%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT188-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 92.98s 12.03s
% Output : Proof 94.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT188-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 14:05:04 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.98/12.03 Command-line arguments: --no-flatten-goal
% 92.98/12.03
% 92.98/12.03 % SZS status Unsatisfiable
% 92.98/12.03
% 93.79/12.16 % SZS output start Proof
% 93.79/12.16 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 93.79/12.16 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 93.79/12.16 Axiom 3 (complement_join): join(X, complement(X)) = one.
% 93.79/12.16 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 93.79/12.16 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 93.79/12.16 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 93.79/12.16 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 93.79/12.16 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 93.79/12.16 Axiom 9 (absorption1): meet(X, join(X, Y)) = X.
% 93.79/12.16 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 93.79/12.16 Axiom 11 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 93.79/12.16 Axiom 12 (equation_H16): meet(X, join(meet(X, Y), meet(X, Z))) = meet(X, join(meet(X, Y), meet(Z, join(Y, meet(Z, join(X, Y)))))).
% 93.79/12.16
% 93.79/12.16 Lemma 13: meet(X, one) = X.
% 93.79/12.16 Proof:
% 93.79/12.16 meet(X, one)
% 93.79/12.16 = { by axiom 3 (complement_join) R->L }
% 93.79/12.16 meet(X, join(X, complement(X)))
% 93.79/12.16 = { by axiom 9 (absorption1) }
% 93.79/12.16 X
% 93.79/12.16
% 93.79/12.16 Lemma 14: join(X, one) = one.
% 93.79/12.16 Proof:
% 93.79/12.16 join(X, one)
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 join(one, X)
% 93.79/12.16 = { by lemma 13 R->L }
% 93.79/12.16 join(one, meet(X, one))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.16 join(one, meet(one, X))
% 93.79/12.16 = { by axiom 7 (absorption2) }
% 93.79/12.16 one
% 93.79/12.16
% 93.79/12.16 Lemma 15: complement(complement(X)) = X.
% 93.79/12.16 Proof:
% 93.79/12.16 complement(complement(X))
% 93.79/12.16 = { by axiom 6 (ifeq_axiom) R->L }
% 93.79/12.16 ifeq(zero, zero, complement(complement(X)), X)
% 93.79/12.16 = { by axiom 5 (complement_meet) R->L }
% 93.79/12.16 ifeq(meet(X, complement(X)), zero, complement(complement(X)), X)
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.16 ifeq(meet(complement(X), X), zero, complement(complement(X)), X)
% 93.79/12.16 = { by axiom 6 (ifeq_axiom) R->L }
% 93.79/12.16 ifeq(one, one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 93.79/12.16 = { by axiom 3 (complement_join) R->L }
% 93.79/12.16 ifeq(join(X, complement(X)), one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 ifeq(join(complement(X), X), one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 93.79/12.16 = { by axiom 11 (meet_join_complement) }
% 93.79/12.16 X
% 93.79/12.16
% 93.79/12.16 Lemma 16: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 93.79/12.16 Proof:
% 93.79/12.16 meet(X, meet(Y, Z))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.16 meet(meet(Y, Z), X)
% 93.79/12.16 = { by axiom 10 (associativity_of_meet) }
% 93.79/12.16 meet(Y, meet(Z, X))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.16 meet(Y, meet(X, Z))
% 93.79/12.16
% 93.79/12.16 Lemma 17: meet(X, join(Y, X)) = X.
% 93.79/12.16 Proof:
% 93.79/12.16 meet(X, join(Y, X))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 meet(X, join(X, Y))
% 93.79/12.16 = { by axiom 9 (absorption1) }
% 93.79/12.16 X
% 93.79/12.16
% 93.79/12.16 Lemma 18: join(X, meet(Y, X)) = X.
% 93.79/12.16 Proof:
% 93.79/12.16 join(X, meet(Y, X))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.16 join(X, meet(X, Y))
% 93.79/12.16 = { by axiom 7 (absorption2) }
% 93.79/12.16 X
% 93.79/12.16
% 93.79/12.16 Lemma 19: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 93.79/12.16 Proof:
% 93.79/12.16 join(Y, join(X, Z))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 join(join(X, Z), Y)
% 93.79/12.16 = { by axiom 8 (associativity_of_join) }
% 93.79/12.16 join(X, join(Z, Y))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.16 join(X, join(Y, Z))
% 93.79/12.16
% 93.79/12.16 Lemma 20: join(X, join(Y, meet(Z, X))) = join(X, Y).
