%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT185-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:44:30 AM UTC 2026
% Result : Unsatisfiable 106.82s 13.99s
% Output : Proof 108.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT185-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 14:05:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.82/13.99 Command-line arguments: --no-flatten-goal
% 106.82/13.99
% 106.82/13.99 % SZS status Unsatisfiable
% 106.82/13.99
% 107.58/14.11 % SZS output start Proof
% 107.58/14.11 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 107.58/14.11 Axiom 2 (complement_join): join(X, complement(X)) = one.
% 107.58/14.11 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 107.58/14.11 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 107.58/14.11 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 107.58/14.11 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 107.58/14.11 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 107.58/14.11 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 107.58/14.11 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 107.58/14.11 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 107.58/14.11 Axiom 11 (equation_H10): meet(X, join(Y, meet(X, Z))) = meet(X, join(Y, meet(Z, join(X, meet(Y, Z))))).
% 107.58/14.11 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 107.58/14.11
% 107.58/14.11 Lemma 13: meet(X, one) = X.
% 107.58/14.11 Proof:
% 107.58/14.11 meet(X, one)
% 107.58/14.11 = { by axiom 2 (complement_join) R->L }
% 107.58/14.11 meet(X, join(X, complement(X)))
% 107.58/14.11 = { by axiom 9 (absorption1) }
% 107.58/14.11 X
% 107.58/14.11
% 107.58/14.11 Lemma 14: meet(one, X) = X.
% 107.58/14.11 Proof:
% 107.58/14.11 meet(one, X)
% 107.58/14.11 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.11 meet(X, one)
% 107.58/14.11 = { by lemma 13 }
% 107.58/14.11 X
% 107.58/14.11
% 107.58/14.11 Lemma 15: join(X, one) = one.
% 107.58/14.11 Proof:
% 107.58/14.11 join(X, one)
% 107.58/14.11 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.11 join(one, X)
% 107.58/14.11 = { by lemma 14 R->L }
% 107.58/14.11 join(one, meet(one, X))
% 107.58/14.11 = { by axiom 7 (absorption2) }
% 107.58/14.11 one
% 107.58/14.11
% 107.58/14.11 Lemma 16: ifeq(join(X, Y), one, ifeq(meet(Y, X), zero, complement(Y), X), X) = X.
% 107.58/14.11 Proof:
% 107.58/14.11 ifeq(join(X, Y), one, ifeq(meet(Y, X), zero, complement(Y), X), X)
% 107.58/14.11 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.11 ifeq(join(Y, X), one, ifeq(meet(Y, X), zero, complement(Y), X), X)
% 107.58/14.11 = { by axiom 12 (meet_join_complement) }
% 107.58/14.11 X
% 107.58/14.11
% 107.58/14.11 Lemma 17: complement(complement(X)) = X.
% 107.58/14.11 Proof:
% 107.58/14.11 complement(complement(X))
% 107.58/14.11 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.11 ifeq(zero, zero, complement(complement(X)), X)
% 107.58/14.11 = { by axiom 5 (complement_meet) R->L }
% 107.58/14.11 ifeq(meet(X, complement(X)), zero, complement(complement(X)), X)
% 107.58/14.11 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.11 ifeq(meet(complement(X), X), zero, complement(complement(X)), X)
% 107.58/14.11 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.11 ifeq(one, one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 107.58/14.11 = { by axiom 2 (complement_join) R->L }
% 107.58/14.11 ifeq(join(X, complement(X)), one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 107.58/14.11 = { by lemma 16 }
% 107.58/14.11 X
% 107.58/14.11
% 107.58/14.11 Lemma 18: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 107.58/14.11 Proof:
% 107.58/14.11 meet(X, meet(Y, Z))
% 107.58/14.11 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.11 meet(meet(Y, Z), X)
% 107.58/14.11 = { by axiom 10 (associativity_of_meet) }
% 107.58/14.11 meet(Y, meet(Z, X))
% 107.58/14.11 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.11 meet(Y, meet(X, Z))
% 107.58/14.11
% 107.58/14.11 Lemma 19: meet(X, join(Y, X)) = X.
% 107.58/14.11 Proof:
% 107.58/14.11 meet(X, join(Y, X))
% 107.58/14.11 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.11 meet(X, join(X, Y))
% 107.58/14.11 = { by axiom 9 (absorption1) }
% 107.58/14.11 X
% 107.58/14.11
% 107.58/14.11 Lemma 20: meet(X, meet(Y, join(Z, X))) = meet(X, Y).
% 107.58/14.11 Proof:
% 107.58/14.11 meet(X, meet(Y, join(Z, X)))
% 107.58/14.11 = { by lemma 18 R->L }
% 107.58/14.11 meet(Y, meet(X, join(Z, X)))
% 107.58/14.11 = { by lemma 19 }
% 107.58/14.11 meet(Y, X)
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.12 meet(X, Y)
% 107.58/14.12
% 107.58/14.12 Lemma 21: join(X, meet(Y, X)) = X.
% 107.58/14.12 Proof:
% 107.58/14.12 join(X, meet(Y, X))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 join(X, meet(X, Y))
% 107.58/14.12 = { by axiom 7 (absorption2) }
% 107.58/14.12 X
% 107.58/14.12
% 107.58/14.12 Lemma 22: join(meet(X, Y), meet(X, join(Z, Y))) = meet(X, join(Z, Y)).
% 107.58/14.12 Proof:
% 107.58/14.12 join(meet(X, Y), meet(X, join(Z, Y)))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 join(meet(Y, X), meet(X, join(Z, Y)))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(meet(X, join(Z, Y)), meet(Y, X))
% 107.58/14.12 = { by lemma 20 R->L }
% 107.58/14.12 join(meet(X, join(Z, Y)), meet(Y, meet(X, join(Z, Y))))
% 107.58/14.12 = { by lemma 21 }
% 107.58/14.12 meet(X, join(Z, Y))
% 107.58/14.12
% 107.58/14.12 Lemma 23: join(X, meet(join(X, Y), complement(meet(X, Y)))) = join(X, meet(Y, complement(meet(X, Y)))).
