TSTP Solution File: LAT230-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT230-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:27:51 EDT 2023
% Result : Unsatisfiable 136.95s 17.90s
% Output : Proof 137.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT230-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 07:11:12 EDT 2023
% 0.16/0.34 % CPUTime :
% 136.95/17.90 Command-line arguments: --no-flatten-goal
% 136.95/17.90
% 136.95/17.90 % SZS status Unsatisfiable
% 136.95/17.90
% 136.95/17.92 % SZS output start Proof
% 136.95/17.92 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 136.95/17.92 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 136.95/17.92 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 136.95/17.92 Axiom 4 (prove_distributivity_hypothesis): meet(b, a) = a.
% 136.95/17.92 Axiom 5 (complement_join): join(X, complement(X)) = one.
% 136.95/17.92 Axiom 6 (complement_meet): meet(X, complement(X)) = zero.
% 136.95/17.92 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 136.95/17.92 Axiom 8 (absorption2): join(X, meet(X, Y)) = X.
% 136.95/17.92 Axiom 9 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 136.95/17.92 Axiom 10 (absorption1): meet(X, join(X, Y)) = X.
% 136.95/17.92 Axiom 11 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 136.95/17.92 Axiom 12 (meet_join_complement): ifeq(join(X, Y), one, ifeq(meet(X, Y), zero, complement(X), Y), Y) = Y.
% 136.95/17.92 Axiom 13 (equation_H18): join(meet(X, Y), meet(X, Z)) = meet(X, join(meet(X, Y), join(meet(X, Z), meet(Y, join(X, Z))))).
% 136.95/17.92
% 136.95/17.92 Lemma 14: meet(X, one) = X.
% 136.95/17.92 Proof:
% 136.95/17.92 meet(X, one)
% 136.95/17.92 = { by axiom 5 (complement_join) R->L }
% 136.95/17.92 meet(X, join(X, complement(X)))
% 136.95/17.92 = { by axiom 10 (absorption1) }
% 136.95/17.92 X
% 136.95/17.92
% 136.95/17.92 Lemma 15: join(X, one) = one.
% 136.95/17.92 Proof:
% 136.95/17.92 join(X, one)
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.92 join(one, X)
% 136.95/17.92 = { by lemma 14 R->L }
% 136.95/17.92 join(one, meet(X, one))
% 136.95/17.92 = { by axiom 3 (commutativity_of_meet) }
% 136.95/17.92 join(one, meet(one, X))
% 136.95/17.92 = { by axiom 8 (absorption2) }
% 136.95/17.92 one
% 136.95/17.92
% 136.95/17.92 Lemma 16: complement(complement(X)) = X.
% 136.95/17.92 Proof:
% 136.95/17.92 complement(complement(X))
% 136.95/17.92 = { by axiom 7 (ifeq_axiom) R->L }
% 136.95/17.92 ifeq(zero, zero, complement(complement(X)), X)
% 136.95/17.92 = { by axiom 6 (complement_meet) R->L }
% 136.95/17.92 ifeq(meet(X, complement(X)), zero, complement(complement(X)), X)
% 136.95/17.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 136.95/17.92 ifeq(meet(complement(X), X), zero, complement(complement(X)), X)
% 136.95/17.92 = { by axiom 7 (ifeq_axiom) R->L }
% 136.95/17.92 ifeq(one, one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 136.95/17.92 = { by axiom 5 (complement_join) R->L }
% 136.95/17.92 ifeq(join(X, complement(X)), one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.92 ifeq(join(complement(X), X), one, ifeq(meet(complement(X), X), zero, complement(complement(X)), X), X)
% 136.95/17.92 = { by axiom 12 (meet_join_complement) }
% 136.95/17.92 X
% 136.95/17.92
% 136.95/17.92 Lemma 17: join(X, meet(Y, X)) = X.
