TSTP Solution File: REL019+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL019+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 : n027.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 13:44:00 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : REL019+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.36 % Computer : n027.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Fri Aug 25 20:29:34 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.21/0.53 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.53
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53
% 0.21/0.56 % SZS output start Proof
% 0.21/0.56 Axiom 1 (composition_identity): composition(X, one) = X.
% 0.21/0.56 Axiom 2 (goals): composition(x1, top) = x1.
% 0.21/0.56 Axiom 3 (goals_1): composition(x0, top) = x0.
% 0.21/0.56 Axiom 4 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.21/0.56 Axiom 5 (converse_idempotence): converse(converse(X)) = X.
% 0.21/0.56 Axiom 6 (def_zero): zero = meet(X, complement(X)).
% 0.21/0.56 Axiom 7 (def_top): top = join(X, complement(X)).
% 0.21/0.56 Axiom 8 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.21/0.56 Axiom 9 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.21/0.56 Axiom 10 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.21/0.56 Axiom 11 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.21/0.56 Axiom 12 (maddux4_definiton_of_meet): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.21/0.56 Axiom 13 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.21/0.56 Axiom 14 (converse_cancellativity): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 0.21/0.56 Axiom 15 (maddux3_a_kind_of_de_Morgan): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 0.21/0.56
% 0.21/0.56 Lemma 16: complement(top) = zero.
% 0.21/0.56 Proof:
% 0.21/0.56 complement(top)
% 0.21/0.56 = { by axiom 7 (def_top) }
% 0.21/0.56 complement(join(complement(X), complement(complement(X))))
% 0.21/0.56 = { by axiom 12 (maddux4_definiton_of_meet) R->L }
% 0.21/0.56 meet(X, complement(X))
% 0.21/0.56 = { by axiom 6 (def_zero) R->L }
% 0.21/0.56 zero
% 0.21/0.56
% 0.21/0.56 Lemma 17: join(X, join(Y, complement(X))) = join(Y, top).
% 0.21/0.56 Proof:
% 0.21/0.56 join(X, join(Y, complement(X)))
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.56 join(X, join(complement(X), Y))
% 0.21/0.56 = { by axiom 11 (maddux2_join_associativity) }
% 0.21/0.56 join(join(X, complement(X)), Y)
% 0.21/0.56 = { by axiom 7 (def_top) R->L }
% 0.21/0.56 join(top, Y)
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) }
% 0.21/0.56 join(Y, top)
% 0.21/0.56
% 0.21/0.56 Lemma 18: composition(converse(one), X) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 composition(converse(one), X)
% 0.21/0.56 = { by axiom 5 (converse_idempotence) R->L }
% 0.21/0.56 composition(converse(one), converse(converse(X)))
% 0.21/0.56 = { by axiom 8 (converse_multiplicativity) R->L }
% 0.21/0.56 converse(composition(converse(X), one))
% 0.21/0.56 = { by axiom 1 (composition_identity) }
% 0.21/0.56 converse(converse(X))
% 0.21/0.56 = { by axiom 5 (converse_idempotence) }
% 0.21/0.56 X
% 0.21/0.56
% 0.21/0.56 Lemma 19: composition(one, X) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 composition(one, X)
% 0.21/0.56 = { by lemma 18 R->L }
% 0.21/0.56 composition(converse(one), composition(one, X))
% 0.21/0.56 = { by axiom 9 (composition_associativity) }
% 0.21/0.56 composition(composition(converse(one), one), X)
% 0.21/0.56 = { by axiom 1 (composition_identity) }
% 0.21/0.56 composition(converse(one), X)
% 0.21/0.56 = { by lemma 18 }
% 0.21/0.56 X
% 0.21/0.56
% 0.21/0.56 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 0.21/0.56 Proof:
% 0.21/0.56 join(complement(X), complement(X))
% 0.21/0.56 = { by lemma 18 R->L }
% 0.21/0.56 join(complement(X), composition(converse(one), complement(X)))
% 0.21/0.56 = { by lemma 19 R->L }
% 0.21/0.56 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.56 join(composition(converse(one), complement(composition(one, X))), complement(X))
% 0.21/0.56 = { by axiom 14 (converse_cancellativity) }
% 0.21/0.56 complement(X)
% 0.21/0.56
% 0.21/0.56 Lemma 21: join(top, complement(X)) = top.
