TSTP Solution File: REL007+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL007+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 : n006.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 13:43:47 EDT 2023
% Result : Theorem 0.19s 0.65s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL007+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
% 0.13/0.34 % Computer : n006.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 21:37:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.65 Command-line arguments: --no-flatten-goal
% 0.19/0.65
% 0.19/0.65 % SZS status Theorem
% 0.19/0.65
% 0.19/0.67 % SZS output start Proof
% 0.19/0.67 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 0.19/0.67 Axiom 2 (composition_identity): composition(X, one) = X.
% 0.19/0.67 Axiom 3 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.19/0.67 Axiom 4 (def_zero): zero = meet(X, complement(X)).
% 0.19/0.67 Axiom 5 (goals): meet(x0, converse(x1)) = zero.
% 0.19/0.67 Axiom 6 (def_top): top = join(X, complement(X)).
% 0.19/0.67 Axiom 7 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.19/0.67 Axiom 8 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.19/0.67 Axiom 9 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.19/0.68 Axiom 10 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.19/0.68 Axiom 11 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.19/0.68 Axiom 12 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.19/0.68 Axiom 13 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.19/0.68
% 0.19/0.68 Lemma 14: complement(top) = zero.
% 0.19/0.68 Proof:
% 0.19/0.68 complement(top)
% 0.19/0.68 = { by axiom 6 (def_top) }
% 0.19/0.68 complement(join(complement(X), complement(complement(X))))
% 0.19/0.68 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.68 meet(X, complement(X))
% 0.19/0.68 = { by axiom 4 (def_zero) R->L }
% 0.19/0.68 zero
% 0.19/0.68
% 0.19/0.68 Lemma 15: join(X, join(Y, complement(X))) = join(Y, top).
% 0.19/0.68 Proof:
% 0.19/0.68 join(X, join(Y, complement(X)))
% 0.19/0.68 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.68 join(X, join(complement(X), Y))
% 0.19/0.68 = { by axiom 10 (maddux2_join_associativity) }
% 0.19/0.68 join(join(X, complement(X)), Y)
% 0.19/0.68 = { by axiom 6 (def_top) R->L }
% 0.19/0.68 join(top, Y)
% 0.19/0.68 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.68 join(Y, top)
% 0.19/0.68
% 0.19/0.68 Lemma 16: composition(converse(one), X) = X.
% 0.19/0.68 Proof:
% 0.19/0.68 composition(converse(one), X)
% 0.19/0.68 = { by axiom 1 (converse_idempotence) R->L }
% 0.19/0.68 composition(converse(one), converse(converse(X)))
% 0.19/0.68 = { by axiom 7 (converse_multiplicativity) R->L }
% 0.19/0.68 converse(composition(converse(X), one))
% 0.19/0.68 = { by axiom 2 (composition_identity) }
% 0.19/0.68 converse(converse(X))
% 0.19/0.68 = { by axiom 1 (converse_idempotence) }
% 0.19/0.68 X
% 0.19/0.68
% 0.19/0.68 Lemma 17: join(complement(X), complement(X)) = complement(X).
% 0.19/0.68 Proof:
% 0.19/0.68 join(complement(X), complement(X))
% 0.19/0.68 = { by lemma 16 R->L }
% 0.19/0.68 join(complement(X), composition(converse(one), complement(X)))
% 0.19/0.68 = { by lemma 16 R->L }
% 0.19/0.68 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 0.19/0.68 = { by axiom 2 (composition_identity) R->L }
% 0.19/0.68 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 0.19/0.68 = { by axiom 8 (composition_associativity) R->L }
% 0.19/0.68 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 0.19/0.68 = { by lemma 16 }
% 0.19/0.68 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.19/0.68 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.68 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.19/0.68 = { by axiom 12 (converse_cancellativity) }
% 0.19/0.68 complement(X)
% 0.19/0.68
% 0.19/0.68 Lemma 18: join(top, complement(X)) = top.
% 0.19/0.68 Proof:
% 0.19/0.68 join(top, complement(X))
% 0.19/0.68 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.68 join(complement(X), top)
% 0.19/0.68 = { by lemma 15 R->L }
% 0.19/0.68 join(X, join(complement(X), complement(X)))
% 0.19/0.68 = { by lemma 17 }
% 0.19/0.68 join(X, complement(X))
% 0.19/0.68 = { by axiom 6 (def_top) R->L }
% 0.19/0.68 top
% 0.19/0.68
% 0.19/0.68 Lemma 19: join(Y, top) = join(X, top).