% 107.58/14.12 Proof:
% 107.58/14.12 join(X, meet(join(X, Y), complement(meet(X, Y))))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(X, meet(join(Y, X), complement(meet(X, Y))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 join(X, meet(complement(meet(X, Y)), join(Y, X)))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(X, meet(complement(meet(X, Y)), join(X, Y)))
% 107.58/14.12 = { by lemma 22 R->L }
% 107.58/14.12 join(X, join(meet(complement(meet(X, Y)), Y), meet(complement(meet(X, Y)), join(X, Y))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.12 join(X, join(meet(Y, complement(meet(X, Y))), meet(complement(meet(X, Y)), join(X, Y))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.12 join(X, join(meet(Y, complement(meet(X, Y))), meet(join(X, Y), complement(meet(X, Y)))))
% 107.58/14.12 = { by axiom 8 (associativity_of_join) R->L }
% 107.58/14.12 join(join(X, meet(Y, complement(meet(X, Y)))), meet(join(X, Y), complement(meet(X, Y))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 join(join(X, meet(Y, complement(meet(X, Y)))), meet(complement(meet(X, Y)), join(X, Y)))
% 107.58/14.12 = { by lemma 13 R->L }
% 107.58/14.12 join(join(X, meet(Y, complement(meet(X, Y)))), meet(complement(meet(X, Y)), join(X, meet(Y, one))))
% 107.58/14.12 = { by axiom 2 (complement_join) R->L }
% 107.58/14.12 join(join(X, meet(Y, complement(meet(X, Y)))), meet(complement(meet(X, Y)), join(X, meet(Y, join(meet(X, Y), complement(meet(X, Y)))))))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(join(X, meet(Y, complement(meet(X, Y)))), meet(complement(meet(X, Y)), join(X, meet(Y, join(complement(meet(X, Y)), meet(X, Y))))))
% 107.58/14.12 = { by axiom 11 (equation_H10) R->L }
% 107.58/14.12 join(join(X, meet(Y, complement(meet(X, Y)))), meet(complement(meet(X, Y)), join(X, meet(complement(meet(X, Y)), Y))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.12 join(join(X, meet(Y, complement(meet(X, Y)))), meet(complement(meet(X, Y)), join(X, meet(Y, complement(meet(X, Y))))))
% 107.58/14.12 = { by lemma 21 }
% 107.58/14.12 join(X, meet(Y, complement(meet(X, Y))))
% 107.58/14.12
% 107.58/14.12 Lemma 24: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 107.58/14.12 Proof:
% 107.58/14.12 join(X, join(Y, meet(X, Z)))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(X, join(meet(X, Z), Y))
% 107.58/14.12 = { by axiom 8 (associativity_of_join) R->L }
% 107.58/14.12 join(join(X, meet(X, Z)), Y)
% 107.58/14.12 = { by axiom 7 (absorption2) }
% 107.58/14.12 join(X, Y)
% 107.58/14.12
% 107.58/14.12 Lemma 25: join(X, complement(meet(X, Y))) = one.
% 107.58/14.12 Proof:
% 107.58/14.12 join(X, complement(meet(X, Y)))
% 107.58/14.12 = { by lemma 24 R->L }
% 107.58/14.12 join(X, join(complement(meet(X, Y)), meet(X, Y)))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.12 join(X, join(meet(X, Y), complement(meet(X, Y))))
% 107.58/14.12 = { by axiom 2 (complement_join) }
% 107.58/14.12 join(X, one)
% 107.58/14.12 = { by lemma 15 }
% 107.58/14.12 one
% 107.58/14.12
% 107.58/14.12 Lemma 26: meet(X, meet(Y, complement(meet(X, Y)))) = zero.
% 107.58/14.12 Proof:
% 107.58/14.12 meet(X, meet(Y, complement(meet(X, Y))))
% 107.58/14.12 = { by axiom 10 (associativity_of_meet) R->L }
% 107.58/14.12 meet(meet(X, Y), complement(meet(X, Y)))
% 107.58/14.12 = { by axiom 5 (complement_meet) }
% 107.58/14.12 zero
% 107.58/14.12
% 107.58/14.12 Lemma 27: meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))) = complement(X).
% 107.58/14.12 Proof:
% 107.58/14.12 meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))
% 107.58/14.12 = { by axiom 12 (meet_join_complement) R->L }
% 107.58/14.12 ifeq(join(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 ifeq(join(X, meet(complement(meet(Y, X)), complement(meet(X, complement(meet(X, Y)))))), one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 ifeq(join(X, meet(complement(meet(Y, X)), complement(meet(X, complement(meet(Y, X)))))), one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by lemma 23 R->L }
% 107.58/14.12 ifeq(join(X, meet(join(X, complement(meet(Y, X))), complement(meet(X, complement(meet(Y, X)))))), one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 ifeq(join(X, meet(join(X, complement(meet(X, Y))), complement(meet(X, complement(meet(Y, X)))))), one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by lemma 25 }
% 107.58/14.12 ifeq(join(X, meet(one, complement(meet(X, complement(meet(Y, X)))))), one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by lemma 14 }
% 107.58/14.12 ifeq(join(X, complement(meet(X, complement(meet(Y, X))))), one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by lemma 25 }
% 107.58/14.12 ifeq(one, one, ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by axiom 6 (ifeq_axiom) }
% 107.58/14.12 ifeq(meet(X, meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))), zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by lemma 26 }
% 107.58/14.12 ifeq(zero, zero, complement(X), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by axiom 6 (ifeq_axiom) }
% 107.58/14.12 complement(X)
% 107.58/14.12
% 107.58/14.12 Lemma 28: join(complement(X), complement(meet(X, Y))) = complement(meet(X, Y)).
% 107.58/14.12 Proof:
% 107.58/14.12 join(complement(X), complement(meet(X, Y)))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(complement(meet(X, Y)), complement(X))
% 107.58/14.12 = { by lemma 27 R->L }
% 107.58/14.12 join(complement(meet(X, Y)), meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by axiom 7 (absorption2) }
% 107.58/14.12 complement(meet(X, Y))
% 107.58/14.12
% 107.58/14.12 Lemma 29: join(complement(complement(X)), complement(complement(meet(X, Y)))) = complement(complement(X)).
% 107.58/14.12 Proof:
% 107.58/14.12 join(complement(complement(X)), complement(complement(meet(X, Y))))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(complement(complement(meet(X, Y))), complement(complement(X)))
% 107.58/14.12 = { by lemma 27 R->L }
% 107.58/14.12 join(complement(complement(meet(X, Y))), complement(meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y)))))))
% 107.58/14.12 = { by lemma 28 }
% 107.58/14.12 complement(meet(complement(meet(X, Y)), complement(meet(X, complement(meet(X, Y))))))
% 107.58/14.12 = { by lemma 27 }
% 107.58/14.12 complement(complement(X))
% 107.58/14.12
% 107.58/14.12 Lemma 30: join(X, join(Y, complement(X))) = one.
