TSTP Solution File: LAT228-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT228-1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n014.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 95.69s 12.64s
% Output : Proof 96.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT228-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 09:10:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 95.69/12.64 Command-line arguments: --no-flatten-goal
% 95.69/12.64
% 95.69/12.64 % SZS status Unsatisfiable
% 95.69/12.64
% 95.69/12.66 % SZS output start Proof
% 95.69/12.66 Take the following subset of the input axioms:
% 95.69/12.66 fof(absorption1, axiom, ![X, Y]: meet(X, join(X, Y))=X).
% 95.69/12.66 fof(absorption2, axiom, ![X2, Y2]: join(X2, meet(X2, Y2))=X2).
% 95.69/12.66 fof(associativity_of_join, axiom, ![Z, X2, Y2]: join(join(X2, Y2), Z)=join(X2, join(Y2, Z))).
% 95.69/12.66 fof(associativity_of_meet, axiom, ![X2, Y2, Z2]: meet(meet(X2, Y2), Z2)=meet(X2, meet(Y2, Z2))).
% 95.69/12.66 fof(commutativity_of_join, axiom, ![X2, Y2]: join(X2, Y2)=join(Y2, X2)).
% 95.69/12.66 fof(commutativity_of_meet, axiom, ![X2, Y2]: meet(X2, Y2)=meet(Y2, X2)).
% 95.69/12.66 fof(complement_join, axiom, ![X2]: join(X2, complement(X2))=one).
% 95.69/12.66 fof(complement_meet, axiom, ![X2]: meet(X2, complement(X2))=zero).
% 95.69/12.66 fof(equation_H16, axiom, ![X2, Y2, Z2]: meet(X2, join(meet(X2, Y2), meet(X2, Z2)))=meet(X2, join(meet(X2, Y2), meet(Z2, join(Y2, meet(Z2, join(X2, Y2))))))).
% 95.69/12.66 fof(idempotence_of_meet, axiom, ![X2]: meet(X2, X2)=X2).
% 95.69/12.66 fof(meet_join_complement, axiom, ![X2, Y2]: (meet(X2, Y2)!=zero | (join(X2, Y2)!=one | complement(X2)=Y2))).
% 95.69/12.66 fof(prove_distributivity, negated_conjecture, join(complement(b), complement(a))!=complement(a)).
% 95.69/12.66 fof(prove_distributivity_hypothesis, hypothesis, meet(b, a)=a).
% 95.69/12.66
% 95.69/12.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 95.69/12.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 95.69/12.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 95.69/12.66 fresh(y, y, x1...xn) = u
% 95.69/12.66 C => fresh(s, t, x1...xn) = v
% 95.69/12.66 where fresh is a fresh function symbol and x1..xn are the free
% 95.69/12.66 variables of u and v.
% 95.69/12.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 95.69/12.66 input problem has no model of domain size 1).
% 95.69/12.66
% 95.69/12.66 The encoding turns the above axioms into the following unit equations and goals:
% 95.69/12.66
% 95.69/12.66 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 95.69/12.66 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 95.69/12.66 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 95.69/12.66 Axiom 4 (prove_distributivity_hypothesis): meet(b, a) = a.
% 95.69/12.66 Axiom 5 (complement_join): join(X, complement(X)) = one.
% 95.69/12.66 Axiom 6 (complement_meet): meet(X, complement(X)) = zero.
% 95.69/12.66 Axiom 7 (meet_join_complement): fresh(X, X, Y, Z) = Z.
% 95.69/12.66 Axiom 8 (meet_join_complement): fresh2(X, X, Y, Z) = complement(Y).
% 95.69/12.66 Axiom 9 (absorption2): join(X, meet(X, Y)) = X.
% 95.69/12.66 Axiom 10 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 95.69/12.66 Axiom 11 (absorption1): meet(X, join(X, Y)) = X.
% 95.69/12.66 Axiom 12 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 95.69/12.66 Axiom 13 (meet_join_complement): fresh2(join(X, Y), one, X, Y) = fresh(meet(X, Y), zero, X, Y).
% 95.69/12.66 Axiom 14 (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)))))).
% 95.69/12.66
% 95.69/12.66 Lemma 15: complement(complement(X)) = X.