% 0.21/0.56 Proof:
% 0.21/0.56 join(top, complement(X))
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.56 join(complement(X), top)
% 0.21/0.56 = { by lemma 17 R->L }
% 0.21/0.56 join(X, join(complement(X), complement(X)))
% 0.21/0.56 = { by lemma 20 }
% 0.21/0.56 join(X, complement(X))
% 0.21/0.56 = { by axiom 7 (def_top) R->L }
% 0.21/0.56 top
% 0.21/0.56
% 0.21/0.56 Lemma 22: join(top, X) = join(Y, top).
% 0.21/0.56 Proof:
% 0.21/0.56 join(top, X)
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.56 join(X, top)
% 0.21/0.56 = { by lemma 21 R->L }
% 0.21/0.56 join(X, join(top, complement(X)))
% 0.21/0.56 = { by lemma 17 }
% 0.21/0.56 join(top, top)
% 0.21/0.56 = { by lemma 17 R->L }
% 0.21/0.56 join(Y, join(top, complement(Y)))
% 0.21/0.56 = { by lemma 21 }
% 0.21/0.56 join(Y, top)
% 0.21/0.56
% 0.21/0.56 Lemma 23: join(X, top) = top.
% 0.21/0.56 Proof:
% 0.21/0.56 join(X, top)
% 0.21/0.56 = { by lemma 22 R->L }
% 0.21/0.56 join(top, complement(top))
% 0.21/0.56 = { by axiom 7 (def_top) R->L }
% 0.21/0.56 top
% 0.21/0.56
% 0.21/0.56 Lemma 24: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 join(meet(X, Y), complement(join(complement(X), Y)))
% 0.21/0.56 = { by axiom 12 (maddux4_definiton_of_meet) }
% 0.21/0.56 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 0.21/0.56 = { by axiom 15 (maddux3_a_kind_of_de_Morgan) R->L }
% 0.21/0.56 X
% 0.21/0.56
% 0.21/0.56 Lemma 25: join(zero, meet(X, X)) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 join(zero, meet(X, X))
% 0.21/0.56 = { by axiom 12 (maddux4_definiton_of_meet) }
% 0.21/0.56 join(zero, complement(join(complement(X), complement(X))))
% 0.21/0.56 = { by axiom 6 (def_zero) }
% 0.21/0.56 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 0.21/0.56 = { by lemma 24 }
% 0.21/0.56 X
% 0.21/0.56
% 0.21/0.56 Lemma 26: join(X, zero) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 join(X, zero)
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.56 join(zero, X)
% 0.21/0.56 = { by lemma 25 R->L }
% 0.21/0.56 join(zero, join(zero, meet(X, X)))
% 0.21/0.56 = { by axiom 11 (maddux2_join_associativity) }
% 0.21/0.56 join(join(zero, zero), meet(X, X))
% 0.21/0.56 = { by lemma 16 R->L }
% 0.21/0.56 join(join(zero, complement(top)), meet(X, X))
% 0.21/0.56 = { by lemma 16 R->L }
% 0.21/0.56 join(join(complement(top), complement(top)), meet(X, X))
% 0.21/0.56 = { by lemma 20 }
% 0.21/0.56 join(complement(top), meet(X, X))
% 0.21/0.56 = { by lemma 16 }
% 0.21/0.56 join(zero, meet(X, X))
% 0.21/0.56 = { by lemma 25 }
% 0.21/0.56 X
% 0.21/0.56
% 0.21/0.56 Lemma 27: join(zero, X) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 join(zero, X)
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.56 join(X, zero)
% 0.21/0.56 = { by lemma 26 }
% 0.21/0.56 X
% 0.21/0.56
% 0.21/0.56 Lemma 28: complement(complement(X)) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 complement(complement(X))
% 0.21/0.56 = { by lemma 27 R->L }
% 0.21/0.56 join(zero, complement(complement(X)))
% 0.21/0.56 = { by lemma 20 R->L }
% 0.21/0.56 join(zero, complement(join(complement(X), complement(X))))
% 0.21/0.56 = { by axiom 12 (maddux4_definiton_of_meet) R->L }
% 0.21/0.56 join(zero, meet(X, X))
% 0.21/0.56 = { by lemma 25 }
% 0.21/0.56 X
% 0.21/0.56
% 0.21/0.56 Lemma 29: meet(Y, X) = meet(X, Y).
