TSTP Solution File: LAT206-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT206-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n011.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 06:27:45 EDT 2023
% Result : Unsatisfiable 277.17s 36.01s
% Output : Proof 278.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT206-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n011.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 : Thu Aug 24 05:39:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 277.17/36.01 Command-line arguments: --no-flatten-goal
% 277.17/36.01
% 277.17/36.01 % SZS status Unsatisfiable
% 277.17/36.01
% 278.04/36.13 % SZS output start Proof
% 278.04/36.13 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 278.04/36.13 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 278.04/36.13 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 278.04/36.13 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 278.04/36.13 Axiom 5 (complement_join): join(X, complement(X)) = one.
% 278.04/36.13 Axiom 6 (complement_meet): meet(X, complement(X)) = zero.
% 278.04/36.13 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 278.04/36.13 Axiom 8 (absorption2): join(X, meet(X, Y)) = X.
% 278.04/36.13 Axiom 9 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 278.04/36.13 Axiom 10 (absorption1): meet(X, join(X, Y)) = X.
% 278.04/36.13 Axiom 11 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 278.04/36.13 Axiom 12 (equation_H60): meet(X, meet(join(Y, Z), join(Y, W))) = meet(X, join(Y, meet(join(Y, Z), join(W, meet(X, Y))))).
% 278.04/36.13 Axiom 13 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 278.04/36.13
% 278.04/36.13 Lemma 14: meet(X, one) = X.
% 278.04/36.13 Proof:
% 278.04/36.13 meet(X, one)
% 278.04/36.13 = { by axiom 5 (complement_join) R->L }
% 278.04/36.13 meet(X, join(X, complement(X)))
% 278.04/36.13 = { by axiom 10 (absorption1) }
% 278.04/36.13 X
% 278.04/36.13
% 278.04/36.13 Lemma 15: join(X, zero) = X.
% 278.04/36.13 Proof:
% 278.04/36.13 join(X, zero)
% 278.04/36.13 = { by axiom 6 (complement_meet) R->L }
% 278.04/36.13 join(X, meet(X, complement(X)))
% 278.04/36.13 = { by axiom 8 (absorption2) }
% 278.04/36.13 X
% 278.04/36.13
% 278.04/36.13 Lemma 16: meet(X, zero) = zero.
% 278.04/36.13 Proof:
% 278.04/36.13 meet(X, zero)
% 278.04/36.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.13 meet(zero, X)
% 278.04/36.13 = { by lemma 15 R->L }
% 278.04/36.13 join(meet(zero, X), zero)
% 278.04/36.13 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.13 join(zero, meet(zero, X))
% 278.04/36.13 = { by axiom 8 (absorption2) }
% 278.04/36.13 zero
% 278.04/36.13
% 278.04/36.13 Lemma 17: complement(complement(X)) = X.
% 278.04/36.13 Proof:
% 278.04/36.13 complement(complement(X))
% 278.04/36.13 = { by axiom 7 (ifeq_axiom) R->L }
% 278.04/36.13 ifeq(zero, zero, complement(complement(X)), X)
% 278.04/36.13 = { by axiom 6 (complement_meet) R->L }
% 278.04/36.13 ifeq(meet(X, complement(X)), zero, complement(complement(X)), X)
% 278.04/36.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.14 ifeq(meet(complement(X), X), zero, complement(complement(X)), X)
% 278.04/36.14 = { by axiom 7 (ifeq_axiom) R->L }
% 278.04/36.14 ifeq(one, one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 278.04/36.14 = { by axiom 5 (complement_join) R->L }
% 278.04/36.14 ifeq(join(X, complement(X)), one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 ifeq(join(complement(X), X), one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 278.04/36.14 = { by axiom 13 (meet_join_complement) }
% 278.04/36.14 X
% 278.04/36.14
% 278.04/36.14 Lemma 18: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 278.04/36.14 Proof:
% 278.04/36.14 meet(X, meet(Y, Z))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.14 meet(meet(Y, Z), X)
% 278.04/36.14 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.14 meet(Y, meet(Z, X))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.14 meet(Y, meet(X, Z))
% 278.04/36.14
% 278.04/36.14 Lemma 19: meet(X, join(Y, X)) = X.
% 278.04/36.14 Proof:
% 278.04/36.14 meet(X, join(Y, X))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(X, join(X, Y))
% 278.04/36.14 = { by axiom 10 (absorption1) }
% 278.04/36.14 X
% 278.04/36.14
% 278.04/36.14 Lemma 20: join(X, meet(Y, X)) = X.
% 278.04/36.14 Proof:
% 278.04/36.14 join(X, meet(Y, X))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.14 join(X, meet(X, Y))
% 278.04/36.14 = { by axiom 8 (absorption2) }
% 278.04/36.14 X
% 278.04/36.14
% 278.04/36.14 Lemma 21: join(X, join(Y, X)) = join(X, Y).
% 278.04/36.14 Proof:
% 278.04/36.14 join(X, join(Y, X))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 join(X, join(X, Y))
% 278.04/36.14 = { by axiom 9 (associativity_of_join) R->L }
% 278.04/36.14 join(join(X, X), Y)
% 278.04/36.14 = { by axiom 1 (idempotence_of_join) }
% 278.04/36.14 join(X, Y)
% 278.04/36.14
% 278.04/36.14 Lemma 22: meet(X, meet(Y, join(Z, X))) = meet(X, Y).
% 278.04/36.14 Proof:
% 278.04/36.14 meet(X, meet(Y, join(Z, X)))
% 278.04/36.14 = { by lemma 18 R->L }
% 278.04/36.14 meet(Y, meet(X, join(Z, X)))
% 278.04/36.14 = { by lemma 19 }
% 278.04/36.14 meet(Y, X)
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.14 meet(X, Y)
% 278.04/36.14
% 278.04/36.14 Lemma 23: meet(X, meet(join(Y, complement(X)), join(Z, complement(X)))) = meet(X, join(complement(X), meet(Z, join(Y, complement(X))))).
