TSTP Solution File: REL024+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL024+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 : n025.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 13:44:04 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL024+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 21:11:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.63 Command-line arguments: --no-flatten-goal
% 0.19/0.63
% 0.19/0.63 % SZS status Theorem
% 0.19/0.63
% 0.19/0.65 % SZS output start Proof
% 0.19/0.65 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 0.19/0.65 Axiom 2 (composition_identity): composition(X, one) = X.
% 0.19/0.65 Axiom 3 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.19/0.65 Axiom 4 (def_zero): zero = meet(X, complement(X)).
% 0.19/0.65 Axiom 5 (def_top): top = join(X, complement(X)).
% 0.19/0.65 Axiom 6 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.19/0.65 Axiom 7 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.19/0.65 Axiom 8 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.19/0.65 Axiom 9 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.19/0.65 Axiom 10 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.19/0.65 Axiom 11 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.19/0.65 Axiom 12 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.19/0.65 Axiom 13 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.19/0.65
% 0.19/0.65 Lemma 14: complement(top) = zero.
% 0.19/0.65 Proof:
% 0.19/0.65 complement(top)
% 0.19/0.65 = { by axiom 5 (def_top) }
% 0.19/0.65 complement(join(complement(X), complement(complement(X))))
% 0.19/0.65 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.19/0.65 meet(X, complement(X))
% 0.19/0.65 = { by axiom 4 (def_zero) R->L }
% 0.19/0.65 zero
% 0.19/0.65
% 0.19/0.65 Lemma 15: join(X, join(Y, complement(X))) = join(Y, top).
% 0.19/0.65 Proof:
% 0.19/0.65 join(X, join(Y, complement(X)))
% 0.19/0.65 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.65 join(X, join(complement(X), Y))
% 0.19/0.65 = { by axiom 9 (maddux2_join_associativity) }
% 0.19/0.65 join(join(X, complement(X)), Y)
% 0.19/0.65 = { by axiom 5 (def_top) R->L }
% 0.19/0.65 join(top, Y)
% 0.19/0.65 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.65 join(Y, top)
% 0.19/0.65
% 0.19/0.65 Lemma 16: composition(converse(one), X) = X.
% 0.19/0.65 Proof:
% 0.19/0.65 composition(converse(one), X)
% 0.19/0.65 = { by axiom 1 (converse_idempotence) R->L }
% 0.19/0.65 composition(converse(one), converse(converse(X)))
% 0.19/0.65 = { by axiom 6 (converse_multiplicativity) R->L }
% 0.19/0.65 converse(composition(converse(X), one))
% 0.19/0.65 = { by axiom 2 (composition_identity) }
% 0.19/0.65 converse(converse(X))
% 0.19/0.65 = { by axiom 1 (converse_idempotence) }
% 0.19/0.65 X
% 0.19/0.65
% 0.19/0.65 Lemma 17: join(complement(X), complement(X)) = complement(X).
% 0.19/0.65 Proof:
% 0.19/0.65 join(complement(X), complement(X))
% 0.19/0.65 = { by lemma 16 R->L }
% 0.19/0.65 join(complement(X), composition(converse(one), complement(X)))
% 0.19/0.65 = { by lemma 16 R->L }
% 0.19/0.65 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.19/0.65 = { by axiom 2 (composition_identity) R->L }
% 0.19/0.65 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.19/0.65 = { by axiom 7 (composition_associativity) R->L }
% 0.19/0.65 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.19/0.65 = { by lemma 16 }
% 0.19/0.65 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.19/0.65 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.65 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.19/0.65 = { by axiom 12 (converse_cancellativity) }
% 0.19/0.65 complement(X)
% 0.19/0.65
% 0.19/0.65 Lemma 18: join(top, complement(X)) = top.