% 0.21/0.56 Proof:
% 0.21/0.56 meet(Y, X)
% 0.21/0.56 = { by axiom 12 (maddux4_definiton_of_meet) }
% 0.21/0.56 complement(join(complement(Y), complement(X)))
% 0.21/0.56 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.56 complement(join(complement(X), complement(Y)))
% 0.21/0.56 = { by axiom 12 (maddux4_definiton_of_meet) R->L }
% 0.21/0.56 meet(X, Y)
% 0.21/0.56
% 0.21/0.56 Lemma 30: complement(join(zero, complement(X))) = meet(X, top).
% 0.21/0.56 Proof:
% 0.21/0.56 complement(join(zero, complement(X)))
% 0.21/0.56 = { by lemma 16 R->L }
% 0.21/0.56 complement(join(complement(top), complement(X)))
% 0.21/0.56 = { by axiom 12 (maddux4_definiton_of_meet) R->L }
% 0.21/0.56 meet(top, X)
% 0.21/0.56 = { by lemma 29 R->L }
% 0.21/0.56 meet(X, top)
% 0.21/0.56
% 0.21/0.56 Lemma 31: meet(X, top) = X.
% 0.21/0.56 Proof:
% 0.21/0.56 meet(X, top)
% 0.21/0.56 = { by lemma 30 R->L }
% 0.21/0.56 complement(join(zero, complement(X)))
% 0.21/0.56 = { by lemma 27 }
% 0.21/0.56 complement(complement(X))
% 0.21/0.56 = { by lemma 28 }
% 0.21/0.56 X
% 0.21/0.57
% 0.21/0.57 Lemma 32: converse(composition(X, top)) = composition(top, converse(X)).
% 0.21/0.57 Proof:
% 0.21/0.57 converse(composition(X, top))
% 0.21/0.57 = { by axiom 8 (converse_multiplicativity) }
% 0.21/0.57 composition(converse(top), converse(X))
% 0.21/0.57 = { by lemma 23 R->L }
% 0.21/0.57 composition(converse(join(converse(top), top)), converse(X))
% 0.21/0.57 = { by axiom 10 (converse_additivity) }
% 0.21/0.57 composition(join(converse(converse(top)), converse(top)), converse(X))
% 0.21/0.57 = { by axiom 5 (converse_idempotence) }
% 0.21/0.57 composition(join(top, converse(top)), converse(X))
% 0.21/0.57 = { by lemma 22 }
% 0.21/0.57 composition(join(Y, top), converse(X))
% 0.21/0.57 = { by lemma 23 }
% 0.21/0.57 composition(top, converse(X))
% 0.21/0.57
% 0.21/0.57 Lemma 33: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 0.21/0.57 Proof:
% 0.21/0.57 join(complement(X), complement(Y))
% 0.21/0.57 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.57 join(complement(Y), complement(X))
% 0.21/0.57 = { by lemma 31 R->L }
% 0.21/0.57 meet(join(complement(Y), complement(X)), top)
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 meet(top, join(complement(Y), complement(X)))
% 0.21/0.57 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.57 meet(top, join(complement(X), complement(Y)))
% 0.21/0.57 = { by lemma 29 }
% 0.21/0.57 meet(join(complement(X), complement(Y)), top)
% 0.21/0.57 = { by axiom 12 (maddux4_definiton_of_meet) }