% 107.58/14.12 Proof:
% 107.58/14.12 join(X, join(Y, complement(X)))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(X, join(complement(X), Y))
% 107.58/14.12 = { by axiom 8 (associativity_of_join) R->L }
% 107.58/14.12 join(join(X, complement(X)), Y)
% 107.58/14.12 = { by axiom 2 (complement_join) }
% 107.58/14.12 join(one, Y)
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(Y, one)
% 107.58/14.12 = { by lemma 15 }
% 107.58/14.12 one
% 107.58/14.12
% 107.58/14.12 Lemma 31: meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))) = complement(Y).
% 107.58/14.12 Proof:
% 107.58/14.12 meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))
% 107.58/14.12 = { by axiom 12 (meet_join_complement) R->L }
% 107.58/14.12 ifeq(join(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), one, ifeq(meet(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.12 = { by lemma 23 R->L }
% 107.58/14.12 ifeq(join(Y, meet(join(Y, join(X, complement(Y))), complement(meet(Y, join(X, complement(Y)))))), one, ifeq(meet(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.12 = { by lemma 30 }
% 107.58/14.12 ifeq(join(Y, meet(one, complement(meet(Y, join(X, complement(Y)))))), one, ifeq(meet(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.12 = { by lemma 14 }
% 107.58/14.12 ifeq(join(Y, complement(meet(Y, join(X, complement(Y))))), one, ifeq(meet(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.12 = { by lemma 25 }
% 107.58/14.12 ifeq(one, one, ifeq(meet(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.12 = { by axiom 6 (ifeq_axiom) }
% 107.58/14.12 ifeq(meet(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.12 = { by lemma 26 }
% 107.58/14.12 ifeq(zero, zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.12 = { by axiom 6 (ifeq_axiom) }
% 107.58/14.12 complement(Y)
% 107.58/14.12
% 107.58/14.12 Lemma 32: meet(join(X, Y), complement(meet(complement(Y), join(X, Y)))) = Y.
% 107.58/14.12 Proof:
% 107.58/14.12 meet(join(X, Y), complement(meet(complement(Y), join(X, Y))))
% 107.58/14.12 = { by lemma 17 R->L }
% 107.58/14.12 meet(join(X, Y), complement(meet(complement(Y), join(X, complement(complement(Y))))))
% 107.58/14.12 = { by lemma 17 R->L }
% 107.58/14.12 meet(join(X, complement(complement(Y))), complement(meet(complement(Y), join(X, complement(complement(Y))))))
% 107.58/14.12 = { by lemma 31 }
% 107.58/14.12 complement(complement(Y))
% 107.58/14.12 = { by lemma 17 }
% 107.58/14.12 Y
% 107.58/14.12
% 107.58/14.12 Lemma 33: meet(complement(X), complement(meet(complement(X), join(X, Y)))) = complement(join(X, Y)).
% 107.58/14.12 Proof:
% 107.58/14.12 meet(complement(X), complement(meet(complement(X), join(X, Y))))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 meet(complement(X), complement(meet(complement(X), join(Y, X))))
% 107.58/14.12 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.12 meet(complement(X), complement(meet(join(Y, X), complement(X))))
% 107.58/14.12 = { by lemma 32 R->L }
% 107.58/14.12 meet(complement(X), complement(meet(join(Y, X), complement(meet(join(Y, X), complement(meet(complement(X), join(Y, X))))))))
% 107.58/14.12 = { by lemma 32 R->L }
% 107.58/14.12 meet(complement(meet(join(Y, X), complement(meet(complement(X), join(Y, X))))), complement(meet(join(Y, X), complement(meet(join(Y, X), complement(meet(complement(X), join(Y, X))))))))
% 107.58/14.12 = { by lemma 27 }
% 107.58/14.12 complement(join(Y, X))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.12 complement(join(X, Y))
% 107.58/14.12
% 107.58/14.12 Lemma 34: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 107.58/14.12 Proof:
% 107.58/14.12 join(Y, join(X, Z))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.12 join(join(X, Z), Y)
% 107.58/14.12 = { by axiom 8 (associativity_of_join) }
% 107.58/14.12 join(X, join(Z, Y))
% 107.58/14.12 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.12 join(X, join(Y, Z))
% 107.58/14.12
% 107.58/14.12 Lemma 35: join(X, join(Y, meet(Z, join(X, Y)))) = join(X, Y).
% 107.58/14.13 Proof:
% 107.58/14.13 join(X, join(Y, meet(Z, join(X, Y))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 join(X, join(Y, meet(Z, join(Y, X))))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.13 join(X, join(Y, meet(join(Y, X), Z)))
% 107.58/14.13 = { by lemma 34 }
% 107.58/14.13 join(Y, join(X, meet(join(Y, X), Z)))
% 107.58/14.13 = { by axiom 8 (associativity_of_join) R->L }
% 107.58/14.13 join(join(Y, X), meet(join(Y, X), Z))
% 107.58/14.13 = { by axiom 7 (absorption2) }
% 107.58/14.13 join(Y, X)
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.13 join(X, Y)
% 107.58/14.13
% 107.58/14.13 Lemma 36: meet(X, meet(Y, join(Z, meet(X, Y)))) = meet(X, Y).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(X, meet(Y, join(Z, meet(X, Y))))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.13 meet(X, meet(Y, join(Z, meet(Y, X))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 meet(X, meet(Y, join(meet(Y, X), Z)))
% 107.58/14.13 = { by lemma 18 R->L }
% 107.58/14.13 meet(Y, meet(X, join(meet(Y, X), Z)))
% 107.58/14.13 = { by axiom 10 (associativity_of_meet) R->L }
% 107.58/14.13 meet(meet(Y, X), join(meet(Y, X), Z))
% 107.58/14.13 = { by axiom 9 (absorption1) }
% 107.58/14.13 meet(Y, X)
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 meet(X, Y)
% 107.58/14.13
% 107.58/14.13 Lemma 37: meet(X, join(Y, meet(X, join(Y, Z)))) = meet(X, join(Y, Z)).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(X, join(Y, meet(X, join(Y, Z))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 meet(X, join(Y, meet(X, join(Z, Y))))
% 107.58/14.13 = { by lemma 19 R->L }
% 107.58/14.13 meet(X, meet(join(Y, meet(X, join(Z, Y))), join(Z, join(Y, meet(X, join(Z, Y))))))
% 107.58/14.13 = { by lemma 35 }
% 107.58/14.13 meet(X, meet(join(Y, meet(X, join(Z, Y))), join(Z, Y)))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 meet(X, meet(join(Z, Y), join(Y, meet(X, join(Z, Y)))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.13 meet(X, meet(join(Z, Y), join(Y, meet(X, join(Y, Z)))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.13 meet(X, meet(join(Y, Z), join(Y, meet(X, join(Y, Z)))))
% 107.58/14.13 = { by lemma 36 }
% 107.58/14.13 meet(X, join(Y, Z))
% 107.58/14.13
% 107.58/14.13 Lemma 38: join(X, join(Y, meet(Z, X))) = join(X, Y).
