TSTP Solution File: LAT036-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT036-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n021.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 06:27:13 EDT 2023
% Result : Unsatisfiable 0.19s 0.65s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT036-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 08:33:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.65 Command-line arguments: --flatten
% 0.19/0.65
% 0.19/0.65 % SZS status Unsatisfiable
% 0.19/0.65
% 0.19/0.70 % SZS output start Proof
% 0.19/0.70 Take the following subset of the input axioms:
% 0.19/0.70 fof(absorption1, axiom, ![X, Y]: meet(X, join(X, Y))=X).
% 0.19/0.70 fof(absorption2, axiom, ![X2, Y2]: join(X2, meet(X2, Y2))=X2).
% 0.19/0.70 fof(associativity_of_join, axiom, ![Z, X2, Y2]: join(join(X2, Y2), Z)=join(X2, join(Y2, Z))).
% 0.19/0.70 fof(associativity_of_meet, axiom, ![X2, Y2, Z2]: meet(meet(X2, Y2), Z2)=meet(X2, meet(Y2, Z2))).
% 0.19/0.70 fof(commutativity_of_join, axiom, ![X2, Y2]: join(X2, Y2)=join(Y2, X2)).
% 0.19/0.70 fof(commutativity_of_meet, axiom, ![X2, Y2]: meet(X2, Y2)=meet(Y2, X2)).
% 0.19/0.70 fof(dist_join, hypothesis, ![X2, Y2, Z2]: join(X2, meet(Y2, Z2))=meet(join(X2, Y2), join(X2, Z2))).
% 0.19/0.70 fof(k_on_join, axiom, ![U, V]: k(join(U, V))=meet(k(U), k(V))).
% 0.19/0.70 fof(k_on_meet, axiom, ![U2, V2]: k(meet(U2, V2))=join(k(U2), k(V2))).
% 0.19/0.70 fof(lhs1, hypothesis, join(k(k(aa)), join(aa, k(aa)))=join(aa, k(aa))).
% 0.19/0.70 fof(lhs2, hypothesis, join(k(k(k(bb))), join(aa, k(aa)))=join(aa, k(aa))).
% 0.19/0.70 fof(lhs3, hypothesis, join(k(k(aa)), join(k(aa), join(k(bb), k(cc))))=join(k(aa), join(k(bb), k(cc)))).
% 0.19/0.71 fof(lhs4, hypothesis, join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc))))=join(k(aa), join(k(bb), k(cc)))).
% 0.19/0.71 fof(rhs, negated_conjecture, join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))!=join(meet(aa, k(meet(bb, cc))), k(aa))).
% 0.19/0.71
% 0.19/0.71 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.71 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.71 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.71 fresh(y, y, x1...xn) = u
% 0.19/0.71 C => fresh(s, t, x1...xn) = v
% 0.19/0.71 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.71 variables of u and v.
% 0.19/0.71 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.71 input problem has no model of domain size 1).
% 0.19/0.71
% 0.19/0.71 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.71
% 0.19/0.71 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.19/0.71 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.19/0.71 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 0.19/0.71 Axiom 4 (k_on_join): k(join(X, Y)) = meet(k(X), k(Y)).
% 0.19/0.71 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.19/0.71 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 0.19/0.71 Axiom 7 (k_on_meet): k(meet(X, Y)) = join(k(X), k(Y)).
% 0.19/0.71 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.19/0.71 Axiom 9 (dist_join): join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)).
% 0.19/0.71 Axiom 10 (lhs1): join(k(k(aa)), join(aa, k(aa))) = join(aa, k(aa)).
% 0.19/0.71 Axiom 11 (lhs2): join(k(k(k(bb))), join(aa, k(aa))) = join(aa, k(aa)).
% 0.19/0.71 Axiom 12 (lhs3): join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))) = join(k(aa), join(k(bb), k(cc))).
% 0.19/0.71 Axiom 13 (lhs4): join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))) = join(k(aa), join(k(bb), k(cc))).
% 0.19/0.71
% 0.19/0.71 Lemma 14: meet(X, join(Y, X)) = X.
% 0.19/0.71 Proof:
% 0.19/0.71 meet(X, join(Y, X))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.71 meet(X, join(X, Y))
% 0.19/0.71 = { by axiom 3 (absorption1) }
% 0.19/0.71 X
% 0.19/0.71
% 0.19/0.71 Lemma 15: meet(join(X, Y), Y) = Y.