% 278.04/36.14 Proof:
% 278.04/36.14 meet(X, meet(join(Y, complement(X)), join(Z, complement(X))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(X)), join(complement(X), Z)))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(X, meet(join(complement(X), Y), join(complement(X), Z)))
% 278.04/36.14 = { by axiom 12 (equation_H60) }
% 278.04/36.14 meet(X, join(complement(X), meet(join(complement(X), Y), join(Z, meet(X, complement(X))))))
% 278.04/36.14 = { by axiom 6 (complement_meet) }
% 278.04/36.14 meet(X, join(complement(X), meet(join(complement(X), Y), join(Z, zero))))
% 278.04/36.14 = { by lemma 15 }
% 278.04/36.14 meet(X, join(complement(X), meet(join(complement(X), Y), Z)))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.14 meet(X, join(complement(X), meet(Z, join(complement(X), Y))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.14 meet(X, join(complement(X), meet(Z, join(Y, complement(X)))))
% 278.04/36.14
% 278.04/36.14 Lemma 24: meet(complement(X), meet(join(X, Y), join(X, Z))) = meet(complement(X), join(X, meet(Y, join(X, Z)))).
% 278.04/36.14 Proof:
% 278.04/36.14 meet(complement(X), meet(join(X, Y), join(X, Z)))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(complement(X), meet(join(X, Y), join(Z, X)))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(complement(X), meet(join(Y, X), join(Z, X)))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.14 meet(complement(X), meet(join(Z, X), join(Y, X)))
% 278.04/36.14 = { by lemma 17 R->L }
% 278.04/36.14 meet(complement(X), meet(join(Z, X), join(Y, complement(complement(X)))))
% 278.04/36.14 = { by lemma 17 R->L }
% 278.04/36.14 meet(complement(X), meet(join(Z, complement(complement(X))), join(Y, complement(complement(X)))))
% 278.04/36.14 = { by lemma 23 }
% 278.04/36.14 meet(complement(X), join(complement(complement(X)), meet(Y, join(Z, complement(complement(X))))))
% 278.04/36.14 = { by lemma 17 }
% 278.04/36.14 meet(complement(X), join(X, meet(Y, join(Z, complement(complement(X))))))
% 278.04/36.14 = { by lemma 17 }
% 278.04/36.14 meet(complement(X), join(X, meet(Y, join(Z, X))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.14 meet(complement(X), join(X, meet(Y, join(X, Z))))
% 278.04/36.14
% 278.04/36.14 Lemma 25: meet(X, meet(Y, complement(X))) = zero.
% 278.04/36.14 Proof:
% 278.04/36.14 meet(X, meet(Y, complement(X)))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.14 meet(X, meet(complement(X), Y))
% 278.04/36.14 = { by axiom 11 (associativity_of_meet) R->L }
% 278.04/36.14 meet(meet(X, complement(X)), Y)
% 278.04/36.14 = { by axiom 6 (complement_meet) }
% 278.04/36.14 meet(zero, Y)
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.14 meet(Y, zero)
% 278.04/36.14 = { by lemma 16 }
% 278.04/36.14 zero
% 278.04/36.14
% 278.04/36.14 Lemma 26: meet(X, join(Y, complement(join(X, Y)))) = meet(X, Y).
% 278.04/36.14 Proof:
% 278.04/36.14 meet(X, join(Y, complement(join(X, Y))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(X, join(Y, complement(join(Y, X))))
% 278.04/36.14 = { by lemma 22 R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, X))), join(Y, X)))
% 278.04/36.14 = { by lemma 21 R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(Y, X)))
% 278.04/36.14 = { by lemma 22 R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), meet(join(Y, X), join(Y, join(Y, complement(join(Y, join(X, Y))))))))
% 278.04/36.14 = { by axiom 12 (equation_H60) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(Y, meet(join(Y, X), join(join(Y, complement(join(Y, join(X, Y)))), meet(join(Y, complement(join(Y, join(X, Y)))), Y))))))
% 278.04/36.14 = { by axiom 8 (absorption2) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(Y, meet(join(Y, X), join(Y, complement(join(Y, join(X, Y))))))))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(Y, meet(join(Y, complement(join(Y, join(X, Y)))), join(Y, X)))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(Y, meet(join(Y, complement(join(Y, join(X, Y)))), join(X, Y)))))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(Y, meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y)))
% 278.04/36.14 = { by lemma 17 R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))))
% 278.04/36.14 = { by axiom 13 (meet_join_complement) R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(join(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), one, ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(join(complement(Y), join(complement(complement(Y)), meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))))), one, ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by axiom 9 (associativity_of_join) R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(join(join(complement(Y), complement(complement(Y))), meet(join(X, Y), join(Y, complement(join(Y, join(X, Y)))))), one, ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by axiom 5 (complement_join) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(join(one, meet(join(X, Y), join(Y, complement(join(Y, join(X, Y)))))), one, ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by lemma 14 R->L }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(join(one, meet(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), one)), one, ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(join(one, meet(one, meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))))), one, ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by axiom 8 (absorption2) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(one, one, ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by axiom 7 (ifeq_axiom) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y)))), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by lemma 17 }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y)), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), complement(complement(Y))))))
% 278.04/36.14 = { by lemma 17 }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y)), zero, complement(complement(Y)), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.14 = { by lemma 17 }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y)), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.14 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(Y, meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.14 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(Y, meet(join(X, Y), join(Y, complement(join(join(X, Y), Y)))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 24 R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(Y, join(X, Y)), join(Y, complement(join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(join(X, Y), Y), join(Y, complement(join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(join(X, Y), Y), join(complement(join(join(X, Y), Y)), Y))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 18 R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(join(join(X, Y), Y), meet(complement(Y), join(complement(join(join(X, Y), Y)), Y))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 19 