top.
% 19.84/2.91 Proof:
% 19.84/2.91 join(X, top)
% 19.84/2.91 = { by lemma 22 }
% 19.84/2.91 join(zero, top)
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(top, zero)
% 19.84/2.91 = { by lemma 15 R->L }
% 19.84/2.91 join(top, complement(top))
% 19.84/2.91 = { by axiom 6 (def_top_12) R->L }
% 19.84/2.91 top
% 19.84/2.91
% 19.84/2.91 Lemma 24: meet(Y, X) = meet(X, Y).
% 19.84/2.91 Proof:
% 19.84/2.91 meet(Y, X)
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 19.84/2.91 complement(join(complement(Y), complement(X)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 complement(join(complement(X), complement(Y)))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 19.84/2.91 meet(X, Y)
% 19.84/2.91
% 19.84/2.91 Lemma 25: complement(join(zero, complement(X))) = meet(X, top).
% 19.84/2.91 Proof:
% 19.84/2.91 complement(join(zero, complement(X)))
% 19.84/2.91 = { by lemma 15 R->L }
% 19.84/2.91 complement(join(complement(top), complement(X)))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 19.84/2.91 meet(top, X)
% 19.84/2.91 = { by lemma 24 R->L }
% 19.84/2.91 meet(X, top)
% 19.84/2.91
% 19.84/2.91 Lemma 26: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 19.84/2.91 Proof:
% 19.84/2.91 join(meet(X, Y), complement(join(complement(X), Y)))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 19.84/2.91 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 19.84/2.91 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 19.84/2.91 X
% 19.84/2.91
% 19.84/2.91 Lemma 27: join(zero, join(X, complement(complement(Y)))) = join(X, Y).
% 19.84/2.91 Proof:
% 19.84/2.91 join(zero, join(X, complement(complement(Y))))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(zero, join(complement(complement(Y)), X))
% 19.84/2.91 = { by lemma 20 R->L }
% 19.84/2.91 join(zero, join(complement(join(complement(Y), complement(Y))), X))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 19.84/2.91 join(zero, join(meet(Y, Y), X))
% 19.84/2.91 = { by axiom 8 (maddux2_join_associativity_2) }
% 19.84/2.91 join(join(zero, meet(Y, Y)), X)
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 19.84/2.91 join(join(zero, complement(join(complement(Y), complement(Y)))), X)
% 19.84/2.91 = { by axiom 5 (def_zero_13) }
% 19.84/2.91 join(join(meet(Y, complement(Y)), complement(join(complement(Y), complement(Y)))), X)
% 19.84/2.91 = { by lemma 26 }
% 19.84/2.91 join(Y, X)
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) }
% 19.84/2.91 join(X, Y)
% 19.84/2.91
% 19.84/2.91 Lemma 28: join(zero, complement(X)) = complement(X).
% 19.84/2.91 Proof:
% 19.84/2.91 join(zero, complement(X))
% 19.84/2.91 = { by lemma 26 R->L }
% 19.84/2.91 join(zero, join(meet(complement(X), complement(complement(X))), complement(join(complement(complement(X)), complement(complement(X))))))
% 19.84/2.91 = { by lemma 20 }
% 19.84/2.91 join(zero, join(meet(complement(X), complement(complement(X))), complement(complement(complement(X)))))
% 19.84/2.91 = { by axiom 5 (def_zero_13) R->L }
% 19.84/2.91 join(zero, join(zero, complement(complement(complement(X)))))
% 19.84/2.91 = { by lemma 20 R->L }
% 19.84/2.91 join(zero, join(zero, join(complement(complement(complement(X))), complement(complement(complement(X))))))
% 19.84/2.91 = { by lemma 27 }
% 19.84/2.91 join(zero, join(complement(complement(complement(X))), complement(X)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) }
% 19.84/2.91 join(zero, join(complement(X), complement(complement(complement(X)))))
% 19.84/2.91 = { by lemma 27 }
% 19.84/2.91 join(complement(X), complement(X))
% 19.84/2.91 = { by lemma 20 }
% 19.84/2.91 complement(X)
% 19.84/2.91
% 19.84/2.91 Lemma 29: join(X, join(complement(X), Y)) = top.
% 19.84/2.91 Proof:
% 19.84/2.91 join(X, join(complement(X), Y))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(X, join(Y, complement(X)))
% 19.84/2.91 = { by lemma 16 }
% 19.84/2.91 join(Y, top)
% 19.84/2.91 = { by lemma 22 R->L }
% 19.84/2.91 join(Z, top)
% 19.84/2.91 = { by lemma 23 }
% 19.84/2.91 top
% 19.84/2.91
% 19.84/2.91 Lemma 30: join(X, complement(zero)) = top.
% 19.84/2.91 Proof:
% 19.84/2.91 join(X, complement(zero))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(complement(zero), X)
% 19.84/2.91 = { by lemma 27 R->L }
% 19.84/2.91 join(zero, join(complement(zero), complement(complement(X))))
% 19.84/2.91 = { by lemma 29 }
% 19.84/2.91 top
% 19.84/2.91
% 19.84/2.91 Lemma 31: meet(X, top) = X.
