%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT036-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:42:53 AM UTC 2026
% Result : Unsatisfiable 3.02s 0.80s
% Output : Proof 3.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT036-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:57:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.02/0.80 Command-line arguments: --flatten --complete-subsets
% 3.02/0.80
% 3.02/0.80 % SZS status Unsatisfiable
% 3.02/0.80
% 3.02/0.85 % SZS output start Proof
% 3.02/0.85 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 3.02/0.85 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 3.02/0.85 Axiom 3 (k_on_meet): k(meet(X, Y)) = join(k(X), k(Y)).
% 3.02/0.85 Axiom 4 (k_on_join): k(join(X, Y)) = meet(k(X), k(Y)).
% 3.02/0.85 Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
% 3.02/0.85 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 3.02/0.85 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 3.02/0.85 Axiom 8 (lhs1): join(k(k(aa)), join(aa, k(aa))) = join(aa, k(aa)).
% 3.02/0.85 Axiom 9 (lhs2): join(k(k(k(bb))), join(aa, k(aa))) = join(aa, k(aa)).
% 3.02/0.85 Axiom 10 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 3.02/0.85 Axiom 11 (dist_join): join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z)).
% 3.02/0.85 Axiom 12 (lhs3): join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))) = join(k(aa), join(k(bb), k(cc))).
% 3.02/0.85 Axiom 13 (lhs4): join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))) = join(k(aa), join(k(bb), k(cc))).
% 3.02/0.85
% 3.02/0.85 Lemma 14: meet(X, join(Y, X)) = X.
% 3.02/0.85 Proof:
% 3.02/0.85 meet(X, join(Y, X))
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.85 meet(X, join(X, Y))
% 3.02/0.85 = { by axiom 5 (absorption1) }
% 3.02/0.85 X
% 3.02/0.85
% 3.02/0.85 Lemma 15: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 3.02/0.85 Proof:
% 3.02/0.85 join(Y, join(Z, X))
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.85 join(join(Z, X), Y)
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.85 join(join(X, Z), Y)
% 3.02/0.85 = { by axiom 10 (associativity_of_join) }
% 3.02/0.85 join(X, join(Z, Y))
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.02/0.85 join(X, join(Y, Z))
% 3.02/0.85
% 3.02/0.85 Lemma 16: meet(join(k(X), k(Y)), Z) = meet(Z, k(meet(X, Y))).
% 3.02/0.85 Proof:
% 3.02/0.85 meet(join(k(X), k(Y)), Z)
% 3.02/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.02/0.85 meet(Z, join(k(X), k(Y)))
% 3.02/0.85 = { by axiom 3 (k_on_meet) R->L }
% 3.02/0.85 meet(Z, k(meet(X, Y)))
% 3.02/0.85
% 3.02/0.85 Lemma 17: join(k(k(X)), join(Y, k(k(Z)))) = join(Y, k(k(join(Z, X)))).
% 3.02/0.85 Proof:
% 3.02/0.85 join(k(k(X)), join(Y, k(k(Z))))
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.85 join(k(k(X)), join(k(k(Z)), Y))
% 3.02/0.85 = { by axiom 10 (associativity_of_join) R->L }
% 3.02/0.85 join(join(k(k(X)), k(k(Z))), Y)
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.85 join(join(k(k(Z)), k(k(X))), Y)
% 3.02/0.85 = { by axiom 3 (k_on_meet) R->L }
% 3.02/0.85 join(k(meet(k(Z), k(X))), Y)
% 3.02/0.85 = { by axiom 4 (k_on_join) R->L }
% 3.02/0.85 join(k(k(join(Z, X))), Y)
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.02/0.85 join(Y, k(k(join(Z, X))))
% 3.02/0.85
% 3.02/0.85 Lemma 18: join(k(k(k(bb))), join(aa, k(aa))) = join(k(k(aa)), join(aa, k(aa))).