R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(join(join(X, Y), Y), meet(complement(Y), join(complement(join(join(X, Y), Y)), meet(Y, join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(join(join(X, Y), Y), meet(complement(Y), join(complement(join(join(X, Y), Y)), meet(join(join(X, Y), Y), Y)))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 18 R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(join(X, Y), Y), join(complement(join(join(X, Y), Y)), meet(join(join(X, Y), Y), Y)))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 17 R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(join(X, Y), Y), join(complement(join(join(X, Y), Y)), meet(join(join(X, Y), Y), complement(complement(Y)))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 8 (absorption2) R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(join(join(X, Y), Y), meet(join(join(X, Y), Y), complement(complement(Y)))), join(complement(join(join(X, Y), Y)), meet(join(join(X, Y), Y), complement(complement(Y)))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(join(join(X, Y), Y), meet(join(join(X, Y), Y), complement(complement(Y)))), join(meet(join(join(X, Y), Y), complement(complement(Y))), complement(join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(join(meet(join(join(X, Y), Y), complement(complement(Y))), join(join(X, Y), Y)), join(meet(join(join(X, Y), Y), complement(complement(Y))), complement(join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 12 (equation_H60) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(complement(Y))), meet(join(meet(join(join(X, Y), Y), complement(complement(Y))), join(join(X, Y), Y)), join(complement(join(join(X, Y), Y)), meet(complement(Y), meet(join(join(X, Y), Y), complement(complement(Y)))))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 25 }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(complement(Y))), meet(join(meet(join(join(X, Y), Y), complement(complement(Y))), join(join(X, Y), Y)), join(complement(join(join(X, Y), Y)), zero)))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 15 }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(complement(Y))), meet(join(meet(join(join(X, Y), Y), complement(complement(Y))), join(join(X, Y), Y)), complement(join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(complement(Y))), meet(complement(join(join(X, Y), Y)), join(meet(join(join(X, Y), Y), complement(complement(Y))), join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(complement(Y))), meet(complement(join(join(X, Y), Y)), join(join(join(X, Y), Y), meet(join(join(X, Y), Y), complement(complement(Y))))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 8 (absorption2) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(complement(Y))), meet(complement(join(join(X, Y), Y)), join(join(X, Y), Y)))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(complement(join(join(X, Y), Y)), join(join(X, Y), Y)), meet(join(join(X, Y), Y), complement(complement(Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(join(join(X, Y), Y))), meet(join(join(X, Y), Y), complement(complement(Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 17 }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), complement(join(join(X, Y), Y))), meet(join(join(X, Y), Y), Y))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(join(join(X, Y), Y), Y), meet(join(join(X, Y), Y), complement(join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(Y, join(join(X, Y), Y)), meet(join(join(X, Y), Y), complement(join(join(X, Y), Y))))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 6 (complement_meet) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), join(meet(Y, join(join(X, Y), Y)), zero)), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 15 }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(complement(Y), meet(Y, join(join(X, Y), Y))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 18 }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(Y, meet(complement(Y), join(join(X, Y), Y))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(meet(Y, meet(join(join(X, Y), Y), complement(Y))), zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by lemma 25 }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), ifeq(zero, zero, Y, join(meet(join(X, Y), join(Y, complement(join(Y, join(X, Y))))), Y))))
% 278.04/36.15 = { by axiom 7 (ifeq_axiom) }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, join(X, Y)))), Y))
% 278.04/36.15 = { by lemma 21 }
% 278.04/36.15 meet(X, meet(join(Y, complement(join(Y, X))), Y))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.15 meet(X, meet(Y, join(Y, complement(join(Y, X)))))
% 278.04/36.15 = { by axiom 10 (absorption1) }
% 278.04/36.15 meet(X, Y)
% 278.04/36.15
% 278.04/36.15 Lemma 27: ifeq(meet(X, Y), zero, complement(X), join(Y, complement(join(X, Y)))) = join(Y, complement(join(X, Y))).
% 278.04/36.15 Proof:
% 278.04/36.15 ifeq(meet(X, Y), zero, complement(X), join(Y, complement(join(X, Y))))
% 278.04/36.15 = { by lemma 26 R->L }
% 278.04/36.15 ifeq(meet(X, join(Y, complement(join(X, Y)))), zero, complement(X), join(Y, complement(join(X, Y))))
% 278.04/36.15 = { by axiom 7 (ifeq_axiom) R->L }
% 278.04/36.15 ifeq(one, one, ifeq(meet(X, join(Y, complement(join(X, Y)))), zero, complement(X), join(Y, complement(join(X, Y)))), join(Y, complement(join(X, Y))))
% 278.04/36.15 = { by axiom 5 (complement_join) R->L }
% 278.04/36.15 ifeq(join(join(X, Y), complement(join(X, Y))), one, ifeq(meet(X, join(Y, complement(join(X, Y)))), zero, complement(X), join(Y, complement(join(X, Y)))), join(Y, complement(join(X, Y))))
% 278.04/36.15 = { by axiom 9 (associativity_of_join) }
% 278.04/36.15 ifeq(join(X, join(Y, complement(join(X, Y)))), one, ifeq(meet(X, join(Y, complement(join(X, Y)))), zero, complement(X), join(Y, complement(join(X, Y)))), join(Y, complement(join(X, Y))))
% 278.04/36.15 = { by axiom 13 (meet_join_complement) }
% 278.04/36.15 join(Y, complement(join(X, Y)))
% 278.04/36.15
% 278.04/36.15 Lemma 28: join(meet(X, complement(Y)), complement(join(Y, meet(X, complement(Y))))) = complement(Y).
% 278.04/36.15 Proof:
% 278.04/36.15 join(meet(X, complement(Y)), complement(join(Y, meet(X, complement(Y)))))
% 278.04/36.15 = { by lemma 27 R->L }
% 278.04/36.15 ifeq(meet(Y, meet(X, complement(Y))), zero, complement(Y), join(meet(X, complement(Y)), complement(join(Y, meet(X, complement(Y))))))
% 278.04/36.15 = { by lemma 25 }
% 278.04/36.15 ifeq(zero, zero, complement(Y), join(meet(X, complement(Y)), complement(join(Y, meet(X, complement(Y))))))
% 278.04/36.15 = { by axiom 7 (ifeq_axiom) }
% 278.04/36.15 complement(Y)
% 278.04/36.15
% 278.04/36.15 Lemma 29: meet(X, complement(join(X, Y))) = zero.
% 278.04/36.15 Proof:
% 278.04/36.15 meet(X, complement(join(X, Y)))
% 278.04/36.15 = { by axiom 10 (absorption1) R->L }
% 278.04/36.15 meet(meet(X, join(X, Y)), complement(join(X, Y)))
% 278.04/36.15 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.15 meet(X, meet(join(X, Y), complement(join(X, Y))))
% 278.04/36.15 = { by axiom 6 (complement_meet) }
% 278.04/36.15 meet(X, zero)
% 278.04/36.15 = { by lemma 16 }
% 278.04/36.15 zero
% 278.04/36.15
% 278.04/36.15 Lemma 30: meet(X, complement(join(Y, X))) = zero.