% 95.69/12.66 Proof:
% 95.69/12.66 complement(complement(X))
% 95.69/12.66 = { by axiom 8 (meet_join_complement) R->L }
% 95.69/12.66 fresh2(one, one, complement(X), X)
% 95.69/12.66 = { by axiom 5 (complement_join) R->L }
% 95.69/12.66 fresh2(join(X, complement(X)), one, complement(X), X)
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.66 fresh2(join(complement(X), X), one, complement(X), X)
% 95.69/12.66 = { by axiom 13 (meet_join_complement) }
% 95.69/12.66 fresh(meet(complement(X), X), zero, complement(X), X)
% 95.69/12.66 = { by axiom 3 (commutativity_of_meet) }
% 95.69/12.66 fresh(meet(X, complement(X)), zero, complement(X), X)
% 95.69/12.66 = { by axiom 6 (complement_meet) }
% 95.69/12.66 fresh(zero, zero, complement(X), X)
% 95.69/12.66 = { by axiom 7 (meet_join_complement) }
% 95.69/12.66 X
% 95.69/12.66
% 95.69/12.66 Lemma 16: meet(X, one) = X.
% 95.69/12.66 Proof:
% 95.69/12.66 meet(X, one)
% 95.69/12.66 = { by axiom 5 (complement_join) R->L }
% 95.69/12.66 meet(X, join(X, complement(X)))
% 95.69/12.66 = { by axiom 11 (absorption1) }
% 95.69/12.66 X
% 95.69/12.66
% 95.69/12.66 Lemma 17: join(X, one) = one.
% 95.69/12.66 Proof:
% 95.69/12.66 join(X, one)
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.66 join(one, X)
% 95.69/12.66 = { by lemma 16 R->L }
% 95.69/12.66 join(one, meet(X, one))
% 95.69/12.66 = { by axiom 3 (commutativity_of_meet) }
% 95.69/12.66 join(one, meet(one, X))
% 95.69/12.66 = { by axiom 9 (absorption2) }
% 95.69/12.66 one
% 95.69/12.66
% 95.69/12.66 Lemma 18: meet(X, join(Y, X)) = X.
% 95.69/12.66 Proof:
% 95.69/12.66 meet(X, join(Y, X))
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.66 meet(X, join(X, Y))
% 95.69/12.66 = { by axiom 11 (absorption1) }
% 95.69/12.66 X
% 95.69/12.66
% 95.69/12.66 Lemma 19: join(X, join(Y, complement(X))) = one.
% 95.69/12.66 Proof:
% 95.69/12.66 join(X, join(Y, complement(X)))
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.66 join(X, join(complement(X), Y))
% 95.69/12.66 = { by axiom 10 (associativity_of_join) R->L }
% 95.69/12.66 join(join(X, complement(X)), Y)
% 95.69/12.66 = { by axiom 5 (complement_join) }
% 95.69/12.66 join(one, Y)
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.66 join(Y, one)
% 95.69/12.66 = { by lemma 17 }
% 95.69/12.66 one
% 95.69/12.66
% 95.69/12.66 Lemma 20: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 95.69/12.66 Proof:
% 95.69/12.66 join(X, join(Y, meet(X, Z)))
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.66 join(X, join(meet(X, Z), Y))
% 95.69/12.66 = { by axiom 10 (associativity_of_join) R->L }
% 95.69/12.66 join(join(X, meet(X, Z)), Y)
% 95.69/12.66 = { by axiom 9 (absorption2) }
% 95.69/12.66 join(X, Y)
% 95.69/12.66
% 95.69/12.66 Lemma 21: join(X, join(meet(X, Y), Z)) = join(X, Z).
% 95.69/12.66 Proof:
% 95.69/12.66 join(X, join(meet(X, Y), Z))
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.66 join(X, join(Z, meet(X, Y)))
% 95.69/12.66 = { by lemma 20 }
% 95.69/12.66 join(X, Z)
% 95.69/12.66
% 95.69/12.66 Lemma 22: meet(X, join(meet(X, Y), meet(Z, join(Y, X)))) = join(meet(X, Y), meet(X, Z)).