% 93.79/12.16 Proof:
% 93.79/12.16 join(X, join(Y, meet(Z, X)))
% 93.79/12.16 = { by lemma 19 }
% 93.79/12.16 join(Y, join(X, meet(Z, X)))
% 93.79/12.16 = { by lemma 18 }
% 93.79/12.16 join(Y, X)
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.16 join(X, Y)
% 93.79/12.16
% 93.79/12.16 Lemma 21: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 93.79/12.16 Proof:
% 93.79/12.16 join(X, join(Y, meet(X, Z)))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 join(X, join(meet(X, Z), Y))
% 93.79/12.16 = { by axiom 8 (associativity_of_join) R->L }
% 93.79/12.16 join(join(X, meet(X, Z)), Y)
% 93.79/12.16 = { by axiom 7 (absorption2) }
% 93.79/12.16 join(X, Y)
% 93.79/12.16
% 93.79/12.16 Lemma 22: join(X, join(meet(X, Y), Z)) = join(X, Z).
% 93.79/12.16 Proof:
% 93.79/12.16 join(X, join(meet(X, Y), Z))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 join(X, join(Z, meet(X, Y)))
% 93.79/12.16 = { by lemma 21 }
% 93.79/12.16 join(X, Z)
% 93.79/12.16
% 93.79/12.16 Lemma 23: meet(X, meet(Y, join(Z, meet(X, Y)))) = meet(X, Y).
% 93.79/12.16 Proof:
% 93.79/12.16 meet(X, meet(Y, join(Z, meet(X, Y))))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.16 meet(X, meet(Y, join(Z, meet(Y, X))))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 meet(X, meet(Y, join(meet(Y, X), Z)))
% 93.79/12.16 = { by lemma 16 R->L }
% 93.79/12.16 meet(Y, meet(X, join(meet(Y, X), Z)))
% 93.79/12.16 = { by axiom 10 (associativity_of_meet) R->L }
% 93.79/12.16 meet(meet(Y, X), join(meet(Y, X), Z))
% 93.79/12.16 = { by axiom 9 (absorption1) }
% 93.79/12.16 meet(Y, X)
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.16 meet(X, Y)
% 93.79/12.16
% 93.79/12.16 Lemma 24: meet(join(X, Y), join(Y, meet(X, Z))) = join(Y, meet(X, Z)).
% 93.79/12.16 Proof:
% 93.79/12.16 meet(join(X, Y), join(Y, meet(X, Z)))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.16 meet(join(Y, meet(X, Z)), join(X, Y))
% 93.79/12.16 = { by lemma 21 R->L }
% 93.79/12.16 meet(join(Y, meet(X, Z)), join(X, join(Y, meet(X, Z))))
% 93.79/12.16 = { by lemma 17 }
% 93.79/12.16 join(Y, meet(X, Z))
% 93.79/12.16
% 93.79/12.16 Lemma 25: meet(X, join(meet(X, Y), meet(X, Z))) = join(meet(X, Y), meet(X, Z)).
% 93.79/12.16 Proof:
% 93.79/12.16 meet(X, join(meet(X, Y), meet(X, Z)))
% 93.79/12.16 = { by axiom 7 (absorption2) R->L }
% 93.79/12.16 meet(join(X, meet(X, Y)), join(meet(X, Y), meet(X, Z)))
% 93.79/12.16 = { by lemma 24 }
% 93.79/12.16 join(meet(X, Y), meet(X, Z))
% 93.79/12.16
% 93.79/12.16 Lemma 26: meet(X, join(meet(X, Y), meet(Z, join(Y, X)))) = join(meet(X, Y), meet(X, Z)).
% 93.79/12.16 Proof:
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, join(Y, X))))
% 93.79/12.16 = { by lemma 23 R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, X), join(Y, meet(Z, join(Y, X)))))))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(X, Y), join(Y, meet(Z, join(Y, X)))))))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(X, Y), join(Y, meet(Z, join(X, Y)))))))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(X, Y)))))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(Y, X)))))
% 93.79/12.16 = { by axiom 7 (absorption2) R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(join(Y, X), meet(join(Y, X), Z))))))
% 93.79/12.16 = { by axiom 8 (associativity_of_join) }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(Y, join(X, meet(join(Y, X), Z)))))))
% 93.79/12.16 = { by lemma 19 R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(X, join(Y, meet(join(Y, X), Z)))))))
% 93.79/12.16 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(X, join(Y, meet(Z, join(Y, X))))))))
% 93.79/12.16 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(X, join(Y, meet(Z, join(X, Y))))))))
% 93.79/12.16 = { by lemma 17 }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(Z, join(Y, meet(Z, join(X, Y))))))
% 93.79/12.16 = { by axiom 12 (equation_H16) R->L }
% 93.79/12.16 meet(X, join(meet(X, Y), meet(X, Z)))
% 93.79/12.16 = { by lemma 25 }
% 93.79/12.16 join(meet(X, Y), meet(X, Z))
% 93.79/12.16
% 93.79/12.16 Lemma 27: join(X, join(Y, complement(X))) = one.