% 0.19/0.68 Proof:
% 0.19/0.68 join(Y, top)
% 0.19/0.68 = { by lemma 18 R->L }
% 0.19/0.68 join(Y, join(top, complement(Y)))
% 0.19/0.68 = { by lemma 15 }
% 0.19/0.68 join(top, top)
% 0.19/0.68 = { by lemma 15 R->L }
% 0.19/0.68 join(X, join(top, complement(X)))
% 0.19/0.68 = { by lemma 18 }
% 0.19/0.68 join(X, top)
% 0.19/0.68
% 0.19/0.68 Lemma 20: join(X, top) = top.
% 0.19/0.68 Proof:
% 0.19/0.68 join(X, top)
% 0.19/0.68 = { by lemma 19 }
% 0.19/0.68 join(join(zero, zero), top)
% 0.19/0.68 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.68 join(top, join(zero, zero))
% 0.19/0.68 = { by lemma 14 R->L }
% 0.19/0.68 join(top, join(zero, complement(top)))
% 0.19/0.68 = { by lemma 14 R->L }
% 0.19/0.68 join(top, join(complement(top), complement(top)))
% 0.19/0.68 = { by lemma 17 }
% 0.19/0.68 join(top, complement(top))
% 0.19/0.68 = { by axiom 6 (def_top) R->L }
% 0.19/0.68 top
% 0.19/0.68
% 0.19/0.68 Lemma 21: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.19/0.68 Proof:
% 0.19/0.68 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.19/0.68 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.68 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.19/0.68 = { by axiom 13 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.19/0.68 X
% 0.19/0.68
% 0.19/0.68 Lemma 22: join(zero, meet(X, X)) = X.
% 0.19/0.69 Proof:
% 0.19/0.69 join(zero, meet(X, X))
% 0.19/0.69 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.69 join(zero, complement(join(complement(X), complement(X))))
% 0.19/0.69 = { by axiom 4 (def_zero) }
% 0.19/0.69 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.19/0.69 = { by lemma 21 }
% 0.19/0.69 X
% 0.19/0.69
% 0.19/0.69 Lemma 23: complement(complement(X)) = meet(X, X).
% 0.19/0.69 Proof:
% 0.19/0.69 complement(complement(X))
% 0.19/0.69 = { by lemma 17 R->L }
% 0.19/0.69 complement(join(complement(X), complement(X)))
% 0.19/0.69 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.69 meet(X, X)
% 0.19/0.69
% 0.19/0.69 Lemma 24: meet(Y, X) = meet(X, Y).
% 0.19/0.69 Proof:
% 0.19/0.69 meet(Y, X)
% 0.19/0.69 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.69 complement(join(complement(Y), complement(X)))
% 0.19/0.69 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.69 complement(join(complement(X), complement(Y)))
% 0.19/0.69 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.69 meet(X, Y)
% 0.19/0.69
% 0.19/0.69 Lemma 25: complement(join(zero, complement(X))) = meet(X, top).
% 0.19/0.69 Proof:
% 0.19/0.69 complement(join(zero, complement(X)))
% 0.19/0.69 = { by lemma 14 R->L }
% 0.19/0.69 complement(join(complement(top), complement(X)))
% 0.19/0.69 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.69 meet(top, X)
% 0.19/0.69 = { by lemma 24 R->L }
% 0.19/0.69 meet(X, top)
% 0.19/0.69
% 0.19/0.69 Lemma 26: join(X, join(complement(X), Y)) = top.
% 0.19/0.69 Proof:
% 0.19/0.69 join(X, join(complement(X), Y))
% 0.19/0.69 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.69 join(X, join(Y, complement(X)))
% 0.19/0.69 = { by lemma 15 }
% 0.19/0.69 join(Y, top)
% 0.19/0.69 = { by lemma 19 R->L }
% 0.19/0.69 join(Z, top)
% 0.19/0.69 = { by lemma 20 }
% 0.19/0.69 top
% 0.19/0.69
% 0.19/0.69 Lemma 27: join(X, complement(zero)) = top.
% 0.19/0.69 Proof:
% 0.19/0.69 join(X, complement(zero))
% 0.19/0.69 = { by lemma 22 R->L }
% 0.19/0.69 join(join(zero, meet(X, X)), complement(zero))
% 0.19/0.69 = { by axiom 10 (maddux2_join_associativity) R->L }
% 0.19/0.69 join(zero, join(meet(X, X), complement(zero)))
% 0.19/0.69 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.69 join(zero, join(complement(zero), meet(X, X)))
% 0.19/0.69 = { by lemma 26 }
% 0.19/0.69 top
% 0.19/0.69
% 0.19/0.69 Lemma 28: join(meet(X, Y), meet(X, complement(Y))) = X.