% 95.69/12.66 Proof:
% 95.69/12.66 meet(X, join(meet(X, Y), meet(Z, join(Y, X))))
% 95.69/12.66 = { by axiom 11 (absorption1) R->L }
% 95.69/12.66 meet(X, join(meet(X, Y), meet(meet(Z, join(Y, X)), join(meet(Z, join(Y, X)), Y))))
% 95.69/12.66 = { by axiom 12 (associativity_of_meet) }
% 95.69/12.66 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, X), join(meet(Z, join(Y, X)), Y)))))
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) }
% 95.69/12.66 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, X), join(Y, meet(Z, join(Y, X)))))))
% 95.69/12.66 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.67 meet(X, join(meet(X, Y), meet(Z, meet(join(X, Y), join(Y, meet(Z, join(Y, X)))))))
% 95.69/12.67 = { by axiom 1 (commutativity_of_join) R->L }
% 95.69/12.67 meet(X, join(meet(X, Y), meet(Z, meet(join(X, Y), join(Y, meet(Z, join(X, Y)))))))
% 95.69/12.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 95.69/12.67 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(X, Y)))))
% 95.69/12.67 = { by axiom 9 (absorption2) R->L }
% 95.69/12.67 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(join(X, Y), meet(join(X, Y), Z))))))
% 95.69/12.67 = { by axiom 10 (associativity_of_join) }
% 95.69/12.67 meet(X, join(meet(X, Y), meet(Z, meet(join(Y, meet(Z, join(X, Y))), join(X, join(Y, meet(join(X, Y), Z)))))))
% 95.69/12.67 = { by axiom 3 (commutativity_of_meet) }
% 95.69/12.67 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))))))))
% 95.69/12.67 = { by lemma 18 }
% 95.69/12.67 meet(X, join(meet(X, Y), meet(Z, join(Y, meet(Z, join(X, Y))))))
% 95.69/12.67 = { by axiom 14 (equation_H16) R->L }
% 95.69/12.67 meet(X, join(meet(X, Y), meet(X, Z)))
% 95.69/12.67 = { by axiom 9 (absorption2) R->L }
% 95.69/12.67 meet(join(X, meet(X, Y)), join(meet(X, Y), meet(X, Z)))
% 95.69/12.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 95.69/12.67 meet(join(meet(X, Y), meet(X, Z)), join(X, meet(X, Y)))
% 95.69/12.67 = { by lemma 20 R->L }
% 95.69/12.67 meet(join(meet(X, Y), meet(X, Z)), join(X, join(meet(X, Y), meet(X, Z))))
% 95.69/12.67 = { by lemma 18 }
% 95.69/12.67 join(meet(X, Y), meet(X, Z))
% 95.69/12.67
% 95.69/12.67 Lemma 23: meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))) = complement(Y).
% 95.69/12.67 Proof:
% 95.69/12.67 meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))
% 95.69/12.67 = { by axiom 7 (meet_join_complement) R->L }
% 95.69/12.67 fresh(zero, zero, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by axiom 6 (complement_meet) R->L }
% 95.69/12.67 fresh(meet(meet(Y, join(X, complement(Y))), complement(meet(Y, join(X, complement(Y))))), zero, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by axiom 12 (associativity_of_meet) }
% 95.69/12.67 fresh(meet(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), zero, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by axiom 13 (meet_join_complement) R->L }
% 95.69/12.67 fresh2(join(Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y)))))), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by lemma 21 R->L }
% 95.69/12.67 fresh2(join(Y, join(meet(Y, join(X, complement(Y))), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 95.69/12.67 fresh2(join(Y, join(meet(join(X, complement(Y)), Y), meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by lemma 22 R->L }
% 95.69/12.67 fresh2(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, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by axiom 3 (commutativity_of_meet) }
% 95.69/12.67 fresh2(join(Y, meet(join(X, complement(Y)), join(meet(Y, join(X, complement(Y))), meet(complement(meet(Y, join(X, complement(Y)))), join(Y, join(X, complement(Y))))))), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by lemma 19 }
% 95.69/12.67 fresh2(join(Y, meet(join(X, complement(Y)), join(meet(Y, join(X, complement(Y))), meet(complement(meet(Y, join(X, complement(Y)))), one)))), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by lemma 16 }
% 95.69/12.67 fresh2(join(Y, meet(join(X, complement(Y)), join(meet(Y, join(X, complement(Y))), complement(meet(Y, join(X, complement(Y))))))), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by axiom 5 (complement_join) }
% 95.69/12.67 fresh2(join(Y, meet(join(X, complement(Y)), one)), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 95.69/12.67 = { by lemma 16 }
% 95.69/12.67 fresh2(join(Y, join(X, complement(Y))), one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 96.03/12.67 = { by lemma 19 }
% 96.03/12.67 fresh2(one, one, Y, meet(join(X, complement(Y)), complement(meet(Y, join(X, complement(Y))))))
% 96.03/12.67 = { by axiom 8 (meet_join_complement) }
% 96.03/12.67 complement(Y)
% 96.03/12.67
% 96.03/12.67 Lemma 24: meet(join(X, Y), complement(meet(complement(X), join(X, Y)))) = X.