% 136.95/17.92 Proof:
% 136.95/17.92 join(X, meet(Y, X))
% 136.95/17.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 136.95/17.92 join(X, meet(X, Y))
% 136.95/17.92 = { by axiom 8 (absorption2) }
% 136.95/17.92 X
% 136.95/17.92
% 136.95/17.92 Lemma 18: join(X, join(Y, complement(X))) = one.
% 136.95/17.92 Proof:
% 136.95/17.92 join(X, join(Y, complement(X)))
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.92 join(X, join(complement(X), Y))
% 136.95/17.92 = { by axiom 9 (associativity_of_join) R->L }
% 136.95/17.92 join(join(X, complement(X)), Y)
% 136.95/17.92 = { by axiom 5 (complement_join) }
% 136.95/17.92 join(one, Y)
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.92 join(Y, one)
% 136.95/17.92 = { by lemma 15 }
% 136.95/17.92 one
% 136.95/17.92
% 136.95/17.92 Lemma 19: join(X, join(meet(X, Y), Z)) = join(X, Z).
% 136.95/17.92 Proof:
% 136.95/17.92 join(X, join(meet(X, Y), Z))
% 136.95/17.92 = { by axiom 9 (associativity_of_join) R->L }
% 136.95/17.92 join(join(X, meet(X, Y)), Z)
% 136.95/17.92 = { by axiom 8 (absorption2) }
% 136.95/17.92 join(X, Z)
% 136.95/17.92
% 136.95/17.92 Lemma 20: meet(X, join(meet(X, Y), meet(Z, join(X, Y)))) = join(meet(X, Z), meet(X, Y)).
% 136.95/17.92 Proof:
% 136.95/17.92 meet(X, join(meet(X, Y), meet(Z, join(X, Y))))
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.92 meet(X, join(meet(Z, join(X, Y)), meet(X, Y)))
% 136.95/17.92 = { by lemma 17 R->L }
% 136.95/17.92 meet(X, join(join(meet(Z, join(X, Y)), meet(X, meet(Z, join(X, Y)))), meet(X, Y)))
% 136.95/17.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 136.95/17.92 meet(X, join(join(meet(Z, join(X, Y)), meet(X, meet(join(X, Y), Z))), meet(X, Y)))
% 136.95/17.92 = { by axiom 11 (associativity_of_meet) R->L }
% 136.95/17.92 meet(X, join(join(meet(Z, join(X, Y)), meet(meet(X, join(X, Y)), Z)), meet(X, Y)))
% 136.95/17.92 = { by axiom 10 (absorption1) }
% 136.95/17.92 meet(X, join(join(meet(Z, join(X, Y)), meet(X, Z)), meet(X, Y)))
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) }
% 136.95/17.92 meet(X, join(join(meet(X, Z), meet(Z, join(X, Y))), meet(X, Y)))
% 136.95/17.92 = { by axiom 9 (associativity_of_join) }
% 136.95/17.92 meet(X, join(meet(X, Z), join(meet(Z, join(X, Y)), meet(X, Y))))
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) }
% 136.95/17.92 meet(X, join(meet(X, Z), join(meet(X, Y), meet(Z, join(X, Y)))))
% 136.95/17.92 = { by axiom 13 (equation_H18) R->L }
% 136.95/17.92 join(meet(X, Z), meet(X, Y))
% 136.95/17.92
% 136.95/17.92 Lemma 21: meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))) = complement(Y).