% 0.21/0.57 complement(join(complement(join(complement(X), complement(Y))), complement(top)))
% 0.21/0.57 = { by axiom 12 (maddux4_definiton_of_meet) R->L }
% 0.21/0.57 complement(join(meet(X, Y), complement(top)))
% 0.21/0.57 = { by axiom 4 (maddux1_join_commutativity) }
% 0.21/0.57 complement(join(complement(top), meet(X, Y)))
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 complement(join(complement(top), meet(Y, X)))
% 0.21/0.57 = { by lemma 16 }
% 0.21/0.57 complement(join(zero, meet(Y, X)))
% 0.21/0.57 = { by lemma 27 }
% 0.21/0.57 complement(meet(Y, X))
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 complement(meet(X, Y))
% 0.21/0.57
% 0.21/0.57 Lemma 34: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 0.21/0.57 Proof:
% 0.21/0.57 complement(meet(X, complement(Y)))
% 0.21/0.57 = { by lemma 29 }
% 0.21/0.57 complement(meet(complement(Y), X))
% 0.21/0.57 = { by lemma 27 R->L }
% 0.21/0.57 complement(meet(join(zero, complement(Y)), X))
% 0.21/0.57 = { by lemma 33 R->L }
% 0.21/0.57 join(complement(join(zero, complement(Y))), complement(X))
% 0.21/0.57 = { by lemma 30 }
% 0.21/0.57 join(meet(Y, top), complement(X))
% 0.21/0.57 = { by lemma 31 }
% 0.21/0.57 join(Y, complement(X))
% 0.21/0.57
% 0.21/0.57 Lemma 35: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 0.21/0.57 Proof:
% 0.21/0.57 complement(meet(complement(X), Y))
% 0.21/0.57 = { by lemma 29 }
% 0.21/0.57 complement(meet(Y, complement(X)))
% 0.21/0.57 = { by lemma 34 }
% 0.21/0.57 join(X, complement(Y))
% 0.21/0.57
% 0.21/0.57 Lemma 36: meet(X, join(X, complement(Y))) = X.
% 0.21/0.57 Proof:
% 0.21/0.57 meet(X, join(X, complement(Y)))
% 0.21/0.57 = { by lemma 26 R->L }
% 0.21/0.57 join(meet(X, join(X, complement(Y))), zero)
% 0.21/0.57 = { by lemma 16 R->L }
% 0.21/0.57 join(meet(X, join(X, complement(Y))), complement(top))
% 0.21/0.57 = { by lemma 35 R->L }
% 0.21/0.57 join(meet(X, complement(meet(complement(X), Y))), complement(top))
% 0.21/0.57 = { by lemma 23 R->L }
% 0.21/0.57 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(Y), top)))
% 0.21/0.57 = { by lemma 17 R->L }
% 0.21/0.57 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), join(complement(Y), complement(complement(X))))))
% 0.21/0.57 = { by lemma 33 }
% 0.21/0.57 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(Y, complement(X))))))
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 join(meet(X, complement(meet(complement(X), Y))), complement(join(complement(X), complement(meet(complement(X), Y)))))
% 0.21/0.57 = { by lemma 24 }
% 0.21/0.57 X
% 0.21/0.57
% 0.21/0.57 Lemma 37: join(X, meet(X, Y)) = X.