% 107.58/14.13 Proof:
% 107.58/14.13 join(X, join(Y, meet(Z, X)))
% 107.58/14.13 = { by lemma 34 }
% 107.58/14.13 join(Y, join(X, meet(Z, X)))
% 107.58/14.13 = { by lemma 21 }
% 107.58/14.13 join(Y, X)
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.13 join(X, Y)
% 107.58/14.13
% 107.58/14.13 Lemma 39: ifeq(join(X, Y), one, complement(meet(X, complement(meet(X, Y)))), Y) = Y.
% 107.58/14.13 Proof:
% 107.58/14.13 ifeq(join(X, Y), one, complement(meet(X, complement(meet(X, Y)))), Y)
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.13 ifeq(join(X, Y), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 ifeq(join(Y, X), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 107.58/14.13 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.13 ifeq(join(Y, X), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 17 R->L }
% 107.58/14.13 ifeq(join(Y, complement(complement(X))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 29 R->L }
% 107.58/14.13 ifeq(join(Y, join(complement(complement(X)), complement(complement(meet(X, Y))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 ifeq(join(Y, join(complement(complement(meet(X, Y))), complement(complement(X)))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 17 R->L }
% 107.58/14.13 ifeq(join(Y, complement(complement(join(complement(complement(meet(X, Y))), complement(complement(X)))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 33 R->L }
% 107.58/14.13 ifeq(join(Y, complement(meet(complement(complement(complement(meet(X, Y)))), complement(meet(complement(complement(complement(meet(X, Y)))), join(complement(complement(meet(X, Y))), complement(complement(X)))))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 37 R->L }
% 107.58/14.13 ifeq(join(Y, complement(meet(complement(complement(complement(meet(X, Y)))), complement(meet(complement(complement(complement(meet(X, Y)))), join(complement(complement(meet(X, Y))), meet(complement(complement(complement(meet(X, Y)))), join(complement(complement(meet(X, Y))), complement(complement(X)))))))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 33 }
% 107.58/14.13 ifeq(join(Y, complement(complement(join(complement(complement(meet(X, Y))), meet(complement(complement(complement(meet(X, Y)))), join(complement(complement(meet(X, Y))), complement(complement(X)))))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 17 }
% 107.58/14.13 ifeq(join(Y, join(complement(complement(meet(X, Y))), meet(complement(complement(complement(meet(X, Y)))), join(complement(complement(meet(X, Y))), complement(complement(X)))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 17 }
% 107.58/14.13 ifeq(join(Y, join(complement(complement(meet(X, Y))), meet(complement(meet(X, Y)), join(complement(complement(meet(X, Y))), complement(complement(X)))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.13 ifeq(join(Y, join(complement(complement(meet(X, Y))), meet(complement(meet(X, Y)), join(complement(complement(X)), complement(complement(meet(X, Y))))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 29 }
% 107.58/14.13 ifeq(join(Y, join(complement(complement(meet(X, Y))), meet(complement(meet(X, Y)), complement(complement(X))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 17 }
% 107.58/14.13 ifeq(join(Y, join(meet(X, Y), meet(complement(meet(X, Y)), complement(complement(X))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 17 }
% 107.58/14.13 ifeq(join(Y, join(meet(X, Y), meet(complement(meet(X, Y)), X))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 ifeq(join(Y, join(meet(X, Y), meet(X, complement(meet(X, Y))))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 ifeq(join(Y, join(meet(X, complement(meet(X, Y))), meet(X, Y))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 38 }
% 107.58/14.13 ifeq(join(Y, meet(X, complement(meet(X, Y)))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 ifeq(join(Y, meet(X, complement(meet(Y, X)))), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 26 R->L }
% 107.58/14.13 ifeq(join(Y, meet(X, complement(meet(Y, X)))), one, ifeq(meet(Y, meet(X, complement(meet(Y, X)))), zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.13 ifeq(join(Y, meet(X, complement(meet(Y, X)))), one, ifeq(meet(meet(X, complement(meet(Y, X))), Y), zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 107.58/14.13 = { by lemma 16 }
% 107.58/14.13 Y
% 107.58/14.13
% 107.58/14.13 Lemma 40: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(X, meet(Y, join(X, Z)))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.13 meet(X, meet(join(X, Z), Y))
% 107.58/14.13 = { by axiom 10 (associativity_of_meet) R->L }
% 107.58/14.13 meet(meet(X, join(X, Z)), Y)
% 107.58/14.13 = { by axiom 9 (absorption1) }
% 107.58/14.13 meet(X, Y)
% 107.58/14.13
% 107.58/14.13 Lemma 41: join(X, complement(meet(Y, join(X, complement(Y))))) = one.