% 93.79/12.16 Proof:
% 93.79/12.16 join(X, join(Y, complement(X)))
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 join(X, join(complement(X), Y))
% 93.79/12.17 = { by axiom 8 (associativity_of_join) R->L }
% 93.79/12.17 join(join(X, complement(X)), Y)
% 93.79/12.17 = { by axiom 3 (complement_join) }
% 93.79/12.17 join(one, Y)
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 join(Y, one)
% 93.79/12.17 = { by lemma 14 }
% 93.79/12.17 one
% 93.79/12.17
% 93.79/12.17 Lemma 28: join(meet(X, join(Y, complement(X))), meet(join(Y, complement(X)), complement(meet(X, join(Y, complement(X)))))) = join(Y, complement(X)).
% 93.79/12.17 Proof:
% 93.79/12.17 join(meet(X, join(Y, complement(X))), meet(join(Y, complement(X)), complement(meet(X, join(Y, complement(X))))))
% 93.79/12.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.17 join(meet(join(Y, complement(X)), X), meet(join(Y, complement(X)), complement(meet(X, join(Y, complement(X))))))
% 93.79/12.17 = { by lemma 26 R->L }
% 93.79/12.17 meet(join(Y, complement(X)), join(meet(join(Y, complement(X)), X), meet(complement(meet(X, join(Y, complement(X)))), join(X, join(Y, complement(X))))))
% 93.79/12.17 = { by lemma 27 }
% 93.79/12.17 meet(join(Y, complement(X)), join(meet(join(Y, complement(X)), X), meet(complement(meet(X, join(Y, complement(X)))), one)))
% 93.79/12.17 = { by lemma 13 }
% 93.79/12.17 meet(join(Y, complement(X)), join(meet(join(Y, complement(X)), X), complement(meet(X, join(Y, complement(X))))))
% 93.79/12.17 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.17 meet(join(Y, complement(X)), join(meet(X, join(Y, complement(X))), complement(meet(X, join(Y, complement(X))))))
% 93.79/12.17 = { by axiom 3 (complement_join) }
% 93.79/12.17 meet(join(Y, complement(X)), one)
% 93.79/12.17 = { by lemma 13 }
% 93.79/12.17 join(Y, complement(X))
% 93.79/12.17
% 93.79/12.17 Lemma 29: meet(X, meet(Y, complement(meet(X, Y)))) = zero.
% 93.79/12.17 Proof:
% 93.79/12.17 meet(X, meet(Y, complement(meet(X, Y))))
% 93.79/12.17 = { by axiom 10 (associativity_of_meet) R->L }
% 93.79/12.17 meet(meet(X, Y), complement(meet(X, Y)))
% 93.79/12.17 = { by axiom 5 (complement_meet) }
% 93.79/12.17 zero
% 93.79/12.17
% 93.79/12.17 Lemma 30: meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))) = complement(Y).
% 93.79/12.17 Proof:
% 93.79/12.17 meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))
% 93.79/12.17 = { by axiom 11 (meet_join_complement) R->L }
% 93.79/12.17 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))))))
% 93.79/12.17 = { by lemma 22 R->L }
% 93.79/12.17 ifeq(join(Y, join(meet(Y, join(X, complement(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))))))
% 93.79/12.17 = { by lemma 28 }
% 93.79/12.17 ifeq(join(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))))))
% 93.79/12.17 = { by lemma 27 }
% 93.79/12.17 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))))))
% 93.79/12.17 = { by axiom 6 (ifeq_axiom) }
% 93.79/12.17 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))))))
% 93.79/12.17 = { by lemma 29 }
% 93.79/12.17 ifeq(zero, zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 93.79/12.17 = { by axiom 6 (ifeq_axiom) }
% 93.79/12.17 complement(Y)
% 93.79/12.17
% 93.79/12.17 Lemma 31: join(X, meet(complement(X), join(X, Y))) = join(X, Y).