% 0.21/0.57 Proof:
% 0.21/0.57 join(X, meet(X, Y))
% 0.21/0.57 = { by axiom 12 (maddux4_definiton_of_meet) }
% 0.21/0.57 join(X, complement(join(complement(X), complement(Y))))
% 0.21/0.57 = { by lemma 35 R->L }
% 0.21/0.57 complement(meet(complement(X), join(complement(X), complement(Y))))
% 0.21/0.57 = { by lemma 36 }
% 0.21/0.57 complement(complement(X))
% 0.21/0.57 = { by lemma 28 }
% 0.21/0.57 X
% 0.21/0.57
% 0.21/0.57 Lemma 38: meet(X, join(X, Y)) = X.
% 0.21/0.57 Proof:
% 0.21/0.57 meet(X, join(X, Y))
% 0.21/0.57 = { by lemma 31 R->L }
% 0.21/0.57 meet(X, join(X, meet(Y, top)))
% 0.21/0.57 = { by lemma 30 R->L }
% 0.21/0.57 meet(X, join(X, complement(join(zero, complement(Y)))))
% 0.21/0.57 = { by lemma 36 }
% 0.21/0.57 X
% 0.21/0.57
% 0.21/0.57 Lemma 39: meet(X, join(Y, X)) = X.
% 0.21/0.57 Proof:
% 0.21/0.57 meet(X, join(Y, X))
% 0.21/0.57 = { by axiom 4 (maddux1_join_commutativity) R->L }
% 0.21/0.57 meet(X, join(X, Y))
% 0.21/0.57 = { by lemma 38 }
% 0.21/0.57 X
% 0.21/0.57
% 0.21/0.57 Goal 1 (goals_2): composition(meet(x0, x1), top) = meet(x0, x1).
% 0.21/0.57 Proof:
% 0.21/0.57 composition(meet(x0, x1), top)
% 0.21/0.57 = { by lemma 39 R->L }
% 0.21/0.57 meet(composition(meet(x0, x1), top), join(x1, composition(meet(x0, x1), top)))
% 0.21/0.57 = { by axiom 2 (goals) R->L }
% 0.21/0.57 meet(composition(meet(x0, x1), top), join(composition(x1, top), composition(meet(x0, x1), top)))
% 0.21/0.57 = { by axiom 13 (composition_distributivity) R->L }
% 0.21/0.57 meet(composition(meet(x0, x1), top), composition(join(x1, meet(x0, x1)), top))
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 meet(composition(meet(x0, x1), top), composition(join(x1, meet(x1, x0)), top))
% 0.21/0.57 = { by lemma 37 }
% 0.21/0.57 meet(composition(meet(x0, x1), top), composition(x1, top))
% 0.21/0.57 = { by axiom 2 (goals) }
% 0.21/0.57 meet(composition(meet(x0, x1), top), x1)
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 meet(x1, composition(meet(x0, x1), top))
% 0.21/0.57 = { by lemma 39 R->L }
% 0.21/0.57 meet(x1, meet(composition(meet(x0, x1), top), join(x0, composition(meet(x0, x1), top))))
% 0.21/0.57 = { by axiom 3 (goals_1) R->L }
% 0.21/0.57 meet(x1, meet(composition(meet(x0, x1), top), join(composition(x0, top), composition(meet(x0, x1), top))))
% 0.21/0.57 = { by axiom 13 (composition_distributivity) R->L }
% 0.21/0.57 meet(x1, meet(composition(meet(x0, x1), top), composition(join(x0, meet(x0, x1)), top)))
% 0.21/0.57 = { by lemma 37 }
% 0.21/0.57 meet(x1, meet(composition(meet(x0, x1), top), composition(x0, top)))
% 0.21/0.57 = { by axiom 3 (goals_1) }
% 0.21/0.57 meet(x1, meet(composition(meet(x0, x1), top), x0))
% 0.21/0.57 = { by lemma 29 }
% 0.21/0.57 meet(x1, meet(x0, composition(meet(x0, x1), top)))
% 0.21/0.57 = { by lemma 31 R->L }
% 0.21/0.57 meet(meet(x1, meet(x0, composition(meet(x0, x1), top))), top)
% 0.21/0.57 = { by lemma 30 R->L }