% 107.58/14.13 Proof:
% 107.58/14.13 join(X, complement(meet(Y, join(X, complement(Y)))))
% 107.58/14.13 = { by lemma 28 R->L }
% 107.58/14.13 join(X, join(complement(Y), complement(meet(Y, join(X, complement(Y))))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 join(X, join(complement(Y), complement(meet(Y, join(complement(Y), X)))))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.13 join(X, join(complement(Y), complement(meet(join(complement(Y), X), Y))))
% 107.58/14.13 = { by lemma 34 }
% 107.58/14.13 join(complement(Y), join(X, complement(meet(join(complement(Y), X), Y))))
% 107.58/14.13 = { by axiom 8 (associativity_of_join) R->L }
% 107.58/14.13 join(join(complement(Y), X), complement(meet(join(complement(Y), X), Y)))
% 107.58/14.13 = { by lemma 25 }
% 107.58/14.13 one
% 107.58/14.13
% 107.58/14.13 Lemma 42: meet(complement(X), join(X, Y)) = meet(Y, complement(meet(X, Y))).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(complement(X), join(X, Y))
% 107.58/14.13 = { by lemma 17 R->L }
% 107.58/14.13 complement(complement(meet(complement(X), join(X, Y))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 complement(complement(meet(complement(X), join(Y, X))))
% 107.58/14.13 = { by lemma 39 R->L }
% 107.58/14.13 complement(ifeq(join(Y, complement(meet(complement(X), join(Y, X)))), one, complement(meet(Y, complement(meet(Y, complement(meet(complement(X), join(Y, X))))))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by lemma 17 R->L }
% 107.58/14.13 complement(ifeq(join(Y, complement(meet(complement(X), join(Y, X)))), one, complement(meet(Y, complement(meet(Y, complement(meet(complement(X), join(Y, complement(complement(X))))))))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by lemma 40 R->L }
% 107.58/14.13 complement(ifeq(join(Y, complement(meet(complement(X), join(Y, X)))), one, complement(meet(Y, complement(meet(Y, meet(complement(meet(complement(X), join(Y, complement(complement(X))))), join(Y, complement(complement(X)))))))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 complement(ifeq(join(Y, complement(meet(complement(X), join(Y, X)))), one, complement(meet(Y, complement(meet(Y, meet(join(Y, complement(complement(X))), complement(meet(complement(X), join(Y, complement(complement(X)))))))))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by lemma 31 }
% 107.58/14.13 complement(ifeq(join(Y, complement(meet(complement(X), join(Y, X)))), one, complement(meet(Y, complement(meet(Y, complement(complement(X)))))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by lemma 17 }
% 107.58/14.13 complement(ifeq(join(Y, complement(meet(complement(X), join(Y, X)))), one, complement(meet(Y, complement(meet(Y, X)))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by lemma 17 R->L }
% 107.58/14.13 complement(ifeq(join(Y, complement(meet(complement(X), join(Y, complement(complement(X)))))), one, complement(meet(Y, complement(meet(Y, X)))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by lemma 41 }
% 107.58/14.13 complement(ifeq(one, one, complement(meet(Y, complement(meet(Y, X)))), complement(meet(complement(X), join(Y, X)))))
% 107.58/14.13 = { by axiom 6 (ifeq_axiom) }
% 107.58/14.13 complement(complement(meet(Y, complement(meet(Y, X)))))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 complement(complement(meet(Y, complement(meet(X, Y)))))
% 107.58/14.13 = { by lemma 17 }
% 107.58/14.13 meet(Y, complement(meet(X, Y)))
% 107.58/14.13
% 107.58/14.13 Lemma 43: meet(X, meet(X, Y)) = meet(X, Y).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(X, meet(X, Y))
% 107.58/14.13 = { by axiom 10 (associativity_of_meet) R->L }
% 107.58/14.13 meet(meet(X, X), Y)
% 107.58/14.13 = { by axiom 3 (idempotence_of_meet) }
% 107.58/14.13 meet(X, Y)
% 107.58/14.13
% 107.58/14.13 Lemma 44: meet(X, complement(meet(Y, X))) = meet(X, complement(Y)).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(X, complement(meet(Y, X)))
% 107.58/14.13 = { by lemma 42 R->L }
% 107.58/14.13 meet(complement(Y), join(Y, X))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 meet(complement(Y), join(X, Y))
% 107.58/14.13 = { by lemma 37 R->L }
% 107.58/14.13 meet(complement(Y), join(X, meet(complement(Y), join(X, Y))))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.13 meet(complement(Y), join(X, meet(complement(Y), join(Y, X))))
% 107.58/14.13 = { by lemma 42 }
% 107.58/14.13 meet(complement(Y), join(X, meet(X, complement(meet(Y, X)))))
% 107.58/14.13 = { by axiom 7 (absorption2) }
% 107.58/14.13 meet(complement(Y), X)
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 meet(X, complement(Y))
% 107.58/14.13
% 107.58/14.13 Lemma 45: meet(complement(X), join(Y, X)) = meet(Y, complement(X)).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(complement(X), join(Y, X))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.13 meet(complement(X), join(X, Y))
% 107.58/14.13 = { by lemma 42 }
% 107.58/14.13 meet(Y, complement(meet(X, Y)))
% 107.58/14.13 = { by lemma 44 }
% 107.58/14.13 meet(Y, complement(X))
% 107.58/14.13
% 107.58/14.13 Lemma 46: meet(X, join(Y, complement(X))) = meet(X, Y).
% 107.58/14.13 Proof:
% 107.58/14.13 meet(X, join(Y, complement(X)))
% 107.58/14.13 = { by lemma 17 R->L }
% 107.58/14.13 complement(complement(meet(X, join(Y, complement(X)))))
% 107.58/14.13 = { by lemma 13 R->L }
% 107.58/14.13 meet(complement(complement(meet(X, join(Y, complement(X))))), one)
% 107.58/14.13 = { by lemma 41 R->L }
% 107.58/14.13 meet(complement(complement(meet(X, join(Y, complement(X))))), join(Y, complement(meet(X, join(Y, complement(X))))))
% 107.58/14.13 = { by lemma 45 }
% 107.58/14.13 meet(Y, complement(complement(meet(X, join(Y, complement(X))))))
% 107.58/14.13 = { by lemma 17 }
% 107.58/14.13 meet(Y, meet(X, join(Y, complement(X))))
% 107.58/14.13 = { by lemma 40 }
% 107.58/14.13 meet(Y, X)
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 meet(X, Y)
% 107.58/14.13
% 107.58/14.13 Lemma 47: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 107.58/14.13 Proof:
% 107.58/14.13 complement(meet(X, complement(Y)))
% 107.58/14.13 = { by lemma 20 R->L }
% 107.58/14.13 complement(meet(X, meet(complement(Y), join(Y, X))))
% 107.58/14.13 = { by lemma 42 }
% 107.58/14.13 complement(meet(X, meet(X, complement(meet(Y, X)))))
% 107.58/14.13 = { by lemma 43 }
% 107.58/14.13 complement(meet(X, complement(meet(Y, X))))
% 107.58/14.13 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.13 complement(meet(X, complement(meet(X, Y))))
% 107.58/14.13 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.13 ifeq(one, one, complement(meet(X, complement(meet(X, Y)))), join(Y, complement(X)))
% 107.58/14.13 = { by lemma 30 R->L }
% 107.58/14.13 ifeq(join(X, join(Y, complement(X))), one, complement(meet(X, complement(meet(X, Y)))), join(Y, complement(X)))
% 107.58/14.13 = { by lemma 46 R->L }
% 107.58/14.13 ifeq(join(X, join(Y, complement(X))), one, complement(meet(X, complement(meet(X, join(Y, complement(X)))))), join(Y, complement(X)))
% 107.58/14.13 = { by lemma 39 }
% 107.58/14.13 join(Y, complement(X))
% 107.58/14.13
% 107.58/14.13 Lemma 48: complement(meet(X, Y)) = join(complement(X), complement(Y)).