% 0.19/0.65 Proof:
% 0.19/0.65 join(top, complement(X))
% 0.19/0.65 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.65 join(complement(X), top)
% 0.19/0.65 = { by lemma 15 R->L }
% 0.19/0.65 join(X, join(complement(X), complement(X)))
% 0.19/0.65 = { by lemma 17 }
% 0.19/0.65 join(X, complement(X))
% 0.19/0.65 = { by axiom 5 (def_top) R->L }
% 0.19/0.65 top
% 0.19/0.65
% 0.19/0.65 Lemma 19: join(X, top) = top.
% 0.19/0.65 Proof:
% 0.19/0.65 join(X, top)
% 0.19/0.65 = { by lemma 18 R->L }
% 0.19/0.65 join(X, join(top, complement(X)))
% 0.19/0.65 = { by lemma 15 }
% 0.19/0.65 join(top, top)
% 0.19/0.65 = { by lemma 15 R->L }
% 0.19/0.65 join(join(zero, zero), join(top, complement(join(zero, zero))))
% 0.19/0.65 = { by lemma 18 }
% 0.19/0.65 join(join(zero, zero), top)
% 0.19/0.65 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.65 join(top, join(zero, zero))
% 0.19/0.65 = { by lemma 14 R->L }
% 0.19/0.65 join(top, join(zero, complement(top)))
% 0.19/0.65 = { by lemma 14 R->L }
% 0.19/0.65 join(top, join(complement(top), complement(top)))
% 0.19/0.65 = { by lemma 17 }
% 0.19/0.65 join(top, complement(top))
% 0.19/0.65 = { by axiom 5 (def_top) R->L }
% 0.19/0.65 top
% 0.19/0.65
% 0.19/0.65 Lemma 20: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.19/0.65 Proof:
% 0.19/0.65 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.19/0.65 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.19/0.65 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.19/0.65 = { by axiom 13 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.19/0.65 X
% 0.19/0.65
% 0.19/0.65 Lemma 21: join(zero, meet(X, X)) = X.
% 0.19/0.65 Proof:
% 0.19/0.65 join(zero, meet(X, X))
% 0.19/0.65 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.19/0.65 join(zero, complement(join(complement(X), complement(X))))
% 0.19/0.65 = { by axiom 4 (def_zero) }
% 0.19/0.65 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.19/0.65 = { by lemma 20 }
% 0.19/0.65 X
% 0.19/0.65
% 0.19/0.65 Lemma 22: complement(complement(X)) = meet(X, X).
% 0.19/0.65 Proof:
% 0.19/0.65 complement(complement(X))
% 0.19/0.65 = { by lemma 17 R->L }
% 0.19/0.65 complement(join(complement(X), complement(X)))
% 0.19/0.65 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.19/0.65 meet(X, X)
% 0.19/0.65
% 0.19/0.65 Lemma 23: meet(Y, X) = meet(X, Y).
% 0.19/0.65 Proof:
% 0.19/0.65 meet(Y, X)
% 0.19/0.65 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.19/0.65 complement(join(complement(Y), complement(X)))
% 0.19/0.65 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.65 complement(join(complement(X), complement(Y)))
% 0.19/0.65 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.19/0.65 meet(X, Y)
% 0.19/0.65
% 0.19/0.65 Lemma 24: complement(join(zero, complement(X))) = meet(X, top).
% 0.19/0.65 Proof:
% 0.19/0.65 complement(join(zero, complement(X)))
% 0.19/0.65 = { by lemma 14 R->L }
% 0.19/0.65 complement(join(complement(top), complement(X)))
% 0.19/0.65 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.19/0.65 meet(top, X)
% 0.19/0.65 = { by lemma 23 R->L }
% 0.19/0.65 meet(X, top)
% 0.19/0.65
% 0.19/0.65 Lemma 25: join(X, complement(zero)) = top.
% 0.19/0.65 Proof:
% 0.19/0.66 join(X, complement(zero))
% 0.19/0.66 = { by lemma 21 R->L }
% 0.19/0.66 join(join(zero, meet(X, X)), complement(zero))
% 0.19/0.66 = { by axiom 9 (maddux2_join_associativity) R->L }
% 0.19/0.66 join(zero, join(meet(X, X), complement(zero)))
% 0.19/0.66 = { by lemma 15 }
% 0.19/0.66 join(meet(X, X), top)
% 0.19/0.66 = { by lemma 19 }
% 0.19/0.66 top
% 0.19/0.66
% 0.19/0.66 Lemma 26: join(zero, meet(X, top)) = X.