% 0.19/0.69 Proof:
% 0.19/0.69 join(meet(X, Y), meet(X, complement(Y)))
% 0.19/0.69 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.69 join(meet(X, complement(Y)), meet(X, Y))
% 0.19/0.69 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.69 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 0.19/0.69 = { by lemma 21 }
% 0.19/0.70 X
% 0.19/0.70
% 0.19/0.70 Lemma 29: join(zero, meet(X, top)) = X.
% 0.19/0.70 Proof:
% 0.19/0.70 join(zero, meet(X, top))
% 0.19/0.70 = { by lemma 27 R->L }
% 0.19/0.70 join(zero, meet(X, join(complement(zero), complement(zero))))
% 0.19/0.70 = { by lemma 17 }
% 0.19/0.70 join(zero, meet(X, complement(zero)))
% 0.19/0.70 = { by lemma 14 R->L }
% 0.19/0.70 join(complement(top), meet(X, complement(zero)))
% 0.19/0.70 = { by lemma 27 R->L }
% 0.19/0.70 join(complement(join(complement(X), complement(zero))), meet(X, complement(zero)))
% 0.19/0.70 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.70 join(meet(X, zero), meet(X, complement(zero)))
% 0.19/0.70 = { by lemma 28 }
% 0.19/0.70 X
% 0.19/0.70
% 0.19/0.70 Lemma 30: join(zero, complement(X)) = complement(X).
% 0.19/0.70 Proof:
% 0.19/0.70 join(zero, complement(X))
% 0.19/0.70 = { by lemma 22 R->L }
% 0.19/0.70 join(zero, complement(join(zero, meet(X, X))))
% 0.19/0.70 = { by lemma 23 R->L }
% 0.19/0.70 join(zero, complement(join(zero, complement(complement(X)))))
% 0.19/0.70 = { by lemma 25 }
% 0.19/0.70 join(zero, meet(complement(X), top))
% 0.19/0.70 = { by lemma 29 }
% 0.19/0.70 complement(X)
% 0.19/0.70
% 0.19/0.70 Lemma 31: complement(complement(X)) = X.
% 0.19/0.70 Proof:
% 0.19/0.70 complement(complement(X))
% 0.19/0.70 = { by lemma 30 R->L }
% 0.19/0.70 join(zero, complement(complement(X)))
% 0.19/0.70 = { by lemma 23 }
% 0.19/0.70 join(zero, meet(X, X))
% 0.19/0.70 = { by lemma 22 }
% 0.19/0.70 X
% 0.19/0.70
% 0.19/0.70 Lemma 32: join(X, zero) = X.
% 0.19/0.70 Proof:
% 0.19/0.70 join(X, zero)
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.70 join(zero, X)
% 0.19/0.70 = { by lemma 31 R->L }
% 0.19/0.70 join(zero, complement(complement(X)))
% 0.19/0.70 = { by lemma 23 }
% 0.19/0.70 join(zero, meet(X, X))
% 0.19/0.70 = { by lemma 22 }
% 0.19/0.70 X
% 0.19/0.70
% 0.19/0.70 Lemma 33: meet(X, top) = X.
% 0.19/0.70 Proof:
% 0.19/0.70 meet(X, top)
% 0.19/0.70 = { by lemma 25 R->L }
% 0.19/0.70 complement(join(zero, complement(X)))
% 0.19/0.70 = { by lemma 30 R->L }
% 0.19/0.70 join(zero, complement(join(zero, complement(X))))
% 0.19/0.70 = { by lemma 25 }
% 0.19/0.70 join(zero, meet(X, top))
% 0.19/0.70 = { by lemma 29 }
% 0.19/0.70 X
% 0.19/0.70
% 0.19/0.70 Lemma 34: meet(top, X) = X.
% 0.19/0.70 Proof:
% 0.19/0.70 meet(top, X)
% 0.19/0.70 = { by lemma 24 }
% 0.19/0.70 meet(X, top)
% 0.19/0.70 = { by lemma 33 }
% 0.19/0.70 X
% 0.19/0.70
% 0.19/0.70 Lemma 35: complement(join(zero, meet(X, Y))) = join(complement(X), complement(Y)).