% 93.79/12.17 Proof:
% 93.79/12.17 join(X, meet(complement(X), join(X, Y)))
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 join(X, meet(complement(X), join(Y, X)))
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 join(meet(complement(X), join(Y, X)), X)
% 93.79/12.17 = { by lemma 15 R->L }
% 93.79/12.17 join(meet(complement(X), join(Y, X)), complement(complement(X)))
% 93.79/12.17 = { by lemma 30 R->L }
% 93.79/12.17 join(meet(complement(X), join(Y, X)), meet(join(Y, complement(complement(X))), complement(meet(complement(X), join(Y, complement(complement(X)))))))
% 93.79/12.17 = { by lemma 15 R->L }
% 93.79/12.17 join(meet(complement(X), join(Y, complement(complement(X)))), meet(join(Y, complement(complement(X))), complement(meet(complement(X), join(Y, complement(complement(X)))))))
% 93.79/12.17 = { by lemma 28 }
% 93.79/12.17 join(Y, complement(complement(X)))
% 93.79/12.17 = { by lemma 15 }
% 93.79/12.17 join(Y, X)
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.17 join(X, Y)
% 93.79/12.17
% 93.79/12.17 Lemma 32: join(meet(X, Y), meet(X, complement(meet(X, Y)))) = X.
% 93.79/12.17 Proof:
% 93.79/12.17 join(meet(X, Y), meet(X, complement(meet(X, Y))))
% 93.79/12.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.17 join(meet(X, Y), meet(complement(meet(X, Y)), X))
% 93.79/12.17 = { by axiom 7 (absorption2) R->L }
% 93.79/12.17 join(meet(X, Y), meet(complement(meet(X, Y)), join(X, meet(X, Y))))
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 join(meet(X, Y), meet(complement(meet(X, Y)), join(meet(X, Y), X)))
% 93.79/12.17 = { by lemma 31 }
% 93.79/12.17 join(meet(X, Y), X)
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.17 join(X, meet(X, Y))
% 93.79/12.17 = { by axiom 7 (absorption2) }
% 93.79/12.17 X
% 93.79/12.17
% 93.79/12.17 Lemma 33: ifeq(join(X, Y), one, complement(meet(X, complement(meet(X, Y)))), Y) = Y.
% 93.79/12.17 Proof:
% 93.79/12.17 ifeq(join(X, Y), one, complement(meet(X, complement(meet(X, Y)))), Y)
% 93.79/12.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.17 ifeq(join(X, Y), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 ifeq(join(Y, X), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 93.79/12.17 = { by lemma 32 R->L }
% 93.79/12.17 ifeq(join(Y, join(meet(X, Y), meet(X, complement(meet(X, Y))))), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 ifeq(join(Y, join(meet(X, complement(meet(X, Y))), meet(X, Y))), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 93.79/12.17 = { by lemma 20 }
% 93.79/12.17 ifeq(join(Y, meet(X, complement(meet(X, Y)))), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 93.79/12.17 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.17 ifeq(join(Y, meet(X, complement(meet(Y, X)))), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 ifeq(join(meet(X, complement(meet(Y, X))), Y), one, complement(meet(X, complement(meet(Y, X)))), Y)
% 93.79/12.17 = { by axiom 6 (ifeq_axiom) R->L }
% 93.79/12.17 ifeq(join(meet(X, complement(meet(Y, X))), Y), one, ifeq(zero, zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 93.79/12.17 = { by lemma 29 R->L }
% 93.79/12.17 ifeq(join(meet(X, complement(meet(Y, X))), Y), one, ifeq(meet(Y, meet(X, complement(meet(Y, X)))), zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 93.79/12.17 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.17 ifeq(join(meet(X, complement(meet(Y, X))), Y), one, ifeq(meet(meet(X, complement(meet(Y, X))), Y), zero, complement(meet(X, complement(meet(Y, X)))), Y), Y)
% 93.79/12.17 = { by axiom 11 (meet_join_complement) }
% 93.79/12.17 Y
% 93.79/12.17
% 93.79/12.17 Lemma 34: meet(X, complement(meet(X, join(Y, complement(X))))) = complement(join(Y, complement(X))).
% 93.79/12.17 Proof:
% 93.79/12.17 meet(X, complement(meet(X, join(Y, complement(X)))))
% 93.79/12.17 = { by lemma 15 R->L }
% 93.79/12.17 complement(complement(meet(X, complement(meet(X, join(Y, complement(X)))))))
% 93.79/12.17 = { by axiom 6 (ifeq_axiom) R->L }
% 93.79/12.17 complement(ifeq(one, one, complement(meet(X, complement(meet(X, join(Y, complement(X)))))), join(Y, complement(X))))
% 93.79/12.17 = { by lemma 27 R->L }
% 93.79/12.17 complement(ifeq(join(X, join(Y, complement(X))), one, complement(meet(X, complement(meet(X, join(Y, complement(X)))))), join(Y, complement(X))))
% 93.79/12.17 = { by lemma 33 }
% 93.79/12.17 complement(join(Y, complement(X)))
% 93.79/12.17
% 93.79/12.17 Lemma 35: complement(meet(complement(X), join(X, Y))) = join(X, complement(join(X, Y))).
