TSTP Solution File: LAT196-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT196-1 : 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 : n024.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 06:27:43 EDT 2023
% Result : Unsatisfiable 103.07s 13.56s
% Output : Proof 103.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT196-1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n024.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 06:26:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 103.07/13.56 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 103.07/13.56
% 103.07/13.56 % SZS status Unsatisfiable
% 103.07/13.56
% 103.63/13.60 % SZS output start Proof
% 103.63/13.60 Take the following subset of the input axioms:
% 103.63/13.60 fof(absorption1, axiom, ![X, Y]: meet(X, join(X, Y))=X).
% 103.63/13.60 fof(absorption2, axiom, ![X2, Y2]: join(X2, meet(X2, Y2))=X2).
% 103.63/13.60 fof(associativity_of_join, axiom, ![Z, X2, Y2]: join(join(X2, Y2), Z)=join(X2, join(Y2, Z))).
% 103.63/13.60 fof(associativity_of_meet, axiom, ![X2, Y2, Z2]: meet(meet(X2, Y2), Z2)=meet(X2, meet(Y2, Z2))).
% 103.63/13.60 fof(commutativity_of_join, axiom, ![X2, Y2]: join(X2, Y2)=join(Y2, X2)).
% 103.63/13.60 fof(commutativity_of_meet, axiom, ![X2, Y2]: meet(X2, Y2)=meet(Y2, X2)).
% 103.63/13.60 fof(complement_join, axiom, ![X2]: join(X2, complement(X2))=one).
% 103.63/13.60 fof(complement_meet, axiom, ![X2]: meet(X2, complement(X2))=zero).
% 103.63/13.60 fof(equation_H39, axiom, ![U, X2, Y2, Z2]: meet(X2, join(Y2, meet(Z2, join(X2, U))))=meet(X2, join(Y2, meet(Z2, join(U, meet(X2, Z2)))))).
% 103.63/13.60 fof(meet_join_complement, axiom, ![X2, Y2]: (meet(X2, Y2)!=zero | (join(X2, Y2)!=one | complement(X2)=Y2))).
% 103.63/13.60 fof(prove_distributivity, negated_conjecture, meet(a, join(b, c))!=join(meet(a, b), meet(a, c))).
% 103.63/13.60
% 103.63/13.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 103.63/13.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 103.63/13.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 103.63/13.60 fresh(y, y, x1...xn) = u
% 103.63/13.60 C => fresh(s, t, x1...xn) = v
% 103.63/13.60 where fresh is a fresh function symbol and x1..xn are the free
% 103.63/13.60 variables of u and v.
% 103.63/13.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 103.63/13.60 input problem has no model of domain size 1).
% 103.63/13.60
% 103.63/13.60 The encoding turns the above axioms into the following unit equations and goals:
% 103.63/13.60
% 103.63/13.60 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 103.63/13.60 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 103.63/13.60 Axiom 3 (complement_meet): meet(X, complement(X)) = zero.
% 103.63/13.60 Axiom 4 (complement_join): join(X, complement(X)) = one.
% 103.63/13.60 Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
% 103.63/13.60 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 103.63/13.60 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 103.63/13.60 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 103.63/13.60 Axiom 9 (meet_join_complement): fresh(X, X, Y, Z) = Z.
% 103.63/13.60 Axiom 10 (meet_join_complement): fresh2(X, X, Y, Z) = complement(Y).
% 103.63/13.60 Axiom 11 (meet_join_complement): fresh2(join(X, Y), one, X, Y) = fresh(meet(X, Y), zero, X, Y).
% 103.63/13.60 Axiom 12 (equation_H39): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(W, meet(X, Z))))).
% 103.63/13.60
% 103.63/13.60 Lemma 13: meet(X, one) = X.
% 103.63/13.60 Proof:
% 103.63/13.60 meet(X, one)
% 103.63/13.60 = { by axiom 4 (complement_join) R->L }
% 103.63/13.60 meet(X, join(X, complement(X)))
% 103.63/13.60 = { by axiom 5 (absorption1) }
% 103.63/13.60 X
% 103.63/13.60
% 103.63/13.60 Lemma 14: join(X, one) = one.
% 103.63/13.60 Proof:
% 103.63/13.60 join(X, one)
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 join(one, X)
% 103.63/13.60 = { by lemma 13 R->L }
% 103.63/13.60 meet(join(one, X), one)
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) }
% 103.63/13.60 meet(one, join(one, X))
% 103.63/13.60 = { by axiom 5 (absorption1) }
% 103.63/13.60 one
% 103.63/13.60
% 103.63/13.60 Lemma 15: join(one, X) = one.
% 103.63/13.60 Proof:
% 103.63/13.60 join(one, X)
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 join(X, one)
% 103.63/13.60 = { by lemma 14 }
% 103.63/13.60 one
% 103.63/13.60
% 103.63/13.60 Lemma 16: meet(X, join(Y, X)) = X.