% 0.19/0.70 Proof:
% 0.19/0.70 complement(join(zero, meet(X, Y)))
% 0.19/0.70 = { by lemma 24 }
% 0.19/0.70 complement(join(zero, meet(Y, X)))
% 0.19/0.70 = { by lemma 14 R->L }
% 0.19/0.70 complement(join(complement(top), meet(Y, X)))
% 0.19/0.70 = { by lemma 24 }
% 0.19/0.70 complement(join(complement(top), meet(X, Y)))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.70 complement(join(meet(X, Y), complement(top)))
% 0.19/0.70 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.70 complement(join(complement(join(complement(X), complement(Y))), complement(top)))
% 0.19/0.70 = { by axiom 11 (maddux4_definiton_of_meet) R->L }
% 0.19/0.70 meet(join(complement(X), complement(Y)), top)
% 0.19/0.70 = { by lemma 24 R->L }
% 0.19/0.70 meet(top, join(complement(X), complement(Y)))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.70 meet(top, join(complement(Y), complement(X)))
% 0.19/0.70 = { by lemma 34 }
% 0.19/0.70 join(complement(Y), complement(X))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.70 join(complement(X), complement(Y))
% 0.19/0.70
% 0.19/0.70 Lemma 36: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 0.19/0.70 Proof:
% 0.19/0.70 join(complement(X), complement(Y))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.70 join(complement(Y), complement(X))
% 0.19/0.70 = { by lemma 35 R->L }
% 0.19/0.70 complement(join(zero, meet(Y, X)))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.70 complement(join(meet(Y, X), zero))
% 0.19/0.70 = { by lemma 32 }
% 0.19/0.70 complement(meet(Y, X))
% 0.19/0.70 = { by lemma 24 R->L }
% 0.19/0.70 complement(meet(X, Y))
% 0.19/0.70
% 0.19/0.70 Lemma 37: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 0.19/0.70 Proof:
% 0.19/0.70 converse(join(X, converse(Y)))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.70 converse(join(converse(Y), X))
% 0.19/0.70 = { by axiom 9 (converse_additivity) }
% 0.19/0.70 join(converse(converse(Y)), converse(X))
% 0.19/0.70 = { by axiom 1 (converse_idempotence) }
% 0.19/0.70 join(Y, converse(X))
% 0.19/0.70
% 0.19/0.70 Lemma 38: join(complement(converse(X)), converse(join(X, Y))) = top.
% 0.19/0.70 Proof:
% 0.19/0.70 join(complement(converse(X)), converse(join(X, Y)))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.70 join(converse(join(X, Y)), complement(converse(X)))
% 0.19/0.70 = { by axiom 9 (converse_additivity) }
% 0.19/0.70 join(join(converse(X), converse(Y)), complement(converse(X)))
% 0.19/0.70 = { by axiom 10 (maddux2_join_associativity) R->L }
% 0.19/0.70 join(converse(X), join(converse(Y), complement(converse(X))))
% 0.19/0.70 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.70 join(converse(X), join(complement(converse(X)), converse(Y)))
% 0.19/0.70 = { by lemma 26 }
% 0.19/0.70 top
% 0.19/0.70
% 0.19/0.70 Goal 1 (goals_1): meet(converse(x0), x1) = zero.
% 0.19/0.70 Proof:
% 0.19/0.70 meet(converse(x0), x1)
% 0.19/0.70 = { by lemma 24 R->L }
% 0.19/0.70 meet(x1, converse(x0))
% 0.19/0.70 = { by lemma 34 R->L }
% 0.19/0.70 meet(x1, meet(top, converse(x0)))
% 0.19/0.70 = { by lemma 24 }
% 0.19/0.70 meet(x1, meet(converse(x0), top))
% 0.19/0.70 = { by lemma 31 R->L }
% 0.19/0.70 complement(complement(meet(x1, meet(converse(x0), top))))
% 0.19/0.70 = { by lemma 24 }
% 0.19/0.70 complement(complement(meet(x1, meet(top, converse(x0)))))
% 0.19/0.70 = { by axiom 11 (maddux4_definiton_of_meet) }
% 0.19/0.70 complement(complement(meet(x1, complement(join(complement(top), complement(converse(x0)))))))
% 0.19/0.71 = { by lemma 24 }
% 0.19/0.71 complement(complement(meet(complement(join(complement(top), complement(converse(x0)))), x1)))
% 0.19/0.71 = { by lemma 30 R->L }
% 0.19/0.71 complement(complement(meet(join(zero, complement(join(complement(top), complement(converse(x0))))), x1)))
% 0.19/0.71 = { by lemma 36 R->L }
% 0.19/0.71 complement(join(complement(join(zero, complement(join(complement(top), complement(converse(x0)))))), complement(x1)))
% 0.19/0.71 = { by lemma 25 }
% 0.19/0.71 complement(join(meet(join(complement(top), complement(converse(x0))), top), complement(x1)))
% 0.19/0.71 = { by lemma 33 }
% 0.19/0.71 complement(join(join(complement(top), complement(converse(x0))), complement(x1)))
% 0.19/0.71 = { by axiom 10 (maddux2_join_associativity) R->L }
% 0.19/0.71 complement(join(complement(top), join(complement(converse(x0)), complement(x1))))