% 93.79/12.17 Proof:
% 93.79/12.17 complement(meet(complement(X), join(X, Y)))
% 93.79/12.17 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.17 complement(meet(complement(X), join(Y, X)))
% 93.79/12.17 = { by lemma 32 R->L }
% 93.79/12.17 join(meet(complement(meet(complement(X), join(Y, X))), join(complement(X), complement(complement(meet(complement(X), join(Y, X)))))), meet(complement(meet(complement(X), join(Y, X))), complement(meet(complement(meet(complement(X), join(Y, X))), join(complement(X), complement(complement(meet(complement(X), join(Y, X)))))))))
% 93.79/12.17 = { by lemma 34 }
% 93.79/12.17 join(meet(complement(meet(complement(X), join(Y, X))), join(complement(X), complement(complement(meet(complement(X), join(Y, X)))))), complement(join(complement(X), complement(complement(meet(complement(X), join(Y, X)))))))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.18 join(complement(join(complement(X), complement(complement(meet(complement(X), join(Y, X)))))), meet(complement(meet(complement(X), join(Y, X))), join(complement(X), complement(complement(meet(complement(X), join(Y, X)))))))
% 93.79/12.18 = { by lemma 15 }
% 93.79/12.18 join(complement(join(complement(X), meet(complement(X), join(Y, X)))), meet(complement(meet(complement(X), join(Y, X))), join(complement(X), complement(complement(meet(complement(X), join(Y, X)))))))
% 93.79/12.18 = { by lemma 15 }
% 93.79/12.18 join(complement(join(complement(X), meet(complement(X), join(Y, X)))), meet(complement(meet(complement(X), join(Y, X))), join(complement(X), meet(complement(X), join(Y, X)))))
% 93.79/12.18 = { by axiom 7 (absorption2) }
% 93.79/12.18 join(complement(complement(X)), meet(complement(meet(complement(X), join(Y, X))), join(complement(X), meet(complement(X), join(Y, X)))))
% 93.79/12.18 = { by axiom 7 (absorption2) }
% 93.79/12.18 join(complement(complement(X)), meet(complement(meet(complement(X), join(Y, X))), complement(X)))
% 93.79/12.18 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.18 join(complement(complement(X)), meet(complement(X), complement(meet(complement(X), join(Y, X)))))
% 93.79/12.18 = { by lemma 15 R->L }
% 93.79/12.18 join(complement(complement(X)), meet(complement(X), complement(meet(complement(X), join(Y, complement(complement(X)))))))
% 93.79/12.18 = { by lemma 34 }
% 93.79/12.18 join(complement(complement(X)), complement(join(Y, complement(complement(X)))))
% 93.79/12.18 = { by lemma 15 }
% 93.79/12.18 join(complement(complement(X)), complement(join(Y, X)))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.18 join(complement(complement(X)), complement(join(X, Y)))
% 93.79/12.18 = { by lemma 15 }
% 93.79/12.18 join(X, complement(join(X, Y)))
% 93.79/12.18
% 93.79/12.18 Lemma 36: meet(X, join(meet(X, Y), meet(Y, Z))) = meet(X, Y).
% 93.79/12.18 Proof:
% 93.79/12.18 meet(X, join(meet(X, Y), meet(Y, Z)))
% 93.79/12.18 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.18 meet(X, join(meet(X, Y), meet(Z, Y)))
% 93.79/12.18 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.18 meet(X, join(meet(Y, X), meet(Z, Y)))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.18 meet(X, join(meet(Z, Y), meet(Y, X)))
% 93.79/12.18 = { by lemma 24 R->L }
% 93.79/12.18 meet(X, meet(join(Y, meet(Z, Y)), join(meet(Z, Y), meet(Y, X))))
% 93.79/12.18 = { by lemma 18 }
% 93.79/12.18 meet(X, meet(Y, join(meet(Z, Y), meet(Y, X))))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.18 meet(X, meet(Y, join(meet(Y, X), meet(Z, Y))))
% 93.79/12.18 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.18 meet(X, meet(Y, join(meet(X, Y), meet(Z, Y))))
% 93.79/12.18 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.18 meet(X, meet(Y, join(meet(X, Y), meet(Y, Z))))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.18 meet(X, meet(Y, join(meet(Y, Z), meet(X, Y))))
% 93.79/12.18 = { by lemma 23 }
% 93.79/12.18 meet(X, Y)
% 93.79/12.18
% 93.79/12.18 Lemma 37: meet(X, meet(join(X, Y), Z)) = meet(X, Z).