% 278.04/36.15 Proof:
% 278.04/36.15 meet(X, complement(join(Y, X)))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.15 meet(X, complement(join(X, Y)))
% 278.04/36.15 = { by lemma 29 }
% 278.04/36.15 zero
% 278.04/36.15
% 278.04/36.15 Lemma 31: join(complement(join(X, Y)), complement(join(X, complement(join(X, Y))))) = complement(X).
% 278.04/36.15 Proof:
% 278.04/36.15 join(complement(join(X, Y)), complement(join(X, complement(join(X, Y)))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.15 join(complement(join(Y, X)), complement(join(X, complement(join(X, Y)))))
% 278.04/36.15 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.15 join(complement(join(Y, X)), complement(join(X, complement(join(Y, X)))))
% 278.04/36.15 = { by lemma 27 R->L }
% 278.04/36.15 ifeq(meet(X, complement(join(Y, X))), zero, complement(X), join(complement(join(Y, X)), complement(join(X, complement(join(Y, X))))))
% 278.04/36.15 = { by lemma 30 }
% 278.04/36.15 ifeq(zero, zero, complement(X), join(complement(join(Y, X)), complement(join(X, complement(join(Y, X))))))
% 278.04/36.15 = { by axiom 7 (ifeq_axiom) }
% 278.04/36.15 complement(X)
% 278.04/36.15
% 278.04/36.15 Lemma 32: meet(complement(X), complement(join(X, Y))) = complement(join(X, Y)).
% 278.04/36.15 Proof:
% 278.04/36.15 meet(complement(X), complement(join(X, Y)))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.15 meet(complement(join(X, Y)), complement(X))
% 278.04/36.15 = { by lemma 31 R->L }
% 278.04/36.15 meet(complement(join(X, Y)), join(complement(join(X, Y)), complement(join(X, complement(join(X, Y))))))
% 278.04/36.15 = { by axiom 10 (absorption1) }
% 278.04/36.15 complement(join(X, Y))
% 278.04/36.15
% 278.04/36.15 Lemma 33: join(meet(X, Y), complement(join(complement(X), meet(X, Y)))) = X.
% 278.04/36.15 Proof:
% 278.04/36.15 join(meet(X, Y), complement(join(complement(X), meet(X, Y))))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.15 join(meet(Y, X), complement(join(complement(X), meet(X, Y))))
% 278.04/36.15 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.15 join(meet(Y, X), complement(join(complement(X), meet(Y, X))))
% 278.04/36.15 = { by lemma 17 R->L }
% 278.04/36.15 join(meet(Y, X), complement(join(complement(X), meet(Y, complement(complement(X))))))
% 278.04/36.15 = { by lemma 17 R->L }
% 278.04/36.15 join(meet(Y, complement(complement(X))), complement(join(complement(X), meet(Y, complement(complement(X))))))
% 278.04/36.15 = { by lemma 28 }
% 278.04/36.15 complement(complement(X))
% 278.04/36.15 = { by lemma 17 }
% 278.04/36.16 X
% 278.04/36.16
% 278.04/36.16 Lemma 34: meet(X, complement(meet(X, Y))) = meet(X, complement(Y)).
% 278.04/36.16 Proof:
% 278.04/36.16 meet(X, complement(meet(X, Y)))
% 278.04/36.16 = { by axiom 10 (absorption1) R->L }
% 278.04/36.16 meet(meet(X, complement(meet(X, Y))), join(meet(X, complement(meet(X, Y))), complement(join(Y, meet(X, complement(meet(X, Y)))))))
% 278.04/36.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.16 meet(meet(X, complement(meet(X, Y))), join(meet(X, complement(meet(Y, X))), complement(join(Y, meet(X, complement(meet(X, Y)))))))
% 278.04/36.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.16 meet(meet(X, complement(meet(X, Y))), join(meet(X, complement(meet(Y, X))), complement(join(Y, meet(X, complement(meet(Y, X)))))))
% 278.04/36.16 = { by lemma 27 R->L }
% 278.04/36.16 meet(meet(X, complement(meet(X, Y))), ifeq(meet(Y, meet(X, complement(meet(Y, X)))), zero, complement(Y), join(meet(X, complement(meet(Y, X))), complement(join(Y, meet(X, complement(meet(Y, X))))))))
% 278.04/36.16 = { by axiom 11 (associativity_of_meet) R->L }
% 278.04/36.16 meet(meet(X, complement(meet(X, Y))), ifeq(meet(meet(Y, X), complement(meet(Y, X))), zero, complement(Y), join(meet(X, complement(meet(Y, X))), complement(join(Y, meet(X, complement(meet(Y, X))))))))
% 278.04/36.16 = { by axiom 6 (complement_meet) }
% 278.04/36.16 meet(meet(X, complement(meet(X, Y))), ifeq(zero, zero, complement(Y), join(meet(X, complement(meet(Y, X))), complement(join(Y, meet(X, complement(meet(Y, X))))))))
% 278.04/36.16 = { by axiom 7 (ifeq_axiom) }
% 278.04/36.16 meet(meet(X, complement(meet(X, Y))), complement(Y))
% 278.04/36.16 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.16 meet(X, meet(complement(meet(X, Y)), complement(Y)))
% 278.04/36.16 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.16 meet(X, meet(complement(Y), complement(meet(X, Y))))
% 278.04/36.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.16 meet(X, meet(complement(Y), complement(meet(Y, X))))
% 278.04/36.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.16 meet(X, meet(complement(meet(Y, X)), complement(Y)))
% 278.04/36.16 = { by lemma 33 R->L }
% 278.04/36.16 meet(X, meet(complement(meet(Y, X)), complement(join(meet(Y, X), complement(join(complement(Y), meet(Y, X)))))))
% 278.04/36.16 = { by lemma 32 }
% 278.04/36.16 meet(X, complement(join(meet(Y, X), complement(join(complement(Y), meet(Y, X))))))
% 278.04/36.16 = { by lemma 33 }
% 278.04/36.16 meet(X, complement(Y))
% 278.04/36.16
% 278.04/36.16 Lemma 35: meet(X, meet(Y, complement(join(Z, meet(X, Y))))) = zero.