% 107.58/14.13 Proof:
% 107.58/14.13 complement(meet(X, Y))
% 107.58/14.13 = { by lemma 17 R->L }
% 107.58/14.13 complement(meet(X, complement(complement(Y))))
% 107.58/14.13 = { by lemma 47 }
% 107.58/14.13 join(complement(Y), complement(X))
% 107.58/14.13 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.14 join(complement(X), complement(Y))
% 107.58/14.14
% 107.58/14.14 Lemma 49: complement(join(X, Y)) = meet(complement(X), complement(Y)).
% 107.58/14.14 Proof:
% 107.58/14.14 complement(join(X, Y))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 complement(join(Y, X))
% 107.58/14.14 = { by lemma 33 R->L }
% 107.58/14.14 meet(complement(Y), complement(meet(complement(Y), join(Y, X))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.14 meet(complement(Y), complement(meet(complement(Y), join(X, Y))))
% 107.58/14.14 = { by lemma 45 }
% 107.58/14.14 meet(complement(Y), complement(meet(X, complement(Y))))
% 107.58/14.14 = { by lemma 44 }
% 107.58/14.14 meet(complement(Y), complement(X))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.14 meet(complement(X), complement(Y))
% 107.58/14.14
% 107.58/14.14 Lemma 50: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 107.58/14.14 Proof:
% 107.58/14.14 complement(meet(complement(X), Y))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.14 complement(meet(Y, complement(X)))
% 107.58/14.14 = { by lemma 47 }
% 107.58/14.14 join(X, complement(Y))
% 107.58/14.14
% 107.58/14.14 Lemma 51: meet(X, meet(Y, complement(X))) = zero.
% 107.58/14.14 Proof:
% 107.58/14.14 meet(X, meet(Y, complement(X)))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.14 meet(X, meet(complement(X), Y))
% 107.58/14.14 = { by axiom 10 (associativity_of_meet) R->L }
% 107.58/14.14 meet(meet(X, complement(X)), Y)
% 107.58/14.14 = { by axiom 5 (complement_meet) }
% 107.58/14.14 meet(zero, Y)
% 107.58/14.14 = { by axiom 7 (absorption2) R->L }
% 107.58/14.14 join(meet(zero, Y), meet(meet(zero, Y), complement(meet(zero, Y))))
% 107.58/14.14 = { by axiom 5 (complement_meet) }
% 107.58/14.14 join(meet(zero, Y), zero)
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.14 join(zero, meet(zero, Y))
% 107.58/14.14 = { by axiom 7 (absorption2) }
% 107.58/14.14 zero
% 107.58/14.14
% 107.58/14.14 Lemma 52: meet(X, join(complement(X), Y)) = meet(X, Y).
% 107.58/14.14 Proof:
% 107.58/14.14 meet(X, join(complement(X), Y))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 meet(X, join(Y, complement(X)))
% 107.58/14.14 = { by lemma 46 }
% 107.58/14.14 meet(X, Y)
% 107.58/14.14
% 107.58/14.14 Lemma 53: ifeq(meet(X, Y), zero, complement(Y), join(X, complement(Y))) = join(X, complement(Y)).
% 107.58/14.14 Proof:
% 107.58/14.14 ifeq(meet(X, Y), zero, complement(Y), join(X, complement(Y)))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 ifeq(meet(X, complement(complement(Y))), zero, complement(Y), join(X, complement(Y)))
% 107.58/14.14 = { by lemma 45 R->L }
% 107.58/14.14 ifeq(meet(complement(complement(Y)), join(X, complement(Y))), zero, complement(Y), join(X, complement(Y)))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 ifeq(meet(complement(complement(Y)), join(X, complement(Y))), zero, complement(complement(complement(Y))), join(X, complement(Y)))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 ifeq(meet(complement(complement(Y)), join(X, complement(Y))), zero, complement(complement(complement(Y))), join(X, complement(complement(complement(Y)))))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 ifeq(meet(complement(complement(Y)), join(X, complement(complement(complement(Y))))), zero, complement(complement(complement(Y))), join(X, complement(complement(complement(Y)))))
% 107.58/14.14 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.14 ifeq(one, one, ifeq(meet(complement(complement(Y)), join(X, complement(complement(complement(Y))))), zero, complement(complement(complement(Y))), join(X, complement(complement(complement(Y))))), join(X, complement(complement(complement(Y)))))
% 107.58/14.14 = { by lemma 30 R->L }
% 107.58/14.14 ifeq(join(complement(complement(Y)), join(X, complement(complement(complement(Y))))), one, ifeq(meet(complement(complement(Y)), join(X, complement(complement(complement(Y))))), zero, complement(complement(complement(Y))), join(X, complement(complement(complement(Y))))), join(X, complement(complement(complement(Y)))))
% 107.58/14.14 = { by axiom 12 (meet_join_complement) }
% 107.58/14.14 join(X, complement(complement(complement(Y))))
% 107.58/14.14 = { by lemma 17 }
% 107.58/14.14 join(X, complement(Y))
% 107.58/14.14
% 107.58/14.14 Lemma 54: meet(X, join(Y, meet(X, Z))) = meet(X, join(Y, Z)).