% 0.19/0.66 Proof:
% 0.19/0.66 join(zero, meet(X, top))
% 0.19/0.66 = { by lemma 25 R->L }
% 0.19/0.66 join(zero, meet(X, join(complement(zero), complement(zero))))
% 0.19/0.66 = { by lemma 17 }
% 0.19/0.66 join(zero, meet(X, complement(zero)))
% 0.19/0.66 = { by lemma 14 R->L }
% 0.19/0.66 join(complement(top), meet(X, complement(zero)))
% 0.19/0.66 = { by lemma 25 R->L }
% 0.19/0.66 join(complement(join(complement(X), complement(zero))), meet(X, complement(zero)))
% 0.19/0.66 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.19/0.66 join(meet(X, zero), meet(X, complement(zero)))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.66 join(meet(X, complement(zero)), meet(X, zero))
% 0.19/0.66 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.19/0.66 join(meet(X, complement(zero)), complement(join(complement(X), complement(zero))))
% 0.19/0.66 = { by lemma 20 }
% 0.19/0.66 X
% 0.19/0.66
% 0.19/0.66 Lemma 27: join(zero, complement(X)) = complement(X).
% 0.19/0.66 Proof:
% 0.19/0.66 join(zero, complement(X))
% 0.19/0.66 = { by lemma 21 R->L }
% 0.19/0.66 join(zero, complement(join(zero, meet(X, X))))
% 0.19/0.66 = { by lemma 22 R->L }
% 0.19/0.66 join(zero, complement(join(zero, complement(complement(X)))))
% 0.19/0.66 = { by lemma 24 }
% 0.19/0.66 join(zero, meet(complement(X), top))
% 0.19/0.66 = { by lemma 26 }
% 0.19/0.66 complement(X)
% 0.19/0.66
% 0.19/0.66 Lemma 28: complement(complement(X)) = X.
% 0.19/0.66 Proof:
% 0.19/0.66 complement(complement(X))
% 0.19/0.66 = { by lemma 27 R->L }
% 0.19/0.66 join(zero, complement(complement(X)))
% 0.19/0.66 = { by lemma 22 }
% 0.19/0.66 join(zero, meet(X, X))
% 0.19/0.66 = { by lemma 21 }
% 0.19/0.66 X
% 0.19/0.66
% 0.19/0.66 Lemma 29: meet(X, top) = X.
% 0.19/0.66 Proof:
% 0.19/0.66 meet(X, top)
% 0.19/0.66 = { by lemma 24 R->L }
% 0.19/0.66 complement(join(zero, complement(X)))
% 0.19/0.66 = { by lemma 27 R->L }
% 0.19/0.66 join(zero, complement(join(zero, complement(X))))
% 0.19/0.66 = { by lemma 24 }
% 0.19/0.66 join(zero, meet(X, top))
% 0.19/0.66 = { by lemma 26 }
% 0.19/0.66 X
% 0.19/0.66
% 0.19/0.66 Lemma 30: complement(join(complement(X), meet(Y, Z))) = meet(X, join(complement(Y), complement(Z))).