% 278.04/36.16 Proof:
% 278.04/36.16 meet(X, meet(Y, complement(join(Z, meet(X, Y)))))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.16 meet(X, meet(Y, complement(join(meet(X, Y), Z))))
% 278.04/36.16 = { by axiom 11 (associativity_of_meet) R->L }
% 278.04/36.16 meet(meet(X, Y), complement(join(meet(X, Y), Z)))
% 278.04/36.16 = { by lemma 29 }
% 278.04/36.16 zero
% 278.04/36.16
% 278.04/36.16 Lemma 36: join(X, complement(join(X, meet(complement(X), Y)))) = complement(meet(Y, complement(X))).
% 278.04/36.16 Proof:
% 278.04/36.16 join(X, complement(join(X, meet(complement(X), Y))))
% 278.04/36.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.16 join(X, complement(join(X, meet(Y, complement(X)))))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.16 join(complement(join(X, meet(Y, complement(X)))), X)
% 278.04/36.16 = { by lemma 17 R->L }
% 278.04/36.16 join(complement(join(X, meet(Y, complement(X)))), complement(complement(X)))
% 278.04/36.16 = { by lemma 28 R->L }
% 278.04/36.16 join(complement(join(X, meet(Y, complement(X)))), complement(join(meet(Y, complement(X)), complement(join(X, meet(Y, complement(X)))))))
% 278.04/36.16 = { by lemma 27 R->L }
% 278.04/36.16 ifeq(meet(meet(Y, complement(X)), complement(join(X, meet(Y, complement(X))))), zero, complement(meet(Y, complement(X))), join(complement(join(X, meet(Y, complement(X)))), complement(join(meet(Y, complement(X)), complement(join(X, meet(Y, complement(X))))))))
% 278.04/36.16 = { by lemma 28 }
% 278.04/36.16 ifeq(meet(meet(Y, complement(X)), complement(join(X, meet(Y, complement(X))))), zero, complement(meet(Y, complement(X))), join(complement(join(X, meet(Y, complement(X)))), complement(complement(X))))
% 278.04/36.16 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.16 ifeq(meet(Y, meet(complement(X), complement(join(X, meet(Y, complement(X)))))), zero, complement(meet(Y, complement(X))), join(complement(join(X, meet(Y, complement(X)))), complement(complement(X))))
% 278.04/36.16 = { by lemma 35 }
% 278.04/36.16 ifeq(zero, zero, complement(meet(Y, complement(X))), join(complement(join(X, meet(Y, complement(X)))), complement(complement(X))))
% 278.04/36.16 = { by axiom 7 (ifeq_axiom) }
% 278.04/36.16 complement(meet(Y, complement(X)))
% 278.04/36.16
% 278.04/36.16 Lemma 37: join(complement(X), meet(X, Y)) = complement(meet(X, complement(Y))).
% 278.04/36.16 Proof:
% 278.04/36.16 join(complement(X), meet(X, Y))
% 278.04/36.16 = { by lemma 17 R->L }
% 278.04/36.16 complement(complement(join(complement(X), meet(X, Y))))
% 278.04/36.16 = { by axiom 7 (ifeq_axiom) R->L }
% 278.04/36.16 ifeq(zero, zero, complement(complement(join(complement(X), meet(X, Y)))), join(complement(join(complement(X), complement(join(complement(X), meet(X, Y))))), complement(complement(complement(X)))))
% 278.04/36.16 = { by lemma 30 R->L }
% 278.04/36.16 ifeq(meet(complement(join(complement(X), meet(X, Y))), complement(join(complement(X), complement(join(complement(X), meet(X, Y)))))), zero, complement(complement(join(complement(X), meet(X, Y)))), join(complement(join(complement(X), complement(join(complement(X), meet(X, Y))))), complement(complement(complement(X)))))
% 278.04/36.16 = { by lemma 31 R->L }
% 278.04/36.16 ifeq(meet(complement(join(complement(X), meet(X, Y))), complement(join(complement(X), complement(join(complement(X), meet(X, Y)))))), zero, complement(complement(join(complement(X), meet(X, Y)))), join(complement(join(complement(X), complement(join(complement(X), meet(X, Y))))), complement(join(complement(join(complement(X), meet(X, Y))), complement(join(complement(X), complement(join(complement(X), meet(X, Y)))))))))
% 278.04/36.16 = { by lemma 27 }
% 278.04/36.16 join(complement(join(complement(X), complement(join(complement(X), meet(X, Y))))), complement(join(complement(join(complement(X), meet(X, Y))), complement(join(complement(X), complement(join(complement(X), meet(X, Y))))))))
% 278.04/36.16 = { by lemma 31 }
% 278.04/36.16 join(complement(join(complement(X), complement(join(complement(X), meet(X, Y))))), complement(complement(complement(X))))
% 278.04/36.16 = { by lemma 17 }
% 278.04/36.16 join(complement(join(complement(X), complement(join(complement(X), meet(X, Y))))), complement(X))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.16 join(complement(X), complement(join(complement(X), complement(join(complement(X), meet(X, Y))))))
% 278.04/36.16 = { by lemma 14 R->L }
% 278.04/36.16 join(complement(X), complement(join(complement(X), meet(complement(join(complement(X), meet(X, Y))), one))))
% 278.04/36.16 = { by axiom 5 (complement_join) R->L }
% 278.04/36.16 join(complement(X), complement(join(complement(X), meet(complement(join(complement(X), meet(X, Y))), join(complement(X), complement(complement(X)))))))
% 278.04/36.16 = { by lemma 32 R->L }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(join(complement(X), meet(complement(join(complement(X), meet(X, Y))), join(complement(X), complement(complement(X))))))))
% 278.04/36.16 = { by lemma 34 R->L }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), join(complement(X), meet(complement(join(complement(X), meet(X, Y))), join(complement(X), complement(complement(X)))))))))
% 278.04/36.16 = { by lemma 24 R->L }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), meet(join(complement(X), complement(join(complement(X), meet(X, Y)))), join(complement(X), complement(complement(X))))))))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), meet(join(complement(X), complement(join(complement(X), meet(X, Y)))), join(complement(complement(X)), complement(X)))))))
% 278.04/36.16 = { by lemma 17 R->L }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), meet(join(complement(X), complement(join(complement(X), meet(X, Y)))), join(complement(complement(X)), complement(complement(complement(X)))))))))
