TSTP Solution File: LAT020-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT020-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:27:09 EDT 2023
% Result : Unsatisfiable 39.14s 5.43s
% Output : Proof 39.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT020-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n018.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 10:03:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 39.14/5.43 Command-line arguments: --no-flatten-goal
% 39.14/5.43
% 39.14/5.43 % SZS status Unsatisfiable
% 39.14/5.43
% 39.14/5.51 % SZS output start Proof
% 39.14/5.51 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 39.14/5.51 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 39.14/5.51 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 39.14/5.51 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 39.14/5.51 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 39.14/5.51 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 39.14/5.51 Axiom 7 (quasi_lattice1): join(meet(X, join(Y, Z)), meet(X, Y)) = meet(X, join(Y, Z)).
% 39.14/5.51 Axiom 8 (quasi_lattice2): meet(join(X, meet(Y, Z)), join(X, Y)) = join(X, meet(Y, Z)).
% 39.14/5.51 Axiom 9 (self_dual_distributivity): join(meet(join(meet(X, Y), Z), Y), meet(Z, X)) = meet(join(meet(join(X, Y), Z), Y), join(Z, X)).
% 39.14/5.51
% 39.14/5.51 Lemma 10: meet(X, meet(X, Y)) = meet(X, Y).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(X, meet(X, Y))
% 39.14/5.51 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.51 meet(meet(X, X), Y)
% 39.14/5.51 = { by axiom 3 (idempotence_of_meet) }
% 39.14/5.51 meet(X, Y)
% 39.14/5.51
% 39.14/5.51 Lemma 11: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(X, meet(Y, Z))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.51 meet(meet(Y, Z), X)
% 39.14/5.51 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.51 meet(Y, meet(Z, X))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.51 meet(Y, meet(X, Z))
% 39.14/5.51
% 39.14/5.51 Lemma 12: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 39.14/5.51 Proof:
% 39.14/5.51 join(meet(X, Y), meet(X, join(Y, Z)))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 join(meet(X, join(Y, Z)), meet(X, Y))
% 39.14/5.51 = { by axiom 7 (quasi_lattice1) }
% 39.14/5.51 meet(X, join(Y, Z))
% 39.14/5.51
% 39.14/5.51 Lemma 13: join(meet(X, Y), meet(X, join(Z, Y))) = meet(X, join(Y, Z)).
% 39.14/5.51 Proof:
% 39.14/5.51 join(meet(X, Y), meet(X, join(Z, Y)))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 join(meet(X, Y), meet(X, join(Y, Z)))
% 39.14/5.51 = { by lemma 12 }
% 39.14/5.51 meet(X, join(Y, Z))
% 39.14/5.51
% 39.14/5.51 Lemma 14: meet(join(X, Y), join(Z, meet(join(Y, Z), X))) = join(meet(X, Y), meet(Z, join(meet(Y, Z), X))).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(join(X, Y), join(Z, meet(join(Y, Z), X)))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 meet(join(X, Y), join(meet(join(Y, Z), X), Z))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.51 meet(join(meet(join(Y, Z), X), Z), join(X, Y))
% 39.14/5.51 = { by axiom 9 (self_dual_distributivity) R->L }
% 39.14/5.51 join(meet(join(meet(Y, Z), X), Z), meet(X, Y))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.51 join(meet(X, Y), meet(join(meet(Y, Z), X), Z))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.51 join(meet(X, Y), meet(Z, join(meet(Y, Z), X)))
% 39.14/5.51
% 39.14/5.51 Lemma 15: meet(join(X, Y), join(X, meet(Y, Z))) = join(X, meet(Y, Z)).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(join(X, Y), join(X, meet(Y, Z)))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.51 meet(join(X, meet(Y, Z)), join(X, Y))
% 39.14/5.51 = { by axiom 8 (quasi_lattice2) }
% 39.14/5.51 join(X, meet(Y, Z))
% 39.14/5.51
% 39.14/5.51 Lemma 16: meet(join(X, Y), join(Y, meet(X, Z))) = join(Y, meet(X, Z)).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(join(X, Y), join(Y, meet(X, Z)))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 meet(join(Y, X), join(Y, meet(X, Z)))
% 39.14/5.51 = { by lemma 15 }
% 39.14/5.51 join(Y, meet(X, Z))
% 39.14/5.51
% 39.14/5.51 Lemma 17: meet(X, join(X, Y)) = join(X, meet(X, Y)).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(X, join(X, Y))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 meet(X, join(Y, X))
% 39.14/5.51 = { by axiom 3 (idempotence_of_meet) R->L }
% 39.14/5.51 meet(X, join(Y, meet(X, X)))
% 39.14/5.51 = { by lemma 13 R->L }
% 39.14/5.51 join(meet(X, Y), meet(X, join(meet(X, X), Y)))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.51 join(meet(Y, X), meet(X, join(meet(X, X), Y)))
% 39.14/5.51 = { by lemma 14 R->L }
% 39.14/5.51 meet(join(Y, X), join(X, meet(join(X, X), Y)))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.51 meet(join(Y, X), join(X, meet(Y, join(X, X))))
% 39.14/5.51 = { by lemma 16 }
% 39.14/5.51 join(X, meet(Y, join(X, X)))
% 39.14/5.51 = { by axiom 1 (idempotence_of_join) }
% 39.14/5.51 join(X, meet(Y, X))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.51 join(X, meet(X, Y))
% 39.14/5.51
% 39.14/5.51 Lemma 18: join(X, join(X, Y)) = join(X, Y).