% 19.84/2.91 Proof:
% 19.84/2.91 meet(X, top)
% 19.84/2.91 = { by lemma 25 R->L }
% 19.84/2.91 complement(join(zero, complement(X)))
% 19.84/2.91 = { by lemma 28 R->L }
% 19.84/2.91 join(zero, complement(join(zero, complement(X))))
% 19.84/2.91 = { by lemma 25 }
% 19.84/2.91 join(zero, meet(X, top))
% 19.84/2.91 = { by lemma 30 R->L }
% 19.84/2.91 join(zero, meet(X, join(complement(zero), complement(zero))))
% 19.84/2.91 = { by lemma 20 }
% 19.84/2.91 join(zero, meet(X, complement(zero)))
% 19.84/2.91 = { by lemma 15 R->L }
% 19.84/2.91 join(complement(top), meet(X, complement(zero)))
% 19.84/2.91 = { by lemma 30 R->L }
% 19.84/2.91 join(complement(join(complement(X), complement(zero))), meet(X, complement(zero)))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 19.84/2.91 join(meet(X, zero), meet(X, complement(zero)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 join(meet(X, complement(zero)), meet(X, zero))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 19.84/2.91 join(meet(X, complement(zero)), complement(join(complement(X), complement(zero))))
% 19.84/2.91 = { by lemma 26 }
% 19.84/2.91 X
% 19.84/2.91
% 19.84/2.91 Lemma 32: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 19.84/2.91 Proof:
% 19.84/2.91 complement(join(X, complement(Y)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 complement(join(complement(Y), X))
% 19.84/2.91 = { by lemma 31 R->L }
% 19.84/2.91 complement(join(complement(Y), meet(X, top)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 complement(join(meet(X, top), complement(Y)))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 19.84/2.91 complement(join(complement(join(complement(X), complement(top))), complement(Y)))
% 19.84/2.91 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 19.84/2.91 meet(join(complement(X), complement(top)), Y)
% 19.84/2.91 = { by lemma 24 R->L }
% 19.84/2.91 meet(Y, join(complement(X), complement(top)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) }
% 19.84/2.91 meet(Y, join(complement(top), complement(X)))
% 19.84/2.91 = { by lemma 15 }
% 19.84/2.91 meet(Y, join(zero, complement(X)))
% 19.84/2.91 = { by lemma 28 }
% 19.84/2.91 meet(Y, complement(X))
% 19.84/2.91
% 19.84/2.91 Lemma 33: composition(join(X, one), Y) = join(Y, composition(X, Y)).
% 19.84/2.91 Proof:
% 19.84/2.91 composition(join(X, one), Y)
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 composition(join(one, X), Y)
% 19.84/2.91 = { by axiom 12 (composition_distributivity_7) }
% 19.84/2.91 join(composition(one, Y), composition(X, Y))
% 19.84/2.91 = { by lemma 18 }
% 19.84/2.91 join(Y, composition(X, Y))
% 19.84/2.91
% 19.84/2.91 Lemma 34: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 19.84/2.91 Proof:
% 19.84/2.91 converse(join(X, converse(Y)))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 converse(join(converse(Y), X))
% 19.84/2.91 = { by axiom 7 (converse_additivity_9) }
% 19.84/2.91 join(converse(converse(Y)), converse(X))
% 19.84/2.91 = { by axiom 1 (converse_idempotence_8) }
% 19.84/2.91 join(Y, converse(X))
% 19.84/2.91
% 19.84/2.91 Lemma 35: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 19.84/2.91 Proof:
% 19.84/2.91 converse(join(converse(X), Y))
% 19.84/2.91 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.91 converse(join(Y, converse(X)))
% 19.84/2.91 = { by lemma 34 }
% 19.84/2.91 join(X, converse(Y))
% 19.84/2.91
% 19.84/2.91 Lemma 36: converse(composition(X, converse(Y))) = composition(Y, converse(X)).
% 19.84/2.91 Proof:
% 19.84/2.91 converse(composition(X, converse(Y)))
% 19.84/2.91 = { by axiom 9 (converse_multiplicativity_10) }
% 19.84/2.91 composition(converse(converse(Y)), converse(X))
% 19.84/2.91 = { by axiom 1 (converse_idempotence_8) }
% 19.84/2.91 composition(Y, converse(X))
% 19.84/2.91
% 19.84/2.91 Lemma 37: join(complement(one), converse(complement(one))) = complement(one).