% 0.19/0.71 Proof:
% 0.19/0.71 meet(join(X, Y), Y)
% 0.19/0.71 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.71 meet(Y, join(X, Y))
% 0.19/0.71 = { by lemma 14 }
% 0.19/0.71 Y
% 0.19/0.71
% 0.19/0.71 Lemma 16: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 0.19/0.71 Proof:
% 0.19/0.71 join(Y, join(Z, X))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.71 join(join(Z, X), Y)
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.71 join(join(X, Z), Y)
% 0.19/0.71 = { by axiom 8 (associativity_of_join) }
% 0.19/0.71 join(X, join(Z, Y))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.71 join(X, join(Y, Z))
% 0.19/0.71
% 0.19/0.71 Lemma 17: meet(join(k(X), k(Y)), Z) = meet(Z, k(meet(X, Y))).
% 0.19/0.71 Proof:
% 0.19/0.71 meet(join(k(X), k(Y)), Z)
% 0.19/0.71 = { by axiom 7 (k_on_meet) R->L }
% 0.19/0.71 meet(k(meet(X, Y)), Z)
% 0.19/0.71 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.71 meet(Z, k(meet(X, Y)))
% 0.19/0.71
% 0.19/0.71 Lemma 18: join(k(k(X)), k(k(Y))) = k(k(join(Y, X))).
% 0.19/0.71 Proof:
% 0.19/0.71 join(k(k(X)), k(k(Y)))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.71 join(k(k(Y)), k(k(X)))
% 0.19/0.71 = { by axiom 7 (k_on_meet) R->L }
% 0.19/0.71 k(meet(k(Y), k(X)))
% 0.19/0.71 = { by axiom 1 (commutativity_of_meet) }
% 0.19/0.71 k(meet(k(X), k(Y)))
% 0.19/0.71 = { by axiom 4 (k_on_join) R->L }
% 0.19/0.71 k(k(join(X, Y)))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.71 k(k(join(Y, X)))
% 0.19/0.71
% 0.19/0.71 Lemma 19: join(k(k(k(bb))), join(aa, k(aa))) = join(k(k(aa)), join(aa, k(aa))).
% 0.19/0.71 Proof:
% 0.19/0.71 join(k(k(k(bb))), join(aa, k(aa)))
% 0.19/0.71 = { by axiom 11 (lhs2) }
% 0.19/0.71 join(aa, k(aa))
% 0.19/0.71 = { by axiom 10 (lhs1) R->L }
% 0.19/0.71 join(k(k(aa)), join(aa, k(aa)))
% 0.19/0.71
% 0.19/0.71 Lemma 20: join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))) = join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))).
% 0.19/0.71 Proof:
% 0.19/0.71 join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc))))
% 0.19/0.71 = { by axiom 13 (lhs4) }
% 0.19/0.71 join(k(aa), join(k(bb), k(cc)))
% 0.19/0.71 = { by axiom 12 (lhs3) R->L }
% 0.19/0.71 join(k(k(aa)), join(k(aa), join(k(bb), k(cc))))
% 0.19/0.71
% 0.19/0.71 Lemma 21: meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(k(bb))), join(aa, k(aa)))) = join(meet(aa, k(meet(bb, cc))), k(aa)).
% 0.19/0.71 Proof:
% 0.19/0.71 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(k(bb))), join(aa, k(aa))))
% 0.19/0.71 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.71 meet(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))))
% 0.19/0.71 = { by lemma 20 }
% 0.19/0.71 meet(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))))
% 0.19/0.71 = { by axiom 12 (lhs3) }
% 0.19/0.71 meet(join(k(k(k(bb))), join(aa, k(aa))), join(k(aa), join(k(bb), k(cc))))
% 0.19/0.71 = { by lemma 19 }
% 0.19/0.71 meet(join(k(k(aa)), join(aa, k(aa))), join(k(aa), join(k(bb), k(cc))))
% 0.19/0.71 = { by axiom 10 (lhs1) }
% 0.19/0.71 meet(join(aa, k(aa)), join(k(aa), join(k(bb), k(cc))))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.71 meet(join(k(aa), aa), join(k(aa), join(k(bb), k(cc))))
% 0.19/0.71 = { by axiom 9 (dist_join) R->L }
% 0.19/0.71 join(k(aa), meet(aa, join(k(bb), k(cc))))
% 0.19/0.71 = { by axiom 1 (commutativity_of_meet) }
% 0.19/0.71 join(k(aa), meet(join(k(bb), k(cc)), aa))
% 0.19/0.71 = { by lemma 17 }
% 0.19/0.71 join(k(aa), meet(aa, k(meet(bb, cc))))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.71 join(meet(aa, k(meet(bb, cc))), k(aa))
% 0.19/0.71
% 0.19/0.71 Goal 1 (rhs): join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))) = join(meet(aa, k(meet(bb, cc))), k(aa)).