% 93.79/12.18 Proof:
% 93.79/12.18 meet(X, meet(join(X, Y), Z))
% 93.79/12.18 = { by axiom 10 (associativity_of_meet) R->L }
% 93.79/12.18 meet(meet(X, join(X, Y)), Z)
% 93.79/12.18 = { by axiom 9 (absorption1) }
% 93.79/12.18 meet(X, Z)
% 93.79/12.18
% 93.79/12.18 Lemma 38: meet(X, complement(meet(Y, join(X, complement(Y))))) = meet(X, complement(Y)).
% 93.79/12.18 Proof:
% 93.79/12.18 meet(X, complement(meet(Y, join(X, complement(Y)))))
% 93.79/12.18 = { by lemma 37 R->L }
% 93.79/12.18 meet(X, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 93.79/12.18 = { by lemma 30 }
% 93.79/12.18 meet(X, complement(Y))
% 93.79/12.18
% 93.79/12.18 Lemma 39: meet(X, join(complement(X), Y)) = meet(X, Y).
% 93.79/12.18 Proof:
% 93.79/12.18 meet(X, join(complement(X), Y))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.18 meet(X, join(Y, complement(X)))
% 93.79/12.18 = { by lemma 20 R->L }
% 93.79/12.18 meet(X, join(Y, join(complement(X), meet(X, Y))))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.18 meet(X, join(Y, join(meet(X, Y), complement(X))))
% 93.79/12.18 = { by lemma 32 R->L }
% 93.79/12.18 meet(X, join(Y, join(meet(X, Y), complement(join(meet(X, Y), meet(X, complement(meet(X, Y))))))))
% 93.79/12.18 = { by lemma 35 R->L }
% 93.79/12.18 meet(X, join(Y, complement(meet(complement(meet(X, Y)), join(meet(X, Y), meet(X, complement(meet(X, Y))))))))
% 93.79/12.18 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.18 meet(X, join(Y, complement(meet(complement(meet(X, Y)), join(meet(X, Y), meet(complement(meet(X, Y)), X))))))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.18 meet(X, join(Y, complement(meet(complement(meet(X, Y)), join(meet(complement(meet(X, Y)), X), meet(X, Y))))))
% 93.79/12.18 = { by lemma 36 }
% 93.79/12.18 meet(X, join(Y, complement(meet(complement(meet(X, Y)), X))))
% 93.79/12.18 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.18 meet(X, join(Y, complement(meet(X, complement(meet(X, Y))))))
% 93.79/12.18 = { by axiom 6 (ifeq_axiom) R->L }
% 93.79/12.18 meet(X, join(Y, ifeq(one, one, complement(meet(X, complement(meet(X, Y)))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by axiom 3 (complement_join) R->L }
% 93.79/12.18 meet(X, join(Y, ifeq(join(join(X, Y), complement(join(X, Y))), one, complement(meet(X, complement(meet(X, Y)))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by axiom 8 (associativity_of_join) }
% 93.79/12.18 meet(X, join(Y, ifeq(join(X, join(Y, complement(join(X, Y)))), one, complement(meet(X, complement(meet(X, Y)))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by lemma 15 R->L }
% 93.79/12.18 meet(X, join(Y, ifeq(join(X, join(Y, complement(join(X, Y)))), one, complement(meet(X, complement(meet(X, complement(complement(Y)))))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by lemma 38 R->L }
% 93.79/12.18 meet(X, join(Y, ifeq(join(X, join(Y, complement(join(X, Y)))), one, complement(meet(X, complement(meet(X, complement(meet(complement(Y), join(X, complement(complement(Y))))))))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.18 meet(X, join(Y, ifeq(join(X, join(Y, complement(join(X, Y)))), one, complement(meet(X, complement(meet(X, complement(meet(complement(Y), join(complement(complement(Y)), X))))))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by lemma 15 }
% 93.79/12.18 meet(X, join(Y, ifeq(join(X, join(Y, complement(join(X, Y)))), one, complement(meet(X, complement(meet(X, complement(meet(complement(Y), join(Y, X))))))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by lemma 35 }
% 93.79/12.18 meet(X, join(Y, ifeq(join(X, join(Y, complement(join(X, Y)))), one, complement(meet(X, complement(meet(X, join(Y, complement(join(Y, X))))))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.18 meet(X, join(Y, ifeq(join(X, join(Y, complement(join(X, Y)))), one, complement(meet(X, complement(meet(X, join(Y, complement(join(X, Y))))))), join(Y, complement(join(X, Y))))))
% 93.79/12.18 = { by lemma 33 }
% 93.79/12.18 meet(X, join(Y, join(Y, complement(join(X, Y)))))
% 93.79/12.19 = { by axiom 8 (associativity_of_join) R->L }
% 93.79/12.19 meet(X, join(join(Y, Y), complement(join(X, Y))))
% 93.79/12.19 = { by axiom 1 (idempotence_of_join) }
% 93.79/12.19 meet(X, join(Y, complement(join(X, Y))))
% 93.79/12.19 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.19 meet(X, join(Y, complement(join(Y, X))))
% 93.79/12.19 = { by lemma 35 R->L }
% 93.79/12.19 meet(X, complement(meet(complement(Y), join(Y, X))))
% 93.79/12.19 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.19 meet(X, complement(meet(complement(Y), join(X, Y))))
% 93.79/12.19 = { by lemma 15 R->L }
% 93.79/12.19 meet(X, complement(meet(complement(Y), join(X, complement(complement(Y))))))
% 93.79/12.19 = { by lemma 38 }
% 93.79/12.19 meet(X, complement(complement(Y)))
% 93.79/12.19 = { by lemma 15 }
% 93.79/12.19 meet(X, Y)
% 93.79/12.19
% 93.79/12.19 Goal 1 (prove_distributivity): meet(a, join(b, c)) = join(meet(a, b), meet(a, c)).