% 3.02/0.85 Proof:
% 3.02/0.85 join(k(k(k(bb))), join(aa, k(aa)))
% 3.02/0.85 = { by axiom 9 (lhs2) }
% 3.02/0.85 join(aa, k(aa))
% 3.02/0.85 = { by axiom 8 (lhs1) R->L }
% 3.02/0.85 join(k(k(aa)), join(aa, k(aa)))
% 3.02/0.85
% 3.02/0.85 Lemma 19: 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)))).
% 3.02/0.85 Proof:
% 3.02/0.85 join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc))))
% 3.02/0.85 = { by axiom 13 (lhs4) }
% 3.02/0.85 join(k(aa), join(k(bb), k(cc)))
% 3.02/0.85 = { by axiom 12 (lhs3) R->L }
% 3.02/0.85 join(k(k(aa)), join(k(aa), join(k(bb), k(cc))))
% 3.02/0.85
% 3.02/0.85 Lemma 20: 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)).
% 3.02/0.85 Proof:
% 3.02/0.85 meet(join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))), join(k(k(k(bb))), join(aa, k(aa))))
% 3.02/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.02/0.85 meet(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(k(bb))), join(k(aa), join(k(bb), k(cc)))))
% 3.02/0.85 = { by lemma 19 }
% 3.02/0.85 meet(join(k(k(k(bb))), join(aa, k(aa))), join(k(k(aa)), join(k(aa), join(k(bb), k(cc)))))
% 3.02/0.85 = { by axiom 12 (lhs3) }
% 3.02/0.85 meet(join(k(k(k(bb))), join(aa, k(aa))), join(k(aa), join(k(bb), k(cc))))
% 3.02/0.85 = { by lemma 18 }
% 3.02/0.85 meet(join(k(k(aa)), join(aa, k(aa))), join(k(aa), join(k(bb), k(cc))))
% 3.02/0.85 = { by axiom 8 (lhs1) }
% 3.02/0.85 meet(join(aa, k(aa)), join(k(aa), join(k(bb), k(cc))))
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.02/0.85 meet(join(k(aa), aa), join(k(aa), join(k(bb), k(cc))))
% 3.02/0.85 = { by axiom 11 (dist_join) R->L }
% 3.02/0.85 join(k(aa), meet(aa, join(k(bb), k(cc))))
% 3.02/0.85 = { by axiom 1 (commutativity_of_meet) }
% 3.02/0.85 join(k(aa), meet(join(k(bb), k(cc)), aa))
% 3.02/0.85 = { by lemma 16 }
% 3.02/0.85 join(k(aa), meet(aa, k(meet(bb, cc))))
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.02/0.85 join(meet(aa, k(meet(bb, cc))), k(aa))
% 3.02/0.85
% 3.02/0.85 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)).
% 3.02/0.85 Proof:
% 3.02/0.85 join(k(k(join(aa, k(bb)))), join(meet(aa, k(meet(bb, cc))), k(aa)))
% 3.02/0.85 = { by axiom 5 (absorption1) R->L }
% 3.02/0.85 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(k(aa), join(k(bb), k(cc))))))
% 3.02/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.85 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)))))
% 3.02/0.86 = { by lemma 15 }
% 3.02/0.86 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)))))))
% 3.02/0.86 = { by lemma 19 }
% 3.02/0.86 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(join(aa, k(bb)))))))
% 3.02/0.86 = { by axiom 12 (lhs3) }
% 3.02/0.86 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))), k(k(join(aa, k(bb)))))))
% 3.02/0.86 = { by lemma 17 R->L }
% 3.02/0.86 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(join(k(aa), join(k(bb), k(cc))), k(k(aa))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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(k(aa)), join(k(aa), join(k(bb), k(cc)))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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))))))
% 3.02/0.86 = { by axiom 12 (lhs3) }
% 3.02/0.86 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))), k(k(k(bb))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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))))
% 3.02/0.86 = { by lemma 20 R->L }
% 3.02/0.86 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))))))
% 3.02/0.86 = { by axiom 7 (absorption2) }
% 3.02/0.86 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)))))
% 3.02/0.86 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.02/0.86 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))))
% 3.02/0.86 = { by axiom 5 (absorption1) R->L }
% 3.02/0.86 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))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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))))))
% 3.02/0.86 = { by lemma 15 }