% 0.19/0.71 Proof:
% 0.19/0.71 join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))
% 0.19/0.71 = { by axiom 3 (absorption1) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(bb), k(cc))))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))
% 0.19/0.71 = { by axiom 6 (absorption2) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), k(aa)))))
% 0.19/0.71 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), meet(k(aa), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))))
% 0.19/0.71 = { by lemma 15 R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), meet(meet(join(meet(aa, k(meet(bb, cc))), k(aa)), k(aa)), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))))
% 0.19/0.71 = { by axiom 5 (associativity_of_meet) }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), meet(join(meet(aa, k(meet(bb, cc))), k(aa)), meet(k(aa), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))))))))
% 0.19/0.71 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), meet(join(meet(aa, k(meet(bb, cc))), k(aa)), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), k(aa))))))
% 0.19/0.71 = { by axiom 5 (associativity_of_meet) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), meet(meet(join(meet(aa, k(meet(bb, cc))), k(aa)), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))), k(aa)))))
% 0.19/0.71 = { by lemma 14 }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), meet(join(meet(aa, k(meet(bb, cc))), k(aa)), k(aa)))))
% 0.19/0.71 = { by lemma 15 }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), k(aa))))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(bb), k(cc)), join(k(aa), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))))))
% 0.19/0.71 = { by axiom 8 (associativity_of_join) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(join(k(bb), k(cc)), k(aa)), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))
% 0.19/0.71 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(aa), join(k(bb), k(cc))), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))
% 0.19/0.71 = { by axiom 12 (lhs3) R->L }
% 0.19/0.71 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))
% 0.19/0.72 = { by lemma 20 R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))
% 0.19/0.72 = { by lemma 16 }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), k(k(join(aa, k(bb)))))))
% 0.19/0.72 = { by lemma 18 R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(k(bb))), k(k(aa))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(aa)), k(k(k(bb)))))))
% 0.19/0.72 = { by lemma 20 }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))), join(k(k(aa)), k(k(k(bb)))))))
% 0.19/0.72 = { by axiom 12 (lhs3) }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(aa), join(k(bb), k(cc))), join(k(k(aa)), k(k(k(bb)))))))
% 0.19/0.72 = { by axiom 8 (associativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(join(k(aa), join(k(bb), k(cc))), k(k(aa))), k(k(k(bb))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))), k(k(k(bb))))))
% 0.19/0.72 = { by lemma 20 R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), k(k(k(bb))))))
% 0.19/0.72 = { by axiom 3 (absorption1) R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(k(k(k(bb))), join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc))))))))
% 0.19/0.72 = { by axiom 1 (commutativity_of_meet) }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), k(k(k(bb)))))))
% 0.19/0.72 = { by axiom 6 (absorption2) }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(meet(aa, k(meet(bb, cc))), k(aa))))
% 0.19/0.72 = { by lemma 21 R->L }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(k(bb))), join(aa, k(aa))))))
% 0.19/0.72 = { by axiom 6 (absorption2) }
% 0.19/0.72 meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))))
% 0.19/0.72 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))))
% 0.19/0.72 = { by axiom 3 (absorption1) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(k(k(bb))), join(aa, k(aa))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))))))
% 0.19/0.72 = { by lemma 16 }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(aa, k(aa))), k(k(join(aa, k(bb))))))))
% 0.19/0.72 = { by lemma 18 R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(k(bb))), k(k(aa)))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(aa)), k(k(k(bb))))))))