% 93.79/12.19 Proof:
% 93.79/12.19 meet(a, join(b, c))
% 93.79/12.19 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.19 meet(a, join(c, b))
% 93.79/12.19 = { by lemma 39 R->L }
% 93.79/12.19 meet(a, join(complement(a), join(c, b)))
% 93.79/12.19 = { by axiom 8 (associativity_of_join) R->L }
% 93.79/12.19 meet(a, join(join(complement(a), c), b))
% 93.79/12.19 = { by lemma 31 R->L }
% 93.79/12.19 meet(a, join(join(complement(a), meet(complement(complement(a)), join(complement(a), c))), b))
% 93.79/12.19 = { by axiom 8 (associativity_of_join) }
% 93.79/12.19 meet(a, join(complement(a), join(meet(complement(complement(a)), join(complement(a), c)), b)))
% 93.79/12.19 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.19 meet(a, join(complement(a), join(b, meet(complement(complement(a)), join(complement(a), c)))))
% 93.79/12.19 = { by lemma 39 }
% 93.79/12.19 meet(a, join(b, meet(complement(complement(a)), join(complement(a), c))))
% 93.79/12.19 = { by lemma 15 R->L }
% 93.79/12.19 meet(a, join(b, meet(complement(complement(a)), join(complement(complement(complement(a))), c))))
% 93.79/12.19 = { by lemma 39 }
% 93.79/12.19 meet(a, join(b, meet(complement(complement(a)), c)))
% 93.79/12.19 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.19 meet(a, join(b, meet(c, complement(complement(a)))))
% 93.79/12.19 = { by lemma 15 }
% 93.79/12.19 meet(a, join(b, meet(c, a)))
% 93.79/12.19 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.19 meet(a, join(b, meet(a, c)))
% 93.79/12.19 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.19 meet(join(b, meet(a, c)), a)
% 93.79/12.19 = { by lemma 36 R->L }
% 93.79/12.19 meet(join(b, meet(a, c)), join(meet(join(b, meet(a, c)), a), meet(a, c)))
% 93.79/12.19 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.19 meet(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(a, c)))
% 93.79/12.19 = { by lemma 15 R->L }
% 93.79/12.19 meet(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))))
% 93.79/12.19 = { by lemma 15 R->L }
% 93.79/12.19 meet(join(b, complement(complement(meet(a, c)))), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))))
% 93.79/12.19 = { by axiom 4 (commutativity_of_meet) R->L }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(b, complement(complement(meet(a, c)))))
% 93.79/12.19 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), b))
% 93.79/12.19 = { by lemma 13 R->L }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, one)))
% 93.79/12.19 = { by lemma 14 R->L }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), one))))
% 93.79/12.19 = { by axiom 3 (complement_join) R->L }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), join(meet(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), complement(meet(a, c))), complement(meet(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), complement(meet(a, c)))))))))
% 93.79/12.19 = { by lemma 22 }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), complement(meet(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), complement(meet(a, c))))))))
% 93.79/12.19 = { by axiom 8 (associativity_of_join) }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(complement(complement(meet(a, c))), join(meet(a, join(b, meet(a, c))), complement(meet(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), complement(meet(a, c)))))))))
% 93.79/12.19 = { by lemma 19 R->L }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(meet(a, join(b, meet(a, c))), join(complement(complement(meet(a, c))), complement(meet(join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))), complement(meet(a, c)))))))))
% 93.79/12.19 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.19 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(meet(a, join(b, meet(a, c))), join(complement(complement(meet(a, c))), complement(meet(complement(meet(a, c)), join(complement(complement(meet(a, c))), meet(a, join(b, meet(a, c)))))))))))
% 93.79/12.20 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.20 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(meet(a, join(b, meet(a, c))), join(complement(complement(meet(a, c))), complement(meet(complement(meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))))))))))