% 107.58/14.14 Proof:
% 107.58/14.14 meet(X, join(Y, meet(X, Z)))
% 107.58/14.14 = { by lemma 52 R->L }
% 107.58/14.14 meet(X, join(complement(X), join(Y, meet(X, Z))))
% 107.58/14.14 = { by axiom 8 (associativity_of_join) R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(X, Z)))
% 107.58/14.14 = { by axiom 11 (equation_H10) }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, meet(join(complement(X), Y), Z)))))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, meet(Z, join(complement(X), Y))))))
% 107.58/14.14 = { by lemma 21 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(meet(Z, join(complement(X), Y)), meet(complement(X), meet(Z, join(complement(X), Y))))))))
% 107.58/14.14 = { by lemma 40 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(meet(Z, join(complement(X), Y)), meet(complement(X), Z))))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(meet(complement(X), Z), meet(Z, join(complement(X), Y)))))))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(meet(Z, complement(X)), meet(Z, join(complement(X), Y)))))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(meet(Z, join(complement(X), Y)), meet(Z, complement(X)))))))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(complement(complement(meet(Z, join(complement(X), Y)))), meet(Z, complement(X)))))))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(complement(complement(meet(Z, join(complement(X), Y)))), meet(complement(complement(Z)), complement(X)))))))
% 107.58/14.14 = { by lemma 49 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(complement(complement(meet(Z, join(complement(X), Y)))), complement(join(complement(Z), X)))))))
% 107.58/14.14 = { by lemma 48 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, complement(meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))))))
% 107.58/14.14 = { by lemma 50 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))))))
% 107.58/14.14 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, ifeq(zero, zero, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))), join(Z, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))))))))
% 107.58/14.14 = { by lemma 51 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, ifeq(meet(meet(Z, complement(X)), meet(complement(meet(Z, join(complement(X), Y))), complement(meet(Z, complement(X))))), zero, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))), join(Z, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))))))))
% 107.58/14.14 = { by axiom 10 (associativity_of_meet) }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, ifeq(meet(Z, meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), complement(meet(Z, complement(X)))))), zero, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))), join(Z, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))))))))
% 107.58/14.14 = { by lemma 48 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, ifeq(meet(Z, meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), complement(complement(X)))))), zero, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))), join(Z, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))))))))
% 107.58/14.14 = { by lemma 17 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, ifeq(meet(Z, meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))), zero, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))), join(Z, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X)))))))))
% 107.58/14.14 = { by lemma 53 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(Z, complement(meet(complement(X), meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X))))))))
% 107.58/14.14 = { by lemma 50 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(Z, join(X, complement(meet(complement(meet(Z, join(complement(X), Y))), join(complement(Z), X))))))))
% 107.58/14.14 = { by lemma 48 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(Z, join(X, join(complement(complement(meet(Z, join(complement(X), Y)))), complement(join(complement(Z), X))))))))
% 107.58/14.14 = { by lemma 49 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(Z, join(X, join(complement(complement(meet(Z, join(complement(X), Y)))), meet(complement(complement(Z)), complement(X))))))))
% 107.58/14.14 = { by lemma 17 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(Z, join(X, join(complement(complement(meet(Z, join(complement(X), Y)))), meet(Z, complement(X))))))))
% 107.58/14.14 = { by axiom 8 (associativity_of_join) R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(Z, join(join(X, complement(complement(meet(Z, join(complement(X), Y))))), meet(Z, complement(X)))))))
% 107.58/14.14 = { by lemma 24 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(Z, join(X, complement(complement(meet(Z, join(complement(X), Y)))))))))
% 107.58/14.14 = { by lemma 34 R->L }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(Z, complement(complement(meet(Z, join(complement(X), Y)))))))))
% 107.58/14.14 = { by lemma 17 }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, join(Z, meet(Z, join(complement(X), Y)))))))
% 107.58/14.14 = { by axiom 7 (absorption2) }
% 107.58/14.14 meet(X, join(join(complement(X), Y), meet(Z, join(X, Z))))
% 107.58/14.14 = { by axiom 8 (associativity_of_join) }
% 107.58/14.14 meet(X, join(complement(X), join(Y, meet(Z, join(X, Z)))))
% 107.58/14.14 = { by lemma 52 }
% 107.58/14.14 meet(X, join(Y, meet(Z, join(X, Z))))
% 107.58/14.14 = { by lemma 19 }
% 107.58/14.14 meet(X, join(Y, Z))
% 107.58/14.14
% 107.58/14.14 Lemma 55: ifeq(meet(X, Y), zero, complement(X), join(complement(X), Y)) = join(Y, complement(X)).
% 107.58/14.14 Proof:
% 107.58/14.14 ifeq(meet(X, Y), zero, complement(X), join(complement(X), Y))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.14 ifeq(meet(Y, X), zero, complement(X), join(complement(X), Y))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 ifeq(meet(Y, X), zero, complement(X), join(Y, complement(X)))
% 107.58/14.14 = { by lemma 53 }
% 107.58/14.14 join(Y, complement(X))
% 107.58/14.14
% 107.58/14.14 Goal 1 (prove_distributivity): meet(a, join(b, c)) = join(meet(a, b), meet(a, c)).