% 0.21/0.57 complement(join(zero, complement(meet(x1, meet(x0, composition(meet(x0, x1), top))))))
% 0.21/0.57 = { by lemma 29 }
% 0.21/0.57 complement(join(zero, complement(meet(x1, meet(composition(meet(x0, x1), top), x0)))))
% 0.21/0.57 = { by axiom 12 (maddux4_definiton_of_meet) }
% 0.21/0.57 complement(join(zero, complement(meet(x1, complement(join(complement(composition(meet(x0, x1), top)), complement(x0)))))))
% 0.21/0.57 = { by lemma 34 }
% 0.21/0.57 complement(join(zero, join(join(complement(composition(meet(x0, x1), top)), complement(x0)), complement(x1))))
% 0.21/0.57 = { by axiom 11 (maddux2_join_associativity) R->L }
% 0.21/0.57 complement(join(zero, join(complement(composition(meet(x0, x1), top)), join(complement(x0), complement(x1)))))
% 0.21/0.57 = { by lemma 33 }
% 0.21/0.57 complement(join(zero, join(complement(composition(meet(x0, x1), top)), complement(meet(x0, x1)))))
% 0.21/0.57 = { by lemma 33 }
% 0.21/0.57 complement(join(zero, complement(meet(composition(meet(x0, x1), top), meet(x0, x1)))))
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 complement(join(zero, complement(meet(composition(meet(x0, x1), top), meet(x1, x0)))))
% 0.21/0.57 = { by lemma 30 }
% 0.21/0.57 meet(meet(composition(meet(x0, x1), top), meet(x1, x0)), top)
% 0.21/0.57 = { by lemma 31 }
% 0.21/0.57 meet(composition(meet(x0, x1), top), meet(x1, x0))
% 0.21/0.57 = { by lemma 29 }
% 0.21/0.57 meet(composition(meet(x0, x1), top), meet(x0, x1))
% 0.21/0.57 = { by lemma 29 R->L }
% 0.21/0.57 meet(meet(x0, x1), composition(meet(x0, x1), top))
% 0.21/0.57 = { by axiom 5 (converse_idempotence) R->L }
% 0.21/0.57 meet(meet(x0, x1), converse(converse(composition(meet(x0, x1), top))))
% 0.21/0.57 = { by lemma 32 }
% 0.21/0.57 meet(meet(x0, x1), converse(composition(top, converse(meet(x0, x1)))))
% 0.21/0.57 = { by lemma 23 R->L }
% 0.21/0.57 meet(meet(x0, x1), converse(composition(join(one, top), converse(meet(x0, x1)))))
% 0.21/0.57 = { by axiom 13 (composition_distributivity) }
% 0.21/0.57 meet(meet(x0, x1), converse(join(composition(one, converse(meet(x0, x1))), composition(top, converse(meet(x0, x1))))))
% 0.21/0.57 = { by lemma 19 }
% 0.21/0.57 meet(meet(x0, x1), converse(join(converse(meet(x0, x1)), composition(top, converse(meet(x0, x1))))))
% 0.21/0.57 = { by lemma 32 R->L }
% 0.21/0.57 meet(meet(x0, x1), converse(join(converse(meet(x0, x1)), converse(composition(meet(x0, x1), top)))))
% 0.21/0.57 = { by axiom 10 (converse_additivity) R->L }
% 0.21/0.57 meet(meet(x0, x1), converse(converse(join(meet(x0, x1), composition(meet(x0, x1), top)))))
% 0.21/0.57 = { by axiom 5 (converse_idempotence) }
% 0.21/0.57 meet(meet(x0, x1), join(meet(x0, x1), composition(meet(x0, x1), top)))
% 0.21/0.57 = { by lemma 38 }
% 0.21/0.57 meet(x0, x1)
% 0.21/0.57 % SZS output end Proof
% 0.21/0.57
% 0.21/0.57 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------