% 103.63/13.60 Proof:
% 103.63/13.60 meet(X, join(Y, X))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 meet(X, join(X, Y))
% 103.63/13.60 = { by axiom 5 (absorption1) }
% 103.63/13.60 X
% 103.63/13.60
% 103.63/13.60 Lemma 17: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 103.63/13.60 Proof:
% 103.63/13.60 meet(Y, meet(X, Z))
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) R->L }
% 103.63/13.60 meet(meet(X, Z), Y)
% 103.63/13.60 = { by axiom 6 (associativity_of_meet) }
% 103.63/13.60 meet(X, meet(Z, Y))
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) }
% 103.63/13.60 meet(X, meet(Y, Z))
% 103.63/13.60
% 103.63/13.60 Lemma 18: join(X, meet(Y, X)) = X.
% 103.63/13.60 Proof:
% 103.63/13.60 join(X, meet(Y, X))
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) R->L }
% 103.63/13.60 join(X, meet(X, Y))
% 103.63/13.60 = { by axiom 7 (absorption2) }
% 103.63/13.60 X
% 103.63/13.60
% 103.63/13.60 Lemma 19: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 103.63/13.60 Proof:
% 103.63/13.60 join(Y, join(X, Z))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 join(join(X, Z), Y)
% 103.63/13.60 = { by axiom 8 (associativity_of_join) }
% 103.63/13.60 join(X, join(Z, Y))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) }
% 103.63/13.60 join(X, join(Y, Z))
% 103.63/13.60
% 103.63/13.60 Lemma 20: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 103.63/13.60 Proof:
% 103.63/13.60 join(Z, join(X, Y))
% 103.63/13.60 = { by lemma 19 }
% 103.63/13.60 join(X, join(Z, Y))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) }
% 103.63/13.60 join(X, join(Y, Z))
% 103.63/13.60
% 103.63/13.60 Lemma 21: join(X, complement(meet(X, Y))) = one.
% 103.63/13.60 Proof:
% 103.63/13.60 join(X, complement(meet(X, Y)))
% 103.63/13.60 = { by axiom 7 (absorption2) R->L }
% 103.63/13.60 join(join(X, meet(X, Y)), complement(meet(X, Y)))
% 103.63/13.60 = { by axiom 8 (associativity_of_join) }
% 103.63/13.60 join(X, join(meet(X, Y), complement(meet(X, Y))))
% 103.63/13.60 = { by axiom 4 (complement_join) }
% 103.63/13.60 join(X, one)
% 103.63/13.60 = { by lemma 14 }
% 103.63/13.60 one
% 103.63/13.60
% 103.63/13.60 Lemma 22: fresh2(join(X, Y), one, Y, X) = fresh(meet(X, Y), zero, Y, X).
% 103.63/13.60 Proof:
% 103.63/13.60 fresh2(join(X, Y), one, Y, X)
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 fresh2(join(Y, X), one, Y, X)
% 103.63/13.60 = { by axiom 11 (meet_join_complement) }
% 103.63/13.60 fresh(meet(Y, X), zero, Y, X)
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) }
% 103.63/13.60 fresh(meet(X, Y), zero, Y, X)
% 103.63/13.60
% 103.63/13.60 Lemma 23: meet(X, meet(Y, join(Z, X))) = meet(Y, X).
% 103.63/13.60 Proof:
% 103.63/13.60 meet(X, meet(Y, join(Z, X)))
% 103.63/13.60 = { by lemma 17 }
% 103.63/13.60 meet(Y, meet(X, join(Z, X)))
% 103.63/13.60 = { by lemma 16 }
% 103.63/13.60 meet(Y, X)
% 103.63/13.60
% 103.63/13.60 Lemma 24: meet(X, join(Y, join(meet(X, Z), complement(meet(X, W))))) = meet(X, join(Y, join(Z, complement(meet(X, W))))).