% 3.02/0.86 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))))))))
% 3.02/0.86 = { by lemma 18 }
% 3.02/0.86 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(join(aa, k(bb))))))))
% 3.02/0.86 = { by axiom 8 (lhs1) }
% 3.02/0.86 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(join(aa, k(bb))))))))
% 3.02/0.86 = { by lemma 17 R->L }
% 3.02/0.86 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(join(aa, k(aa)), k(k(aa)))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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(k(k(aa)), join(aa, k(aa)))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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)))))))
% 3.02/0.86 = { by axiom 8 (lhs1) }
% 3.02/0.86 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)))))))
% 3.02/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.86 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))))))
% 3.02/0.87 = { by axiom 10 (associativity_of_join) }
% 3.02/0.87 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)))))))
% 3.02/0.87 = { by axiom 2 (commutativity_of_join) }
% 3.02/0.87 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)))))
% 3.02/0.87 = { by axiom 5 (absorption1) R->L }
% 3.02/0.87 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))))))
% 3.02/0.87 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.87 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)))))))
% 3.02/0.87 = { by axiom 8 (lhs1) R->L }
% 3.02/0.87 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))))))))
% 3.02/0.87 = { by lemma 18 R->L }
% 3.02/0.87 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))))))))
% 3.02/0.87 = { by axiom 1 (commutativity_of_meet) }
% 3.02/0.87 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))))))
% 3.02/0.87 = { by axiom 7 (absorption2) }
% 3.02/0.87 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))))))
% 3.02/0.87 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.87 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))))))
% 3.02/0.87 = { by lemma 16 R->L }
% 3.02/0.87 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(join(k(bb), k(cc)), aa))))
% 3.02/0.87 = { by lemma 14 R->L }
% 3.02/0.87 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(join(k(bb), k(cc)), meet(aa, join(k(aa), aa))))))
% 3.02/0.87 = { by axiom 2 (commutativity_of_join) R->L }
% 3.02/0.87 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(join(k(bb), k(cc)), meet(aa, join(aa, k(aa)))))))
% 3.02/0.87 = { by axiom 8 (lhs1) R->L }
% 3.02/0.87 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(join(k(bb), k(cc)), meet(aa, join(k(k(aa)), join(aa, k(aa))))))))
% 3.02/0.88 = { by lemma 18 R->L }
% 3.02/0.88 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(join(k(bb), k(cc)), meet(aa, join(k(k(k(bb))), join(aa, k(aa))))))))
% 3.02/0.88 = { by axiom 6 (associativity_of_meet) R->L }
% 3.02/0.88 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(meet(join(k(bb), k(cc)), aa), join(k(k(k(bb))), join(aa, k(aa)))))))
% 3.02/0.88 = { by lemma 16 }
% 3.02/0.88 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(meet(aa, k(meet(bb, cc))), join(k(k(k(bb))), join(aa, k(aa)))))))
% 3.02/0.88 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.02/0.88 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(join(k(k(k(bb))), join(aa, k(aa))), meet(aa, k(meet(bb, cc)))))))
% 3.02/0.88 = { by axiom 7 (absorption2) }
% 3.02/0.88 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)))))
% 3.02/0.88 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.02/0.88 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)))))
% 3.02/0.88 = { by axiom 6 (associativity_of_meet) R->L }
% 3.02/0.88 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))))
% 3.02/0.88 = { by lemma 20 }
% 3.02/0.88 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))))
% 3.02/0.88 = { by lemma 14 }
% 3.02/0.88 join(meet(aa, k(meet(bb, cc))), k(aa))
% 3.02/0.88 % SZS output end Proof
% 3.02/0.88
% 3.02/0.88 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------