% 278.04/36.16 = { by lemma 17 R->L }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), meet(join(complement(complement(complement(X))), complement(join(complement(X), meet(X, Y)))), join(complement(complement(X)), complement(complement(complement(X)))))))))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), meet(join(complement(join(complement(X), meet(X, Y))), complement(complement(complement(X)))), join(complement(complement(X)), complement(complement(complement(X)))))))))
% 278.04/36.16 = { by lemma 23 }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), join(complement(complement(complement(X))), meet(complement(complement(X)), join(complement(join(complement(X), meet(X, Y))), complement(complement(complement(X))))))))))
% 278.04/36.16 = { by lemma 17 }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), join(complement(complement(complement(X))), meet(complement(complement(X)), join(complement(join(complement(X), meet(X, Y))), complement(X))))))))
% 278.04/36.16 = { by lemma 17 }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), join(complement(X), meet(complement(complement(X)), join(complement(join(complement(X), meet(X, Y))), complement(X))))))))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(meet(complement(complement(X)), join(complement(X), meet(complement(complement(X)), join(complement(X), complement(join(complement(X), meet(X, Y))))))))))
% 278.04/36.16 = { by lemma 34 }
% 278.04/36.16 join(complement(X), meet(complement(complement(X)), complement(join(complement(X), meet(complement(complement(X)), join(complement(X), complement(join(complement(X), meet(X, Y)))))))))
% 278.04/36.16 = { by lemma 32 }
% 278.04/36.16 join(complement(X), complement(join(complement(X), meet(complement(complement(X)), join(complement(X), complement(join(complement(X), meet(X, Y))))))))
% 278.04/36.16 = { by lemma 36 }
% 278.04/36.16 complement(meet(join(complement(X), complement(join(complement(X), meet(X, Y)))), complement(complement(X))))
% 278.04/36.16 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.16 complement(meet(complement(complement(X)), join(complement(X), complement(join(complement(X), meet(X, Y))))))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.16 complement(meet(complement(complement(X)), join(complement(join(complement(X), meet(X, Y))), complement(X))))
% 278.04/36.16 = { by lemma 33 R->L }
% 278.04/36.16 complement(meet(complement(complement(X)), join(complement(join(complement(X), meet(X, Y))), complement(join(meet(X, Y), complement(join(complement(X), meet(X, Y))))))))
% 278.04/36.16 = { by lemma 27 R->L }
% 278.04/36.16 complement(meet(complement(complement(X)), ifeq(meet(meet(X, Y), complement(join(complement(X), meet(X, Y)))), zero, complement(meet(X, Y)), join(complement(join(complement(X), meet(X, Y))), complement(join(meet(X, Y), complement(join(complement(X), meet(X, Y)))))))))
% 278.04/36.16 = { by lemma 33 }
% 278.04/36.16 complement(meet(complement(complement(X)), ifeq(meet(meet(X, Y), complement(join(complement(X), meet(X, Y)))), zero, complement(meet(X, Y)), join(complement(join(complement(X), meet(X, Y))), complement(X)))))
% 278.04/36.16 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.16 complement(meet(complement(complement(X)), ifeq(meet(X, meet(Y, complement(join(complement(X), meet(X, Y))))), zero, complement(meet(X, Y)), join(complement(join(complement(X), meet(X, Y))), complement(X)))))
% 278.04/36.16 = { by lemma 35 }
% 278.04/36.16 complement(meet(complement(complement(X)), ifeq(zero, zero, complement(meet(X, Y)), join(complement(join(complement(X), meet(X, Y))), complement(X)))))
% 278.04/36.16 = { by axiom 7 (ifeq_axiom) }
% 278.04/36.16 complement(meet(complement(complement(X)), complement(meet(X, Y))))
% 278.04/36.16 = { by lemma 17 }
% 278.04/36.16 complement(meet(X, complement(meet(X, Y))))
% 278.04/36.16 = { by lemma 34 }
% 278.04/36.16 complement(meet(X, complement(Y)))
% 278.04/36.16
% 278.04/36.16 Lemma 38: join(X, join(Y, meet(Z, X))) = join(X, Y).
% 278.04/36.16 Proof:
% 278.04/36.16 join(X, join(Y, meet(Z, X)))
% 278.04/36.16 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.16 join(join(Y, meet(Z, X)), X)
% 278.04/36.17 = { by axiom 9 (associativity_of_join) }
% 278.04/36.17 join(Y, join(meet(Z, X), X))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(Y, join(X, meet(Z, X)))
% 278.04/36.17 = { by lemma 20 }
% 278.04/36.17 join(Y, X)
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(X, Y)
% 278.04/36.17
% 278.04/36.17 Lemma 39: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 278.04/36.17 Proof:
% 278.04/36.17 complement(meet(complement(X), Y))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 complement(meet(Y, complement(X)))
% 278.04/36.17 = { by lemma 20 R->L }
% 278.04/36.17 join(complement(meet(Y, complement(X))), meet(X, complement(meet(Y, complement(X)))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(complement(meet(Y, complement(X))), meet(complement(meet(Y, complement(X))), X))
% 278.04/36.17 = { by lemma 17 R->L }
% 278.04/36.17 join(complement(meet(Y, complement(X))), meet(complement(meet(Y, complement(X))), complement(complement(X))))
% 278.04/36.17 = { by lemma 28 R->L }
% 278.04/36.17 join(complement(meet(Y, complement(X))), meet(complement(meet(Y, complement(X))), complement(join(meet(Y, complement(X)), complement(join(X, meet(Y, complement(X))))))))
% 278.04/36.17 = { by lemma 32 }
% 278.04/36.17 join(complement(meet(Y, complement(X))), complement(join(meet(Y, complement(X)), complement(join(X, meet(Y, complement(X)))))))
% 278.04/36.17 = { by lemma 28 }
% 278.04/36.17 join(complement(meet(Y, complement(X))), complement(complement(X)))
% 278.04/36.17 = { by lemma 17 }
% 278.04/36.17 join(complement(meet(Y, complement(X))), X)
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(X, complement(meet(Y, complement(X))))
% 278.04/36.17 = { by lemma 37 R->L }
% 278.04/36.17 join(X, join(complement(Y), meet(Y, X)))
% 278.04/36.17 = { by lemma 38 }
% 278.04/36.17 join(X, complement(Y))
% 278.04/36.17
% 278.04/36.17 Lemma 40: meet(join(X, Y), join(X, meet(join(X, Y), Z))) = join(X, meet(Z, join(X, Y))).