% 19.84/2.91 Proof:
% 19.84/2.91 join(complement(one), converse(complement(one)))
% 19.84/2.92 = { by axiom 4 (composition_identity_6) R->L }
% 19.84/2.92 join(complement(one), composition(converse(complement(one)), one))
% 19.84/2.92 = { by lemma 31 R->L }
% 19.84/2.92 join(complement(one), composition(converse(complement(one)), meet(one, top)))
% 19.84/2.92 = { by lemma 28 R->L }
% 19.84/2.92 join(complement(one), composition(converse(join(zero, complement(one))), meet(one, top)))
% 19.84/2.92 = { by lemma 25 R->L }
% 19.84/2.92 join(complement(one), composition(converse(join(zero, complement(one))), complement(join(zero, complement(one)))))
% 19.84/2.92 = { by axiom 4 (composition_identity_6) R->L }
% 19.84/2.92 join(complement(one), composition(converse(join(zero, complement(one))), complement(composition(join(zero, complement(one)), one))))
% 19.84/2.92 = { by lemma 19 }
% 19.84/2.92 complement(one)
% 19.84/2.92
% 19.84/2.92 Goal 1 (goals_18): meet(complement(composition(sk1, top)), one) = meet(complement(sk1), one).
% 19.84/2.92 Proof:
% 19.84/2.92 meet(complement(composition(sk1, top)), one)
% 19.84/2.92 = { by lemma 24 R->L }
% 19.84/2.92 meet(one, complement(composition(sk1, top)))
% 19.84/2.92 = { by lemma 32 R->L }
% 19.84/2.92 complement(join(composition(sk1, top), complement(one)))
% 19.84/2.92 = { by axiom 2 (maddux1_join_commutativity_1) }
% 19.84/2.92 complement(join(complement(one), composition(sk1, top)))
% 19.84/2.92 = { by lemma 29 R->L }
% 19.84/2.92 complement(join(complement(one), composition(sk1, join(converse(X), join(complement(converse(X)), converse(complement(converse(complement(converse(X))))))))))
% 19.84/2.92 = { by lemma 35 R->L }
% 19.84/2.92 complement(join(complement(one), composition(sk1, join(converse(X), converse(join(converse(complement(converse(X))), complement(converse(complement(converse(X))))))))))
% 19.84/2.92 = { by axiom 6 (def_top_12) R->L }
% 19.84/2.92 complement(join(complement(one), composition(sk1, join(converse(X), converse(top)))))
% 19.84/2.92 = { by axiom 7 (converse_additivity_9) R->L }
% 19.84/2.92 complement(join(complement(one), composition(sk1, converse(join(X, top)))))
% 19.84/2.92 = { by lemma 23 }
% 19.84/2.92 complement(join(complement(one), composition(sk1, converse(top))))
% 19.84/2.92 = { by axiom 6 (def_top_12) }
% 19.84/2.92 complement(join(complement(one), composition(sk1, converse(join(one, complement(one))))))
% 19.84/2.92 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.92 complement(join(complement(one), composition(sk1, converse(join(complement(one), one)))))
% 19.84/2.92 = { by lemma 36 R->L }
% 19.84/2.92 complement(join(complement(one), converse(composition(join(complement(one), one), converse(sk1)))))
% 19.84/2.92 = { by lemma 33 }
% 19.84/2.92 complement(join(complement(one), converse(join(converse(sk1), composition(complement(one), converse(sk1))))))
% 19.84/2.92 = { by lemma 35 }
% 19.84/2.92 complement(join(complement(one), join(sk1, converse(composition(complement(one), converse(sk1))))))
% 19.84/2.92 = { by lemma 36 }
% 19.84/2.92 complement(join(complement(one), join(sk1, composition(sk1, converse(complement(one))))))
% 19.84/2.92 = { by lemma 37 R->L }
% 19.84/2.92 complement(join(complement(one), join(sk1, composition(sk1, converse(join(complement(one), converse(complement(one))))))))
% 19.84/2.92 = { by lemma 34 }
% 19.84/2.92 complement(join(complement(one), join(sk1, composition(sk1, join(complement(one), converse(complement(one)))))))
% 19.84/2.92 = { by lemma 37 }
% 19.84/2.92 complement(join(complement(one), join(sk1, composition(sk1, complement(one)))))
% 19.84/2.92 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 19.84/2.92 complement(join(complement(one), join(composition(sk1, complement(one)), sk1)))
% 19.84/2.92 = { by axiom 8 (maddux2_join_associativity_2) }
% 19.84/2.92 complement(join(join(complement(one), composition(sk1, complement(one))), sk1))
% 19.84/2.92 = { by lemma 33 R->L }
% 19.84/2.92 complement(join(composition(join(sk1, one), complement(one)), sk1))
% 19.84/2.92 = { by axiom 3 (goals_17) }
% 19.84/2.92 complement(join(composition(one, complement(one)), sk1))
% 19.84/2.92 = { by lemma 18 }
% 19.84/2.92 complement(join(complement(one), sk1))
% 19.84/2.92 = { by axiom 2 (maddux1_join_commutativity_1) }
% 19.84/2.92 complement(join(sk1, complement(one)))
% 19.84/2.92 = { by lemma 32 }
% 19.84/2.92 meet(one, complement(sk1))
% 19.84/2.92 = { by lemma 24 }
% 19.84/2.92 meet(complement(sk1), one)
% 19.84/2.92 % SZS output end Proof
% 19.84/2.92
% 19.84/2.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------