% 93.79/12.20 = { by axiom 8 (associativity_of_join) R->L }
% 93.79/12.20 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(complement(complement(meet(a, c))), meet(b, join(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), complement(meet(complement(meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))))))
% 93.79/12.20 = { by lemma 30 R->L }
% 93.79/12.20 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), complement(meet(complement(meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))), meet(b, join(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), complement(meet(complement(meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))))))
% 93.79/12.20 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.20 meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), join(meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), complement(meet(complement(meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))), meet(b, join(complement(meet(complement(meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))))), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))))
% 93.79/12.20 = { by lemma 26 }
% 93.79/12.20 join(meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), complement(meet(complement(meet(a, c)), join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))), meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), b))
% 93.79/12.20 = { by lemma 30 }
% 93.79/12.20 join(complement(complement(meet(a, c))), meet(join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c)))), b))
% 93.79/12.20 = { by axiom 4 (commutativity_of_meet) }
% 93.79/12.20 join(complement(complement(meet(a, c))), meet(b, join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))
% 93.79/12.20 = { by lemma 15 }
% 93.79/12.20 join(meet(a, c), meet(b, join(meet(a, join(b, meet(a, c))), complement(complement(meet(a, c))))))
% 93.79/12.20 = { by lemma 15 }
% 93.79/12.20 join(meet(a, c), meet(b, join(meet(a, join(b, meet(a, c))), meet(a, c))))
% 93.79/12.20 = { by axiom 2 (commutativity_of_join) }
% 93.79/12.20 join(meet(a, c), meet(b, join(meet(a, c), meet(a, join(b, meet(a, c))))))
% 93.79/12.20 = { by axiom 2 (commutativity_of_join) R->L }
% 93.79/12.20 join(meet(a, c), meet(b, join(meet(a, c), meet(a, join(meet(a, c), b)))))
% 93.79/12.20 = { by lemma 25 R->L }
% 94.32/12.20 join(meet(a, c), meet(b, meet(a, join(meet(a, c), meet(a, join(meet(a, c), b))))))
% 94.32/12.20 = { by axiom 4 (commutativity_of_meet) R->L }
% 94.32/12.20 join(meet(a, c), meet(b, meet(join(meet(a, c), meet(a, join(meet(a, c), b))), a)))
% 94.32/12.20 = { by axiom 10 (associativity_of_meet) R->L }
% 94.32/12.20 join(meet(a, c), meet(meet(b, join(meet(a, c), meet(a, join(meet(a, c), b)))), a))
% 94.32/12.20 = { by axiom 4 (commutativity_of_meet) R->L }
% 94.32/12.20 join(meet(a, c), meet(a, meet(b, join(meet(a, c), meet(a, join(meet(a, c), b))))))
% 94.32/12.20 = { by axiom 2 (commutativity_of_join) R->L }
% 94.32/12.20 join(meet(a, c), meet(a, meet(b, join(meet(a, c), meet(a, join(b, meet(a, c)))))))
% 94.32/12.20 = { by axiom 4 (commutativity_of_meet) R->L }
% 94.32/12.20 join(meet(a, c), meet(a, meet(b, join(meet(a, c), meet(join(b, meet(a, c)), a)))))
% 94.32/12.20 = { by lemma 16 R->L }
% 94.32/12.20 join(meet(a, c), meet(b, meet(a, join(meet(a, c), meet(join(b, meet(a, c)), a)))))
% 94.32/12.20 = { by lemma 37 R->L }
% 94.32/12.20 join(meet(a, c), meet(b, meet(join(b, meet(a, c)), meet(a, join(meet(a, c), meet(join(b, meet(a, c)), a))))))
% 94.32/12.20 = { by lemma 23 }
% 94.32/12.20 join(meet(a, c), meet(b, meet(join(b, meet(a, c)), a)))
% 94.32/12.20 = { by lemma 37 }
% 94.32/12.20 join(meet(a, c), meet(b, a))
% 94.32/12.20 = { by axiom 4 (commutativity_of_meet) }
% 94.32/12.20 join(meet(a, c), meet(a, b))
% 94.32/12.20 = { by axiom 2 (commutativity_of_join) }
% 94.32/12.20 join(meet(a, b), meet(a, c))
% 94.32/12.20 % SZS output end Proof
% 94.32/12.20
% 94.32/12.20 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------