% 0.19/0.71 = { by lemma 36 }
% 0.19/0.71 complement(join(complement(top), complement(meet(converse(x0), x1))))
% 0.19/0.71 = { by lemma 36 }
% 0.19/0.71 complement(complement(meet(top, meet(converse(x0), x1))))
% 0.19/0.71 = { by lemma 24 R->L }
% 0.19/0.71 complement(complement(meet(top, meet(x1, converse(x0)))))
% 0.19/0.71 = { by lemma 31 }
% 0.19/0.71 meet(top, meet(x1, converse(x0)))
% 0.19/0.71 = { by lemma 24 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), top)
% 0.19/0.71 = { by lemma 38 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(converse(meet(converse(complement(x1)), x0))), converse(join(meet(converse(complement(x1)), x0), complement(join(complement(converse(complement(x1))), x0))))))
% 0.19/0.71 = { by lemma 21 }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(converse(meet(converse(complement(x1)), x0))), converse(converse(complement(x1)))))
% 0.19/0.71 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(converse(converse(complement(x1))), complement(converse(meet(converse(complement(x1)), x0)))))
% 0.19/0.71 = { by axiom 1 (converse_idempotence) }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(meet(converse(complement(x1)), x0)))))
% 0.19/0.71 = { by lemma 24 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(meet(x0, converse(complement(x1)))))))
% 0.19/0.71 = { by lemma 32 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), zero)))))
% 0.19/0.71 = { by lemma 14 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(top))))))
% 0.19/0.71 = { by lemma 26 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(join(converse(X), join(complement(converse(X)), converse(complement(converse(complement(converse(X)))))))))))))
% 0.19/0.71 = { by lemma 37 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(join(converse(X), converse(join(complement(converse(complement(converse(X)))), converse(complement(converse(X))))))))))))
% 0.19/0.71 = { by axiom 3 (maddux1_join_commutativity) }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(join(converse(X), converse(join(converse(complement(converse(X))), complement(converse(complement(converse(X)))))))))))))
% 0.19/0.71 = { by axiom 6 (def_top) R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(join(converse(X), converse(top))))))))
% 0.19/0.71 = { by axiom 9 (converse_additivity) R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(X, top))))))))
% 0.19/0.71 = { by lemma 20 }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(top)))))))
% 0.19/0.71 = { by lemma 38 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(complement(converse(converse(x1))), converse(join(converse(x1), complement(x0)))))))))))
% 0.19/0.71 = { by axiom 3 (maddux1_join_commutativity) R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(complement(converse(converse(x1))), converse(join(complement(x0), converse(x1)))))))))))
% 0.19/0.71 = { by lemma 31 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(complement(converse(converse(x1))), converse(join(complement(x0), complement(complement(converse(x1)))))))))))))
% 0.19/0.71 = { by lemma 35 R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(complement(converse(converse(x1))), converse(complement(join(zero, meet(x0, complement(converse(x1))))))))))))))
% 0.19/0.71 = { by axiom 5 (goals) R->L }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(complement(converse(converse(x1))), converse(complement(join(meet(x0, converse(x1)), meet(x0, complement(converse(x1))))))))))))))
% 0.19/0.71 = { by lemma 28 }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(complement(converse(converse(x1))), converse(complement(x0))))))))))
% 0.19/0.71 = { by axiom 1 (converse_idempotence) }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(converse(join(complement(x1), converse(complement(x0))))))))))
% 0.19/0.71 = { by lemma 37 }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(join(meet(x0, converse(complement(x1))), complement(join(complement(x0), converse(complement(x1)))))))))
% 0.19/0.71 = { by lemma 21 }
% 0.19/0.71 meet(meet(x1, converse(x0)), join(complement(x1), complement(converse(x0))))
% 0.19/0.72 = { by lemma 36 }
% 0.19/0.72 meet(meet(x1, converse(x0)), complement(meet(x1, converse(x0))))
% 0.19/0.73 = { by axiom 4 (def_zero) R->L }
% 0.19/0.73 zero
% 0.19/0.73 % SZS output end Proof
% 0.19/0.73
% 0.19/0.73 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------