% 103.63/13.60 Proof:
% 103.63/13.60 meet(X, join(Y, join(meet(X, Z), complement(meet(X, W)))))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 meet(X, join(Y, join(complement(meet(X, W)), meet(X, Z))))
% 103.63/13.60 = { by axiom 8 (associativity_of_join) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(X, Z)))
% 103.63/13.60 = { by lemma 23 R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, meet(X, join(V, Z)))))
% 103.63/13.60 = { by axiom 7 (absorption2) R->L }
% 103.63/13.60 meet(X, join(join(join(Y, complement(meet(X, W))), meet(Z, meet(X, join(V, Z)))), meet(join(join(Y, complement(meet(X, W))), meet(Z, meet(X, join(V, Z)))), Z)))
% 103.63/13.60 = { by axiom 8 (associativity_of_join) }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(Z, meet(X, join(V, Z))), meet(join(join(Y, complement(meet(X, W))), meet(Z, meet(X, join(V, Z)))), Z))))
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(Z, meet(X, join(V, Z))), meet(Z, join(join(Y, complement(meet(X, W))), meet(Z, meet(X, join(V, Z))))))))
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(meet(X, join(V, Z)), Z), meet(Z, join(join(Y, complement(meet(X, W))), meet(Z, meet(X, join(V, Z))))))))
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(meet(X, join(V, Z)), Z), meet(Z, join(join(Y, complement(meet(X, W))), meet(meet(X, join(V, Z)), Z))))))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(Z, join(join(Y, complement(meet(X, W))), meet(meet(X, join(V, Z)), Z))), meet(meet(X, join(V, Z)), Z))))
% 103.63/13.60 = { by axiom 5 (absorption1) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(Z, join(join(Y, complement(meet(X, W))), meet(meet(X, join(V, Z)), Z))), meet(meet(meet(X, join(V, Z)), Z), join(meet(meet(X, join(V, Z)), Z), join(Y, complement(meet(X, W))))))))
% 103.63/13.60 = { by axiom 6 (associativity_of_meet) }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(Z, join(join(Y, complement(meet(X, W))), meet(meet(X, join(V, Z)), Z))), meet(meet(X, join(V, Z)), meet(Z, join(meet(meet(X, join(V, Z)), Z), join(Y, complement(meet(X, W)))))))))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), join(meet(Z, join(join(Y, complement(meet(X, W))), meet(meet(X, join(V, Z)), Z))), meet(meet(X, join(V, Z)), meet(Z, join(join(Y, complement(meet(X, W))), meet(meet(X, join(V, Z)), Z)))))))
% 103.63/13.60 = { by lemma 18 }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, join(join(Y, complement(meet(X, W))), meet(meet(X, join(V, Z)), Z)))))
% 103.63/13.60 = { by axiom 1 (commutativity_of_meet) }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, join(join(Y, complement(meet(X, W))), meet(Z, meet(X, join(V, Z)))))))
% 103.63/13.60 = { by lemma 23 }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, join(join(Y, complement(meet(X, W))), meet(X, Z)))))
% 103.63/13.60 = { by axiom 12 (equation_H39) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, join(X, join(Y, complement(meet(X, W)))))))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, join(X, join(complement(meet(X, W)), Y)))))
% 103.63/13.60 = { by axiom 8 (associativity_of_join) R->L }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, join(join(X, complement(meet(X, W))), Y))))
% 103.63/13.60 = { by lemma 21 }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, join(one, Y))))
% 103.63/13.60 = { by lemma 15 }
% 103.63/13.60 meet(X, join(join(Y, complement(meet(X, W))), meet(Z, one)))
% 103.63/13.60 = { by axiom 8 (associativity_of_join) }
% 103.63/13.60 meet(X, join(Y, join(complement(meet(X, W)), meet(Z, one))))
% 103.63/13.60 = { by lemma 13 }
% 103.63/13.60 meet(X, join(Y, join(complement(meet(X, W)), Z)))
% 103.63/13.60 = { by axiom 2 (commutativity_of_join) }
% 103.63/13.61 meet(X, join(Y, join(Z, complement(meet(X, W)))))
% 103.63/13.61
% 103.63/13.61 Goal 1 (prove_distributivity): meet(a, join(b, c)) = join(meet(a, b), meet(a, c)).