% 39.14/5.51 Proof:
% 39.14/5.51 join(X, join(X, Y))
% 39.14/5.51 = { by axiom 5 (associativity_of_join) R->L }
% 39.14/5.51 join(join(X, X), Y)
% 39.14/5.51 = { by axiom 1 (idempotence_of_join) }
% 39.14/5.51 join(X, Y)
% 39.14/5.51
% 39.14/5.51 Lemma 19: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 39.14/5.51 Proof:
% 39.14/5.51 join(Y, join(X, Z))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 join(join(X, Z), Y)
% 39.14/5.51 = { by axiom 5 (associativity_of_join) }
% 39.14/5.51 join(X, join(Z, Y))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.51 join(X, join(Y, Z))
% 39.14/5.51
% 39.14/5.51 Lemma 20: meet(join(X, Y), join(meet(Y, Z), X)) = join(X, meet(Y, Z)).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(join(X, Y), join(meet(Y, Z), X))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 meet(join(X, Y), join(X, meet(Y, Z)))
% 39.14/5.51 = { by lemma 15 }
% 39.14/5.51 join(X, meet(Y, Z))
% 39.14/5.51
% 39.14/5.51 Lemma 21: meet(join(X, meet(X, Y)), Z) = meet(X, meet(Z, join(X, Y))).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(join(X, meet(X, Y)), Z)
% 39.14/5.51 = { by lemma 17 R->L }
% 39.14/5.51 meet(meet(X, join(X, Y)), Z)
% 39.14/5.51 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.51 meet(X, meet(join(X, Y), Z))
% 39.14/5.51 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.51 meet(X, meet(Z, join(X, Y)))
% 39.14/5.51
% 39.14/5.51 Lemma 22: meet(X, meet(Y, join(Z, meet(X, Y)))) = meet(X, meet(Y, join(X, Z))).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(X, meet(Y, join(Z, meet(X, Y))))
% 39.14/5.51 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.51 meet(meet(X, Y), join(Z, meet(X, Y)))
% 39.14/5.51 = { by lemma 20 R->L }
% 39.14/5.51 meet(meet(X, Y), meet(join(Z, X), join(meet(X, Y), Z)))
% 39.14/5.51 = { by lemma 10 R->L }
% 39.14/5.51 meet(meet(X, Y), meet(meet(X, Y), meet(join(Z, X), join(meet(X, Y), Z))))
% 39.14/5.51 = { by lemma 21 R->L }
% 39.14/5.51 meet(meet(X, Y), meet(join(meet(X, Y), meet(meet(X, Y), Z)), join(Z, X)))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.51 meet(meet(X, Y), meet(join(meet(meet(X, Y), Z), meet(X, Y)), join(Z, X)))
% 39.14/5.51 = { by lemma 11 R->L }
% 39.14/5.51 meet(join(meet(meet(X, Y), Z), meet(X, Y)), meet(meet(X, Y), join(Z, X)))
% 39.14/5.51 = { by lemma 12 R->L }
% 39.14/5.51 meet(join(meet(meet(X, Y), Z), meet(X, Y)), join(meet(meet(X, Y), Z), meet(meet(X, Y), join(Z, X))))
% 39.14/5.51 = { by lemma 15 }
% 39.14/5.51 join(meet(meet(X, Y), Z), meet(meet(X, Y), join(Z, X)))
% 39.14/5.51 = { by lemma 12 }
% 39.14/5.51 meet(meet(X, Y), join(Z, X))
% 39.14/5.51 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.51 meet(X, meet(Y, join(Z, X)))
% 39.14/5.51 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.51 meet(X, meet(Y, join(X, Z)))
% 39.14/5.51
% 39.14/5.51 Lemma 23: meet(Y, join(X, meet(X, Z))) = meet(X, meet(Y, join(X, Z))).