% 107.58/14.14 Proof:
% 107.58/14.14 meet(a, join(b, c))
% 107.58/14.14 = { by lemma 54 R->L }
% 107.58/14.14 meet(a, join(b, meet(a, c)))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.14 meet(a, join(b, meet(c, a)))
% 107.58/14.14 = { by lemma 21 R->L }
% 107.58/14.14 meet(join(a, meet(c, a)), join(b, meet(c, a)))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 meet(join(a, meet(c, a)), join(b, complement(complement(meet(c, a)))))
% 107.58/14.14 = { by lemma 17 R->L }
% 107.58/14.14 meet(join(a, complement(complement(meet(c, a)))), join(b, complement(complement(meet(c, a)))))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(a, complement(complement(meet(c, a)))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(complement(complement(meet(c, a))), a))
% 107.58/14.14 = { by lemma 37 R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(complement(complement(meet(c, a))), meet(join(b, complement(complement(meet(c, a)))), join(complement(complement(meet(c, a))), a))))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), join(b, complement(complement(meet(c, a)))))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(meet(join(complement(complement(meet(c, a))), a), join(b, complement(complement(meet(c, a))))), complement(complement(meet(c, a)))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), b)), complement(complement(meet(c, a)))))
% 107.58/14.14 = { by lemma 54 R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))), complement(complement(meet(c, a)))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), join(meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a))))), complement(complement(meet(c, a)))))
% 107.58/14.14 = { by lemma 55 R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a))))))))
% 107.58/14.14 = { by axiom 1 (commutativity_of_join) R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))))
% 107.58/14.14 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(b, join(complement(complement(meet(c, a))), a)))))))
% 107.58/14.14 = { by lemma 21 R->L }
% 107.58/14.14 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), join(meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(b, join(complement(complement(meet(c, a))), a)))), meet(b, meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(b, join(complement(complement(meet(c, a))), a)))))))))
% 107.58/14.14 = { by lemma 36 }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), join(meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(b, join(complement(complement(meet(c, a))), a)))), meet(b, join(complement(complement(meet(c, a))), a))))))
% 107.58/14.15 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), join(meet(b, join(complement(complement(meet(c, a))), a)), meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(b, join(complement(complement(meet(c, a))), a))))))))
% 107.58/14.15 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), join(meet(b, join(complement(complement(meet(c, a))), a)), meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b)))))))
% 107.58/14.15 = { by axiom 4 (commutativity_of_meet) }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), join(meet(join(complement(complement(meet(c, a))), a), b), meet(join(complement(complement(meet(c, a))), a), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b)))))))
% 107.58/14.15 = { by lemma 35 }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by lemma 17 R->L }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(complement(complement(join(complement(complement(meet(c, a))), a))), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by lemma 50 R->L }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(complement(complement(join(complement(complement(meet(c, a))), a))), complement(meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by lemma 49 R->L }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), complement(join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by lemma 17 R->L }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(complement(complement(meet(c, a)))), complement(join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by lemma 49 R->L }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(one, one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by lemma 30 R->L }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))), join(complement(join(complement(complement(meet(c, a))), a)), complement(join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a))))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by axiom 8 (associativity_of_join) }
% 107.58/14.15 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(meet(join(complement(complement(meet(c, a))), a), b), join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), complement(join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.15 = { by lemma 49 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(meet(join(complement(complement(meet(c, a))), a), b), join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(complement(complement(meet(c, a)))))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(meet(join(complement(complement(meet(c, a))), a), b), join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 47 R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(complement(meet(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), complement(meet(join(complement(complement(meet(c, a))), a), b)))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 44 R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(complement(meet(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), complement(meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 47 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), one, complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), one, complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), one, complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), one, complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by axiom 6 (ifeq_axiom) R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), one, ifeq(zero, zero, complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 51 R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(ifeq(join(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), one, ifeq(meet(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), zero, complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a)))))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by axiom 12 (meet_join_complement) }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), complement(join(complement(complement(meet(c, a))), join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 49 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), meet(complement(complement(complement(meet(c, a)))), complement(join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), meet(complement(meet(c, a)), complement(join(complement(join(complement(complement(meet(c, a))), a)), meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 49 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), meet(complement(meet(c, a)), meet(complement(complement(join(complement(complement(meet(c, a))), a))), complement(meet(complement(meet(join(complement(complement(meet(c, a))), a), b)), complement(meet(c, a))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 50 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), meet(complement(meet(c, a)), meet(complement(complement(join(complement(complement(meet(c, a))), a))), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a))))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by axiom 10 (associativity_of_meet) R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), meet(meet(complement(meet(c, a)), complement(complement(join(complement(complement(meet(c, a))), a)))), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 40 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(meet(join(complement(complement(meet(c, a))), a), b), meet(complement(meet(c, a)), complement(complement(join(complement(complement(meet(c, a))), a))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 18 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(join(complement(complement(meet(c, a))), a))))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 17 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(meet(join(complement(complement(meet(c, a))), a), b), join(complement(complement(meet(c, a))), a))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by axiom 10 (associativity_of_meet) }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), meet(b, join(complement(complement(meet(c, a))), a)))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), meet(join(complement(complement(meet(c, a))), a), b))), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 43 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), ifeq(meet(complement(meet(c, a)), meet(join(complement(complement(meet(c, a))), a), b)), zero, complement(complement(meet(c, a))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.16 = { by lemma 55 }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), join(meet(join(complement(complement(meet(c, a))), a), b), complement(complement(meet(c, a)))))
% 107.58/14.16 = { by axiom 1 (commutativity_of_join) }
% 107.58/14.16 meet(join(b, complement(complement(meet(c, a)))), join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b)))
% 107.58/14.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 107.58/14.16 meet(join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b)), join(b, complement(complement(meet(c, a)))))
% 107.58/14.16 = { by lemma 38 R->L }
% 107.58/14.17 meet(join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b)), join(b, join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))))
% 107.58/14.17 = { by lemma 19 }
% 107.58/14.17 join(complement(complement(meet(c, a))), meet(join(complement(complement(meet(c, a))), a), b))
% 108.87/14.17 = { by axiom 4 (commutativity_of_meet) }
% 108.87/14.17 join(complement(complement(meet(c, a))), meet(b, join(complement(complement(meet(c, a))), a)))
% 108.87/14.17 = { by lemma 22 R->L }
% 108.87/14.17 join(complement(complement(meet(c, a))), join(meet(b, a), meet(b, join(complement(complement(meet(c, a))), a))))
% 108.87/14.17 = { by axiom 8 (associativity_of_join) R->L }
% 108.87/14.17 join(join(complement(complement(meet(c, a))), meet(b, a)), meet(b, join(complement(complement(meet(c, a))), a)))
% 108.87/14.17 = { by lemma 54 R->L }
% 108.87/14.17 join(join(complement(complement(meet(c, a))), meet(b, a)), meet(b, join(complement(complement(meet(c, a))), meet(b, a))))
% 108.87/14.17 = { by lemma 21 }
% 108.87/14.17 join(complement(complement(meet(c, a))), meet(b, a))
% 108.87/14.17 = { by axiom 4 (commutativity_of_meet) }
% 108.87/14.17 join(complement(complement(meet(c, a))), meet(a, b))
% 108.87/14.17 = { by lemma 17 }
% 108.87/14.17 join(meet(c, a), meet(a, b))
% 108.87/14.17 = { by axiom 1 (commutativity_of_join) }
% 108.87/14.17 join(meet(a, b), meet(c, a))
% 108.87/14.17 = { by axiom 4 (commutativity_of_meet) }
% 108.87/14.17 join(meet(b, a), meet(c, a))
% 108.87/14.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 108.87/14.17 join(meet(b, a), meet(a, c))
% 108.87/14.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 108.87/14.17 join(meet(a, b), meet(a, c))
% 108.87/14.17 % SZS output end Proof
% 108.87/14.17
% 108.87/14.17 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------