% 103.63/13.61 Proof:
% 103.63/13.61 meet(a, join(b, c))
% 103.63/13.61 = { by axiom 9 (meet_join_complement) R->L }
% 103.63/13.61 fresh(zero, zero, complement(meet(a, join(b, c))), meet(a, join(b, c)))
% 103.63/13.61 = { by axiom 3 (complement_meet) R->L }
% 103.63/13.61 fresh(meet(meet(a, join(b, c)), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), meet(a, join(b, c)))
% 103.63/13.61 = { by lemma 22 R->L }
% 103.63/13.61 fresh2(join(meet(a, join(b, c)), complement(meet(a, join(b, c)))), one, complement(meet(a, join(b, c))), meet(a, join(b, c)))
% 103.63/13.61 = { by axiom 4 (complement_join) }
% 103.63/13.61 fresh2(one, one, complement(meet(a, join(b, c))), meet(a, join(b, c)))
% 103.63/13.61 = { by axiom 10 (meet_join_complement) }
% 103.63/13.61 complement(complement(meet(a, join(b, c))))
% 103.63/13.61 = { by axiom 10 (meet_join_complement) R->L }
% 103.63/13.61 fresh2(one, one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 21 R->L }
% 103.63/13.61 fresh2(join(a, complement(meet(a, join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 7 (absorption2) R->L }
% 103.63/13.61 fresh2(join(join(a, meet(a, b)), complement(meet(a, join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.61 fresh2(join(join(meet(a, b), a), complement(meet(a, join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 7 (absorption2) R->L }
% 103.63/13.61 fresh2(join(join(meet(a, b), join(a, meet(a, c))), complement(meet(a, join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 19 R->L }
% 103.63/13.61 fresh2(join(join(a, join(meet(a, b), meet(a, c))), complement(meet(a, join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 8 (associativity_of_join) }
% 103.63/13.61 fresh2(join(a, join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 19 }
% 103.63/13.61 fresh2(join(join(meet(a, b), meet(a, c)), join(a, complement(meet(a, join(b, c))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.61 fresh2(join(join(meet(a, b), meet(a, c)), join(complement(meet(a, join(b, c))), a)), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 8 (associativity_of_join) R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), a), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 13 R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, one)), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 15 R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(one, join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 4 (complement_join) R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(join(meet(a, join(b, c)), complement(meet(a, join(b, c)))), join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 8 (associativity_of_join) }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(meet(a, join(b, c)), join(complement(meet(a, join(b, c))), join(b, c))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(meet(a, join(b, c)), join(join(b, c), complement(meet(a, join(b, c))))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 8 (associativity_of_join) R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(join(meet(a, join(b, c)), join(b, c)), complement(meet(a, join(b, c)))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(join(join(b, c), meet(a, join(b, c))), complement(meet(a, join(b, c)))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 18 }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(join(b, c), complement(meet(a, join(b, c)))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(complement(meet(a, join(b, c))), join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 20 }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(b, join(c, complement(meet(a, join(b, c))))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 19 }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(c, join(b, complement(meet(a, join(b, c))))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 24 R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(c, join(meet(a, b), complement(meet(a, join(b, c))))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 19 }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(meet(a, b), join(c, complement(meet(a, join(b, c))))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 24 R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(meet(a, b), join(meet(a, c), complement(meet(a, join(b, c))))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 20 R->L }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) }
% 103.63/13.61 fresh2(join(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), meet(a, join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 18 }
% 103.63/13.61 fresh2(join(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), one, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 22 }
% 103.63/13.61 fresh(meet(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 16 R->L }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), join(meet(a, join(b, c)), join(meet(a, b), meet(a, c)))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 19 }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), join(meet(a, b), join(meet(a, join(b, c)), meet(a, c)))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 23 R->L }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), join(meet(a, b), join(meet(a, join(b, c)), meet(c, meet(a, join(b, c)))))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 18 }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), join(meet(a, b), meet(a, join(b, c)))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), join(meet(a, join(b, c)), meet(a, b))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 5 (absorption1) R->L }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), join(meet(a, join(b, c)), meet(a, meet(b, join(b, c))))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 17 R->L }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), join(meet(a, join(b, c)), meet(b, meet(a, join(b, c))))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by lemma 18 }
% 103.63/13.61 fresh(meet(meet(join(meet(a, b), meet(a, c)), meet(a, join(b, c))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 1 (commutativity_of_meet) }
% 103.63/13.61 fresh(meet(meet(meet(a, join(b, c)), join(meet(a, b), meet(a, c))), complement(meet(a, join(b, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 6 (associativity_of_meet) }
% 103.63/13.61 fresh(meet(meet(a, join(b, c)), meet(join(meet(a, b), meet(a, c)), complement(meet(a, join(b, c))))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 1 (commutativity_of_meet) R->L }
% 103.63/13.61 fresh(meet(meet(a, join(b, c)), meet(complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 6 (associativity_of_meet) R->L }
% 103.63/13.61 fresh(meet(meet(meet(a, join(b, c)), complement(meet(a, join(b, c)))), join(meet(a, b), meet(a, c))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 3 (complement_meet) }
% 103.63/13.61 fresh(meet(zero, join(meet(a, b), meet(a, c))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 7 (absorption2) R->L }
% 103.63/13.61 fresh(meet(zero, join(join(meet(a, b), meet(a, c)), meet(join(meet(a, b), meet(a, c)), complement(join(meet(a, b), meet(a, c)))))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 3 (complement_meet) }
% 103.63/13.61 fresh(meet(zero, join(join(meet(a, b), meet(a, c)), zero)), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 2 (commutativity_of_join) }
% 103.63/13.61 fresh(meet(zero, join(zero, join(meet(a, b), meet(a, c)))), zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 5 (absorption1) }
% 103.63/13.61 fresh(zero, zero, complement(meet(a, join(b, c))), join(meet(a, b), meet(a, c)))
% 103.63/13.61 = { by axiom 9 (meet_join_complement) }
% 103.63/13.61 join(meet(a, b), meet(a, c))
% 103.63/13.61 % SZS output end Proof
% 103.63/13.61
% 103.63/13.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------