% 0.19/0.72 = { by lemma 19 }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(aa)), join(aa, k(aa))), join(k(k(aa)), k(k(k(bb))))))))
% 0.19/0.72 = { by axiom 10 (lhs1) }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(aa, k(aa)), join(k(k(aa)), k(k(k(bb))))))))
% 0.19/0.72 = { by axiom 8 (associativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(join(aa, k(aa)), k(k(aa))), k(k(k(bb)))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(k(k(aa)), join(aa, k(aa))), k(k(k(bb)))))))
% 0.19/0.72 = { by axiom 10 (lhs1) }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(join(aa, k(aa)), k(k(k(bb)))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(meet(aa, k(meet(bb, cc))), k(aa)), join(k(k(k(bb))), join(aa, k(aa))))))
% 0.19/0.72 = { by axiom 8 (associativity_of_join) }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(k(aa), join(k(k(k(bb))), join(aa, k(aa)))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(join(k(k(k(bb))), join(aa, k(aa))), k(aa)))))
% 0.19/0.72 = { by axiom 3 (absorption1) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(join(k(k(k(bb))), join(aa, k(aa))), meet(k(aa), join(k(aa), aa))))))
% 0.19/0.72 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(join(k(k(k(bb))), join(aa, k(aa))), meet(k(aa), join(aa, k(aa)))))))
% 0.19/0.72 = { by axiom 10 (lhs1) R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(join(k(k(k(bb))), join(aa, k(aa))), meet(k(aa), join(k(k(aa)), join(aa, k(aa))))))))
% 0.19/0.72 = { by lemma 19 R->L }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(join(k(k(k(bb))), join(aa, k(aa))), meet(k(aa), join(k(k(k(bb))), join(aa, k(aa))))))))
% 0.19/0.72 = { by axiom 1 (commutativity_of_meet) }
% 0.19/0.72 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(join(k(k(k(bb))), join(aa, k(aa))), meet(join(k(k(k(bb))), join(aa, k(aa))), k(aa))))))
% 0.19/0.73 = { by axiom 6 (absorption2) }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(meet(aa, k(meet(bb, cc))), join(k(k(k(bb))), join(aa, k(aa))))))
% 0.19/0.73 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(k(bb))), join(aa, k(aa))), meet(aa, k(meet(bb, cc))))))
% 0.19/0.73 = { by lemma 19 }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(k(aa)), join(aa, k(aa))), meet(aa, k(meet(bb, cc))))))
% 0.19/0.73 = { by axiom 10 (lhs1) }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(aa, k(aa)), meet(aa, k(meet(bb, cc))))))
% 0.19/0.73 = { by axiom 2 (commutativity_of_join) }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(join(k(aa), aa), meet(aa, k(meet(bb, cc))))))
% 0.19/0.73 = { by axiom 8 (associativity_of_join) }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(aa), join(aa, meet(aa, k(meet(bb, cc)))))))
% 0.19/0.73 = { by lemma 17 R->L }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(aa), join(aa, meet(join(k(bb), k(cc)), aa)))))
% 0.19/0.73 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(aa), join(aa, meet(aa, join(k(bb), k(cc)))))))
% 0.19/0.73 = { by axiom 6 (absorption2) }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(aa), aa)))
% 0.19/0.73 = { by axiom 2 (commutativity_of_join) R->L }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(aa, k(aa))))
% 0.19/0.73 = { by axiom 10 (lhs1) R->L }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(k(aa)), join(aa, k(aa)))))
% 0.19/0.73 = { by lemma 19 R->L }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))), join(k(k(k(bb))), join(aa, k(aa)))))
% 0.19/0.73 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.19/0.73 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), meet(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))))
% 0.19/0.73 = { by axiom 5 (associativity_of_meet) R->L }
% 0.19/0.73 meet(meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(k(bb))), join(aa, k(aa)))), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))))
% 0.19/0.73 = { by lemma 21 }
% 0.19/0.73 meet(join(meet(aa, k(meet(bb, cc))), k(aa)), join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa))))
% 0.19/0.73 = { by lemma 14 }
% 0.19/0.73 join(meet(aa, k(meet(bb, cc))), k(aa))
% 0.19/0.73 % SZS output end Proof
% 0.19/0.73
% 0.19/0.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------