% 96.03/12.67 Proof:
% 96.03/12.67 meet(join(X, Y), complement(meet(complement(X), join(X, Y))))
% 96.03/12.67 = { by axiom 1 (commutativity_of_join) R->L }
% 96.03/12.67 meet(join(Y, X), complement(meet(complement(X), join(X, Y))))
% 96.03/12.67 = { by axiom 1 (commutativity_of_join) R->L }
% 96.03/12.67 meet(join(Y, X), complement(meet(complement(X), join(Y, X))))
% 96.03/12.67 = { by lemma 15 R->L }
% 96.03/12.67 meet(join(Y, X), complement(meet(complement(X), join(Y, complement(complement(X))))))
% 96.03/12.67 = { by lemma 15 R->L }
% 96.03/12.67 meet(join(Y, complement(complement(X))), complement(meet(complement(X), join(Y, complement(complement(X))))))
% 96.03/12.67 = { by lemma 23 }
% 96.03/12.67 complement(complement(X))
% 96.03/12.67 = { by lemma 15 }
% 96.03/12.67 X
% 96.03/12.67
% 96.03/12.67 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 96.03/12.67 Proof:
% 96.03/12.67 join(complement(b), complement(a))
% 96.03/12.67 = { by axiom 1 (commutativity_of_join) R->L }
% 96.03/12.67 join(complement(a), complement(b))
% 96.03/12.67 = { by axiom 2 (idempotence_of_meet) R->L }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(b)))
% 96.03/12.67 = { by lemma 23 R->L }
% 96.03/12.67 join(complement(a), meet(complement(b), meet(join(meet(b, a), complement(b)), complement(meet(b, join(meet(b, a), complement(b)))))))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 96.03/12.67 join(complement(a), meet(complement(b), meet(complement(meet(b, join(meet(b, a), complement(b)))), join(meet(b, a), complement(b)))))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 96.03/12.67 join(complement(a), meet(meet(complement(meet(b, join(meet(b, a), complement(b)))), join(meet(b, a), complement(b))), complement(b)))
% 96.03/12.67 = { by axiom 12 (associativity_of_meet) }
% 96.03/12.67 join(complement(a), meet(complement(meet(b, join(meet(b, a), complement(b)))), meet(join(meet(b, a), complement(b)), complement(b))))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) }
% 96.03/12.67 join(complement(a), meet(complement(meet(b, join(meet(b, a), complement(b)))), meet(complement(b), join(meet(b, a), complement(b)))))
% 96.03/12.67 = { by lemma 18 }
% 96.03/12.67 join(complement(a), meet(complement(meet(b, join(meet(b, a), complement(b)))), complement(b)))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(meet(b, join(meet(b, a), complement(b))))))
% 96.03/12.67 = { by axiom 9 (absorption2) R->L }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(meet(join(b, meet(b, a)), join(meet(b, a), complement(b))))))
% 96.03/12.67 = { by axiom 1 (commutativity_of_join) R->L }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), complement(b))))))
% 96.03/12.67 = { by lemma 16 R->L }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(meet(join(meet(b, a), b), join(meet(b, a), meet(complement(b), one))))))
% 96.03/12.67 = { by lemma 17 R->L }
% 96.03/12.67 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)))))))
% 96.03/12.67 = { by axiom 5 (complement_join) R->L }
% 96.03/12.67 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))))))))))))
% 96.03/12.67 = { by lemma 21 }
% 96.03/12.67 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)))))))))))
% 96.03/12.67 = { by axiom 10 (associativity_of_join) }
% 96.03/12.67 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))))))))))))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) }
% 96.03/12.67 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)))))))))))
% 96.03/12.67 = { by axiom 10 (associativity_of_join) R->L }
% 96.03/12.67 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))))))))))
% 96.03/12.67 = { by lemma 24 R->L }
% 96.03/12.67 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))))))))))
% 96.03/12.67 = { by axiom 1 (commutativity_of_join) R->L }
% 96.03/12.67 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(complement(meet(complement(meet(b, a)), join(meet(b, a), b))), join(meet(b, a), b))))))))
% 96.03/12.67 = { by lemma 22 }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(join(meet(b, a), b), complement(meet(complement(meet(b, a)), join(meet(b, a), b)))), meet(join(meet(b, a), b), complement(b))))))
% 96.03/12.67 = { by lemma 24 }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(join(meet(b, a), b), complement(b))))))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(complement(b), join(meet(b, a), b))))))
% 96.03/12.67 = { by axiom 1 (commutativity_of_join) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(complement(b), join(b, meet(b, a)))))))
% 96.03/12.67 = { by axiom 9 (absorption2) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(complement(b), b)))))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(b, complement(b))))))
% 96.03/12.67 = { by axiom 6 (complement_meet) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(b, a), zero))))
% 96.03/12.67 = { by axiom 6 (complement_meet) R->L }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(join(meet(b, a), meet(meet(b, a), complement(meet(b, a)))))))
% 96.03/12.67 = { by axiom 9 (absorption2) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(meet(b, a))))
% 96.03/12.67 = { by axiom 4 (prove_distributivity_hypothesis) }
% 96.03/12.67 join(complement(a), meet(complement(b), complement(a)))
% 96.03/12.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 96.03/12.67 join(complement(a), meet(complement(a), complement(b)))
% 96.03/12.67 = { by axiom 9 (absorption2) }
% 96.03/12.67 complement(a)
% 96.03/12.67 % SZS output end Proof
% 96.03/12.67
% 96.03/12.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------