% 278.04/36.17 Proof:
% 278.04/36.17 meet(join(X, Y), join(X, meet(join(X, Y), Z)))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 meet(join(X, Y), join(X, meet(Z, join(X, Y))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.17 meet(join(Y, X), join(X, meet(Z, join(X, Y))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.17 meet(join(Y, X), join(X, meet(Z, join(Y, X))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 meet(join(X, meet(Z, join(Y, X))), join(Y, X))
% 278.04/36.17 = { by axiom 8 (absorption2) R->L }
% 278.04/36.17 meet(join(X, meet(Z, join(Y, X))), join(join(Y, X), meet(join(Y, X), Z)))
% 278.04/36.17 = { by axiom 9 (associativity_of_join) }
% 278.04/36.17 meet(join(X, meet(Z, join(Y, X))), join(Y, join(X, meet(join(Y, X), Z))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.17 meet(join(X, meet(Z, join(Y, X))), join(Y, join(X, meet(Z, join(Y, X)))))
% 278.04/36.17 = { by lemma 19 }
% 278.04/36.17 join(X, meet(Z, join(Y, X)))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(X, meet(Z, join(X, Y)))
% 278.04/36.17
% 278.04/36.17 Lemma 41: join(X, meet(Y, meet(Z, complement(X)))) = join(X, meet(Y, Z)).
% 278.04/36.17 Proof:
% 278.04/36.17 join(X, meet(Y, meet(Z, complement(X))))
% 278.04/36.17 = { by lemma 18 R->L }
% 278.04/36.17 join(X, meet(Z, meet(Y, complement(X))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.17 join(meet(Z, meet(Y, complement(X))), X)
% 278.04/36.17 = { by lemma 17 R->L }
% 278.04/36.17 join(meet(Z, meet(Y, complement(X))), complement(complement(X)))
% 278.04/36.17 = { by lemma 39 R->L }
% 278.04/36.17 complement(meet(complement(meet(Z, meet(Y, complement(X)))), complement(X)))
% 278.04/36.17 = { by lemma 36 R->L }
% 278.04/36.17 join(X, complement(join(X, meet(complement(X), complement(meet(Z, meet(Y, complement(X))))))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(X, complement(join(X, meet(complement(X), complement(meet(Z, meet(complement(X), Y)))))))
% 278.04/36.17 = { by lemma 18 R->L }
% 278.04/36.17 join(X, complement(join(X, meet(complement(X), complement(meet(complement(X), meet(Z, Y)))))))
% 278.04/36.17 = { by lemma 34 }
% 278.04/36.17 join(X, complement(join(X, meet(complement(X), complement(meet(Z, Y))))))
% 278.04/36.17 = { by lemma 36 }
% 278.04/36.17 complement(meet(complement(meet(Z, Y)), complement(X)))
% 278.04/36.17 = { by lemma 39 }
% 278.04/36.17 join(meet(Z, Y), complement(complement(X)))
% 278.04/36.17 = { by lemma 17 }
% 278.04/36.17 join(meet(Z, Y), X)
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(X, meet(Z, Y))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.17 join(X, meet(Y, Z))
% 278.04/36.17
% 278.04/36.17 Lemma 42: join(meet(X, Y), meet(X, join(Z, meet(X, Y)))) = meet(X, join(Z, meet(X, Y))).
% 278.04/36.17 Proof:
% 278.04/36.17 join(meet(X, Y), meet(X, join(Z, meet(X, Y))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(meet(Y, X), meet(X, join(Z, meet(X, Y))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(meet(Y, X), meet(X, join(Z, meet(Y, X))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.17 join(meet(X, join(Z, meet(Y, X))), meet(Y, X))
% 278.04/36.17 = { by axiom 10 (absorption1) R->L }
% 278.04/36.17 join(meet(X, join(Z, meet(Y, X))), meet(meet(Y, X), join(meet(Y, X), Z)))
% 278.04/36.17 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.17 join(meet(X, join(Z, meet(Y, X))), meet(Y, meet(X, join(meet(Y, X), Z))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(meet(X, join(Z, meet(Y, X))), meet(Y, meet(X, join(Z, meet(Y, X)))))
% 278.04/36.17 = { by lemma 20 }
% 278.04/36.17 meet(X, join(Z, meet(Y, X)))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.17 meet(X, join(Z, meet(X, Y)))
% 278.04/36.17
% 278.04/36.17 Lemma 43: join(X, meet(Y, join(X, Z))) = join(X, meet(Y, Z)).