% 0.19/0.66 Proof:
% 0.19/0.66 complement(join(complement(X), meet(Y, Z)))
% 0.19/0.66 = { by lemma 23 }
% 0.19/0.66 complement(join(complement(X), meet(Z, Y)))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.66 complement(join(meet(Z, Y), complement(X)))
% 0.19/0.66 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.19/0.66 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 0.19/0.66 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.19/0.66 meet(join(complement(Z), complement(Y)), X)
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 meet(X, join(complement(Z), complement(Y)))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.66 meet(X, join(complement(Y), complement(Z)))
% 0.19/0.66
% 0.19/0.66 Lemma 31: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 0.19/0.66 Proof:
% 0.19/0.66 join(complement(X), complement(Y))
% 0.19/0.66 = { by lemma 29 R->L }
% 0.19/0.66 meet(join(complement(X), complement(Y)), top)
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 meet(top, join(complement(X), complement(Y)))
% 0.19/0.66 = { by lemma 30 R->L }
% 0.19/0.66 complement(join(complement(top), meet(X, Y)))
% 0.19/0.66 = { by lemma 14 }
% 0.19/0.66 complement(join(zero, meet(X, Y)))
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 complement(join(zero, meet(Y, X)))
% 0.19/0.66 = { by lemma 28 R->L }
% 0.19/0.66 complement(join(zero, complement(complement(meet(Y, X)))))
% 0.19/0.66 = { by lemma 22 }
% 0.19/0.66 complement(join(zero, meet(meet(Y, X), meet(Y, X))))
% 0.19/0.66 = { by lemma 21 }
% 0.19/0.66 complement(meet(Y, X))
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 complement(meet(X, Y))
% 0.19/0.66
% 0.19/0.66 Lemma 32: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 0.19/0.66 Proof:
% 0.19/0.66 complement(meet(X, complement(Y)))
% 0.19/0.66 = { by lemma 23 }
% 0.19/0.66 complement(meet(complement(Y), X))
% 0.19/0.66 = { by lemma 27 R->L }
% 0.19/0.66 complement(meet(join(zero, complement(Y)), X))
% 0.19/0.66 = { by lemma 31 R->L }
% 0.19/0.66 join(complement(join(zero, complement(Y))), complement(X))
% 0.19/0.66 = { by lemma 24 }
% 0.19/0.66 join(meet(Y, top), complement(X))
% 0.19/0.66 = { by lemma 29 }
% 0.19/0.66 join(Y, complement(X))
% 0.19/0.66
% 0.19/0.66 Goal 1 (goals): join(composition(meet(x0, converse(x1)), meet(x1, x2)), composition(meet(x0, converse(x1)), x2)) = composition(meet(x0, converse(x1)), x2).
% 0.19/0.66 Proof:
% 0.19/0.66 join(composition(meet(x0, converse(x1)), meet(x1, x2)), composition(meet(x0, converse(x1)), x2))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.66 join(composition(meet(x0, converse(x1)), x2), composition(meet(x0, converse(x1)), meet(x1, x2)))
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 join(composition(meet(x0, converse(x1)), x2), composition(meet(x0, converse(x1)), meet(x2, x1)))
% 0.19/0.66 = { by axiom 1 (converse_idempotence) R->L }
% 0.19/0.66 join(composition(meet(x0, converse(x1)), x2), composition(meet(x0, converse(x1)), converse(converse(meet(x2, x1)))))
% 0.19/0.66 = { by axiom 1 (converse_idempotence) R->L }
% 0.19/0.66 converse(converse(join(composition(meet(x0, converse(x1)), x2), composition(meet(x0, converse(x1)), converse(converse(meet(x2, x1)))))))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.66 converse(converse(join(composition(meet(x0, converse(x1)), converse(converse(meet(x2, x1)))), composition(meet(x0, converse(x1)), x2))))
% 0.19/0.66 = { by axiom 8 (converse_additivity) }
% 0.19/0.66 converse(join(converse(composition(meet(x0, converse(x1)), converse(converse(meet(x2, x1))))), converse(composition(meet(x0, converse(x1)), x2))))
% 0.19/0.66 = { by axiom 6 (converse_multiplicativity) }
% 0.19/0.66 converse(join(composition(converse(converse(converse(meet(x2, x1)))), converse(meet(x0, converse(x1)))), converse(composition(meet(x0, converse(x1)), x2))))
% 0.19/0.66 = { by axiom 1 (converse_idempotence) }
% 0.19/0.66 converse(join(composition(converse(meet(x2, x1)), converse(meet(x0, converse(x1)))), converse(composition(meet(x0, converse(x1)), x2))))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.66 converse(join(converse(composition(meet(x0, converse(x1)), x2)), composition(converse(meet(x2, x1)), converse(meet(x0, converse(x1))))))