% 136.95/17.92 Proof:
% 136.95/17.92 meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))
% 136.95/17.92 = { by axiom 12 (meet_join_complement) R->L }
% 136.95/17.92 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))))))
% 136.95/17.92 = { by lemma 19 R->L }
% 136.95/17.92 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))))))
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.92 ifeq(join(Y, join(meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))), 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))))))
% 136.95/17.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 136.95/17.92 ifeq(join(Y, join(meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))), meet(join(X, complement(Y)), 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))))))
% 136.95/17.92 = { by lemma 20 R->L }
% 136.95/17.92 ifeq(join(Y, meet(join(X, complement(Y)), join(meet(join(X, complement(Y)), Y), meet(complement(meet(Y, join(X, complement(Y)))), join(join(X, complement(Y)), 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))))))
% 136.95/17.92 = { by axiom 1 (commutativity_of_join) }
% 136.95/17.93 ifeq(join(Y, meet(join(X, complement(Y)), join(meet(join(X, complement(Y)), Y), meet(complement(meet(Y, join(X, complement(Y)))), 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))))))
% 136.95/17.93 = { by lemma 18 }
% 136.95/17.93 ifeq(join(Y, meet(join(X, complement(Y)), join(meet(join(X, complement(Y)), Y), meet(complement(meet(Y, join(X, complement(Y)))), 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))))))
% 136.95/17.93 = { by lemma 14 }
% 136.95/17.93 ifeq(join(Y, meet(join(X, complement(Y)), join(meet(join(X, complement(Y)), 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))))))
% 136.95/17.93 = { by axiom 3 (commutativity_of_meet) }
% 136.95/17.93 ifeq(join(Y, meet(join(X, complement(Y)), join(meet(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))))))
% 136.95/17.93 = { by axiom 5 (complement_join) }
% 136.95/17.93 ifeq(join(Y, meet(join(X, complement(Y)), 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))))))
% 136.95/17.93 = { by lemma 14 }
% 136.95/17.93 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))))))
% 136.95/17.93 = { by lemma 18 }
% 136.95/17.93 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))))))
% 136.95/17.93 = { by axiom 7 (ifeq_axiom) }
% 136.95/17.93 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))))))
% 136.95/17.93 = { by axiom 11 (associativity_of_meet) R->L }
% 136.95/17.93 ifeq(meet(meet(Y, 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))))))
% 136.95/17.93 = { by axiom 6 (complement_meet) }
% 136.95/17.93 ifeq(zero, zero, complement(Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 136.95/17.93 = { by axiom 7 (ifeq_axiom) }
% 136.95/17.93 complement(Y)
% 136.95/17.93
% 136.95/17.93 Lemma 22: meet(join(X, Y), complement(meet(complement(X), join(X, Y)))) = X.
% 136.95/17.93 Proof:
% 136.95/17.93 meet(join(X, Y), complement(meet(complement(X), join(X, Y))))
% 136.95/17.93 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.93 meet(join(Y, X), complement(meet(complement(X), join(X, Y))))
% 136.95/17.93 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.93 meet(join(Y, X), complement(meet(complement(X), join(Y, X))))
% 136.95/17.93 = { by lemma 16 R->L }
% 136.95/17.93 meet(join(Y, X), complement(meet(complement(X), join(Y, complement(complement(X))))))
% 136.95/17.93 = { by lemma 16 R->L }
% 136.95/17.93 meet(join(Y, complement(complement(X))), complement(meet(complement(X), join(Y, complement(complement(X))))))
% 136.95/17.93 = { by lemma 21 }
% 136.95/17.93 complement(complement(X))
% 136.95/17.93 = { by lemma 16 }
% 136.95/17.93 X
% 136.95/17.93
% 136.95/17.93 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 136.95/17.93 Proof:
% 136.95/17.93 join(complement(b), complement(a))
% 136.95/17.93 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.93 join(complement(a), complement(b))
% 136.95/17.93 = { by axiom 2 (idempotence_of_meet) R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(b)))
% 136.95/17.93 = { by lemma 21 R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), meet(join(meet(b, a), complement(b)), complement(meet(b, join(meet(b, a), complement(b)))))))
% 136.95/17.93 = { by axiom 11 (associativity_of_meet) R->L }
% 136.95/17.93 join(complement(a), meet(meet(complement(b), join(meet(b, a), complement(b))), complement(meet(b, join(meet(b, a), complement(b))))))