% 278.04/36.17 Proof:
% 278.04/36.17 join(X, meet(Y, join(X, Z)))
% 278.04/36.17 = { by lemma 40 R->L }
% 278.04/36.17 meet(join(X, Z), join(X, meet(join(X, Z), Y)))
% 278.04/36.17 = { by lemma 41 R->L }
% 278.04/36.17 meet(join(X, Z), join(X, meet(join(X, Z), meet(Y, complement(X)))))
% 278.04/36.17 = { by lemma 40 }
% 278.04/36.17 join(X, meet(meet(Y, complement(X)), join(X, Z)))
% 278.04/36.17 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), join(X, Z))))
% 278.04/36.17 = { by lemma 20 R->L }
% 278.04/36.17 join(X, meet(Y, join(meet(complement(X), join(X, Z)), meet(Z, meet(complement(X), join(X, Z))))))
% 278.04/36.17 = { by lemma 22 }
% 278.04/36.17 join(X, meet(Y, join(meet(complement(X), join(X, Z)), meet(Z, complement(X)))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(X, meet(Y, join(meet(Z, complement(X)), meet(complement(X), join(X, Z)))))
% 278.04/36.17 = { by lemma 33 R->L }
% 278.04/36.17 join(X, meet(Y, join(meet(Z, complement(X)), meet(complement(X), join(X, join(meet(Z, X), complement(join(complement(Z), meet(Z, X)))))))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.17 join(X, meet(Y, join(meet(Z, complement(X)), meet(complement(X), join(X, join(complement(join(complement(Z), meet(Z, X))), meet(Z, X)))))))
% 278.04/36.17 = { by lemma 38 }
% 278.04/36.17 join(X, meet(Y, join(meet(Z, complement(X)), meet(complement(X), join(X, complement(join(complement(Z), meet(Z, X))))))))
% 278.04/36.17 = { by lemma 37 }
% 278.04/36.17 join(X, meet(Y, join(meet(Z, complement(X)), meet(complement(X), join(X, complement(complement(meet(Z, complement(X)))))))))
% 278.04/36.17 = { by lemma 17 }
% 278.04/36.17 join(X, meet(Y, join(meet(Z, complement(X)), meet(complement(X), join(X, meet(Z, complement(X)))))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(X, meet(Y, join(meet(Z, complement(X)), meet(complement(X), join(X, meet(complement(X), Z))))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(X, meet(Y, join(meet(complement(X), Z), meet(complement(X), join(X, meet(complement(X), Z))))))
% 278.04/36.17 = { by lemma 42 }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), join(X, meet(complement(X), Z)))))
% 278.04/36.17 = { by lemma 17 R->L }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), join(complement(complement(X)), meet(complement(X), Z)))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), join(complement(complement(X)), meet(Z, complement(X))))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), join(meet(Z, complement(X)), complement(complement(X))))))
% 278.04/36.17 = { by lemma 20 R->L }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), join(meet(Z, complement(X)), complement(join(complement(X), meet(Z, complement(X))))))))
% 278.04/36.17 = { by lemma 26 }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), meet(Z, complement(X)))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), meet(complement(X), Z))))
% 278.04/36.17 = { by axiom 11 (associativity_of_meet) R->L }
% 278.04/36.17 join(X, meet(Y, meet(meet(complement(X), complement(X)), Z)))
% 278.04/36.17 = { by axiom 3 (idempotence_of_meet) }
% 278.04/36.17 join(X, meet(Y, meet(complement(X), Z)))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.17 join(X, meet(Y, meet(Z, complement(X))))
% 278.04/36.17 = { by lemma 41 }
% 278.04/36.17 join(X, meet(Y, Z))
% 278.04/36.17
% 278.04/36.17 Lemma 44: meet(join(X, Y), join(Y, meet(X, Z))) = join(Y, meet(X, Z)).
% 278.04/36.17 Proof:
% 278.04/36.17 meet(join(X, Y), join(Y, meet(X, Z)))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 meet(join(Y, meet(X, Z)), join(X, Y))
% 278.04/36.17 = { by axiom 8 (absorption2) R->L }
% 278.04/36.17 meet(join(Y, meet(X, Z)), join(join(X, meet(X, Z)), Y))
% 278.04/36.17 = { by axiom 9 (associativity_of_join) }
% 278.04/36.17 meet(join(Y, meet(X, Z)), join(X, join(meet(X, Z), Y)))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 meet(join(Y, meet(X, Z)), join(X, join(Y, meet(X, Z))))
% 278.04/36.17 = { by lemma 19 }
% 278.04/36.17 join(Y, meet(X, Z))
% 278.04/36.17
% 278.04/36.17 Goal 1 (prove_distributivity): meet(a, join(b, c)) = join(meet(a, b), meet(a, c)).
% 278.04/36.17 Proof:
% 278.04/36.17 meet(a, join(b, c))
% 278.04/36.17 = { by lemma 19 R->L }
% 278.04/36.17 meet(meet(a, join(b, c)), join(b, meet(a, join(b, c))))
% 278.04/36.17 = { by lemma 43 }
% 278.04/36.17 meet(meet(a, join(b, c)), join(b, meet(a, c)))
% 278.04/36.17 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.17 meet(a, meet(join(b, c), join(b, meet(a, c))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) R->L }
% 278.04/36.17 meet(a, meet(join(c, b), join(b, meet(a, c))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 meet(a, meet(join(b, meet(a, c)), join(c, b)))
% 278.04/36.17 = { by lemma 44 R->L }
% 278.04/36.17 meet(a, meet(meet(join(a, b), join(b, meet(a, c))), join(c, b)))
% 278.04/36.17 = { by axiom 11 (associativity_of_meet) }
% 278.04/36.17 meet(a, meet(join(a, b), meet(join(b, meet(a, c)), join(c, b))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.17 meet(a, meet(join(a, b), meet(join(c, b), join(b, meet(a, c)))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 meet(a, meet(join(b, a), meet(join(c, b), join(b, meet(a, c)))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 278.04/36.17 meet(a, meet(join(b, a), meet(join(b, meet(a, c)), join(c, b))))
% 278.04/36.17 = { by lemma 38 R->L }
% 278.04/36.17 meet(a, meet(join(b, a), meet(join(b, meet(a, c)), join(c, join(b, meet(a, c))))))
% 278.04/36.17 = { by lemma 19 }
% 278.04/36.17 meet(a, meet(join(b, a), join(b, meet(a, c))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.17 meet(a, meet(join(b, a), join(b, meet(c, a))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 meet(a, meet(join(a, b), join(b, meet(c, a))))
% 278.04/36.17 = { by axiom 4 (commutativity_of_meet) }
% 278.04/36.17 meet(a, meet(join(a, b), join(b, meet(a, c))))
% 278.04/36.17 = { by lemma 44 }
% 278.04/36.17 meet(a, join(b, meet(a, c)))
% 278.04/36.17 = { by lemma 42 R->L }
% 278.04/36.17 join(meet(a, c), meet(a, join(b, meet(a, c))))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(meet(a, c), meet(a, join(meet(a, c), b)))
% 278.04/36.17 = { by lemma 43 }
% 278.04/36.17 join(meet(a, c), meet(a, b))
% 278.04/36.17 = { by axiom 2 (commutativity_of_join) }
% 278.04/36.17 join(meet(a, b), meet(a, c))
% 278.04/36.17 % SZS output end Proof
% 278.04/36.17
% 278.04/36.17 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------