% 0.19/0.66 = { by axiom 6 (converse_multiplicativity) }
% 0.19/0.66 converse(join(composition(converse(x2), converse(meet(x0, converse(x1)))), composition(converse(meet(x2, x1)), converse(meet(x0, converse(x1))))))
% 0.19/0.66 = { by axiom 11 (composition_distributivity) R->L }
% 0.19/0.66 converse(composition(join(converse(x2), converse(meet(x2, x1))), converse(meet(x0, converse(x1)))))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.66 converse(composition(join(converse(meet(x2, x1)), converse(x2)), converse(meet(x0, converse(x1)))))
% 0.19/0.66 = { by axiom 1 (converse_idempotence) R->L }
% 0.19/0.66 converse(composition(join(converse(converse(converse(meet(x2, x1)))), converse(x2)), converse(meet(x0, converse(x1)))))
% 0.19/0.66 = { by axiom 8 (converse_additivity) R->L }
% 0.19/0.66 converse(composition(converse(join(converse(converse(meet(x2, x1))), x2)), converse(meet(x0, converse(x1)))))
% 0.19/0.66 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.66 converse(composition(converse(join(x2, converse(converse(meet(x2, x1))))), converse(meet(x0, converse(x1)))))
% 0.19/0.66 = { by axiom 6 (converse_multiplicativity) R->L }
% 0.19/0.66 converse(converse(composition(meet(x0, converse(x1)), join(x2, converse(converse(meet(x2, x1)))))))
% 0.19/0.66 = { by axiom 1 (converse_idempotence) }
% 0.19/0.66 composition(meet(x0, converse(x1)), join(x2, converse(converse(meet(x2, x1)))))
% 0.19/0.66 = { by axiom 1 (converse_idempotence) }
% 0.19/0.66 composition(meet(x0, converse(x1)), join(x2, meet(x2, x1)))
% 0.19/0.66 = { by axiom 10 (maddux4_definiton_of_meet) }
% 0.19/0.66 composition(meet(x0, converse(x1)), join(x2, complement(join(complement(x2), complement(x1)))))
% 0.19/0.66 = { by lemma 32 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(meet(join(complement(x2), complement(x1)), complement(x2))))
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(meet(complement(x2), join(complement(x2), complement(x1)))))
% 0.19/0.66 = { by lemma 32 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(meet(complement(x2), complement(meet(x1, complement(complement(x2)))))))
% 0.19/0.66 = { by lemma 31 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(meet(complement(x2), join(complement(x1), complement(complement(complement(x2)))))))
% 0.19/0.66 = { by lemma 30 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(complement(join(complement(complement(x2)), meet(x1, complement(complement(x2)))))))
% 0.19/0.66 = { by lemma 27 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(zero, complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by lemma 14 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(complement(top), complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by lemma 19 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(complement(join(complement(x1), top)), complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by lemma 15 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(complement(join(complement(complement(x2)), join(complement(x1), complement(complement(complement(x2)))))), complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by lemma 31 }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(complement(join(complement(complement(x2)), complement(meet(x1, complement(complement(x2)))))), complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(complement(join(complement(complement(x2)), complement(meet(complement(complement(x2)), x1)))), complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by axiom 10 (maddux4_definiton_of_meet) R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(meet(complement(x2), meet(complement(complement(x2)), x1)), complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by lemma 23 R->L }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(join(meet(complement(x2), meet(x1, complement(complement(x2)))), complement(join(complement(complement(x2)), meet(x1, complement(complement(x2))))))))
% 0.19/0.66 = { by lemma 20 }
% 0.19/0.66 composition(meet(x0, converse(x1)), complement(complement(x2)))
% 0.19/0.66 = { by lemma 28 }
% 0.19/0.66 composition(meet(x0, converse(x1)), x2)
% 0.19/0.66 % SZS output end Proof
% 0.19/0.66
% 0.19/0.66 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------