% 136.95/17.93 = { by axiom 3 (commutativity_of_meet) }
% 136.95/17.93 join(complement(a), meet(complement(meet(b, join(meet(b, a), complement(b)))), meet(complement(b), join(meet(b, a), complement(b)))))
% 136.95/17.93 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.93 join(complement(a), meet(complement(meet(b, join(meet(b, a), complement(b)))), meet(complement(b), join(complement(b), meet(b, a)))))
% 136.95/17.93 = { by axiom 10 (absorption1) }
% 136.95/17.93 join(complement(a), meet(complement(meet(b, join(meet(b, a), complement(b)))), complement(b)))
% 136.95/17.93 = { by axiom 3 (commutativity_of_meet) }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(b, join(meet(b, a), complement(b))))))
% 136.95/17.93 = { by axiom 8 (absorption2) R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(b, meet(b, a)), join(meet(b, a), complement(b))))))
% 136.95/17.93 = { by axiom 1 (commutativity_of_join) R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), complement(b))))))
% 136.95/17.93 = { by lemma 14 R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), one))))))
% 136.95/17.93 = { by lemma 15 R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), join(join(meet(b, a), b), one)))))))
% 136.95/17.93 = { by axiom 5 (complement_join) R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), join(join(meet(b, a), b), join(meet(join(meet(b, a), b), complement(meet(b, a))), complement(meet(join(meet(b, a), b), complement(meet(b, a))))))))))))
% 136.95/17.93 = { by lemma 19 }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), join(join(meet(b, a), b), complement(meet(join(meet(b, a), b), complement(meet(b, a)))))))))))
% 136.95/17.93 = { by axiom 9 (associativity_of_join) }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), join(meet(b, a), join(b, complement(meet(join(meet(b, a), b), complement(meet(b, a))))))))))))
% 136.95/17.93 = { by axiom 3 (commutativity_of_meet) }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), join(meet(b, a), join(b, complement(meet(complement(meet(b, a)), join(meet(b, a), b)))))))))))
% 136.95/17.93 = { by axiom 9 (associativity_of_join) R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), join(join(meet(b, a), b), complement(meet(complement(meet(b, a)), join(meet(b, a), b))))))))))
% 136.95/17.93 = { by lemma 22 R->L }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(join(meet(b, a), b), complement(meet(complement(meet(b, a)), join(meet(b, a), b)))), meet(complement(b), join(join(meet(b, a), b), complement(meet(complement(meet(b, a)), join(meet(b, a), b))))))))))
% 136.95/17.93 = { by lemma 20 }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(join(meet(join(meet(b, a), b), complement(b)), meet(join(meet(b, a), b), complement(meet(complement(meet(b, a)), join(meet(b, a), b))))))))
% 136.95/17.93 = { by lemma 22 }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(join(meet(join(meet(b, a), b), complement(b)), meet(b, a)))))
% 136.95/17.93 = { by axiom 1 (commutativity_of_join) }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(join(meet(b, a), b), complement(b))))))
% 136.95/17.93 = { by axiom 3 (commutativity_of_meet) }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(complement(b), join(meet(b, a), b))))))
% 136.95/17.93 = { by axiom 1 (commutativity_of_join) }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(complement(b), join(b, meet(b, a)))))))
% 136.95/17.93 = { by axiom 8 (absorption2) }
% 136.95/17.93 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(complement(b), b)))))
% 137.56/17.93 = { by axiom 3 (commutativity_of_meet) }
% 137.56/17.93 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(b, complement(b))))))
% 137.56/17.93 = { by axiom 6 (complement_meet) }
% 137.56/17.93 join(complement(a), meet(complement(b), complement(join(meet(b, a), zero))))
% 137.56/17.93 = { by axiom 6 (complement_meet) R->L }
% 137.56/17.93 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(meet(b, a), complement(meet(b, a)))))))
% 137.56/17.93 = { by axiom 8 (absorption2) }
% 137.56/17.93 join(complement(a), meet(complement(b), complement(meet(b, a))))
% 137.56/17.93 = { by axiom 4 (prove_distributivity_hypothesis) }
% 137.56/17.93 join(complement(a), meet(complement(b), complement(a)))
% 137.56/17.93 = { by lemma 17 }
% 137.56/17.93 complement(a)
% 137.56/17.93 % SZS output end Proof
% 137.56/17.93
% 137.56/17.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------