% 39.14/5.51 Proof:
% 39.14/5.51 meet(Y, join(X, meet(X, Z)))
% 39.14/5.51 = { by lemma 17 R->L }
% 39.14/5.51 meet(Y, meet(X, join(X, Z)))
% 39.14/5.51 = { by lemma 11 }
% 39.14/5.52 meet(X, meet(Y, join(X, Z)))
% 39.14/5.52
% 39.14/5.52 Lemma 24: meet(Y, join(X, meet(Z, X))) = meet(X, meet(Y, join(X, Z))).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(Y, join(X, meet(Z, X)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(Y, join(X, meet(X, Z)))
% 39.14/5.52 = { by lemma 23 }
% 39.14/5.52 meet(X, meet(Y, join(X, Z)))
% 39.14/5.52
% 39.14/5.52 Lemma 25: meet(X, meet(Y, join(X, Z))) = meet(X, join(Y, meet(Y, Z))).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(X, meet(Y, join(X, Z)))
% 39.14/5.52 = { by lemma 22 R->L }
% 39.14/5.52 meet(X, meet(Y, join(Z, meet(X, Y))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(meet(Y, join(Z, meet(X, Y))), X)
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.52 meet(Y, meet(join(Z, meet(X, Y)), X))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(Y, meet(X, join(Z, meet(X, Y))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(Y, meet(X, join(Z, meet(Y, X))))
% 39.14/5.52 = { by lemma 22 }
% 39.14/5.52 meet(Y, meet(X, join(Y, Z)))
% 39.14/5.52 = { by lemma 24 R->L }
% 39.14/5.52 meet(X, join(Y, meet(Z, Y)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(X, join(Y, meet(Y, Z)))
% 39.14/5.52
% 39.14/5.52 Lemma 26: meet(X, meet(join(X, Z), Y)) = meet(X, join(Y, meet(Y, Z))).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(X, meet(join(X, Z), Y))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(X, meet(Y, join(X, Z)))
% 39.14/5.52 = { by lemma 25 }
% 39.14/5.52 meet(X, join(Y, meet(Y, Z)))
% 39.14/5.52
% 39.14/5.52 Lemma 27: meet(X, meet(join(X, Y), Z)) = meet(X, join(Z, meet(Y, Z))).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(X, meet(join(X, Y), Z))
% 39.14/5.52 = { by lemma 26 }
% 39.14/5.52 meet(X, join(Z, meet(Z, Y)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(X, join(Z, meet(Y, Z)))
% 39.14/5.52
% 39.14/5.52 Lemma 28: meet(Y, join(X, meet(X, Z))) = meet(X, join(Y, meet(Y, Z))).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(Y, join(X, meet(X, Z)))
% 39.14/5.52 = { by lemma 17 R->L }
% 39.14/5.52 meet(Y, meet(X, join(X, Z)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(Y, meet(join(X, Z), X))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.52 meet(meet(Y, join(X, Z)), X)
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(X, meet(Y, join(X, Z)))
% 39.14/5.52 = { by lemma 25 }
% 39.14/5.52 meet(X, join(Y, meet(Y, Z)))
% 39.14/5.52
% 39.14/5.52 Lemma 29: join(X, meet(X, join(Y, X))) = meet(X, join(X, Y)).
% 39.14/5.52 Proof:
% 39.14/5.52 join(X, meet(X, join(Y, X)))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.52 join(X, meet(X, join(X, Y)))
% 39.14/5.52 = { by axiom 3 (idempotence_of_meet) R->L }
% 39.14/5.52 join(meet(X, X), meet(X, join(X, Y)))
% 39.14/5.52 = { by lemma 12 }
% 39.14/5.52 meet(X, join(X, Y))
% 39.14/5.52
% 39.14/5.52 Lemma 30: meet(Z, join(X, meet(X, Y))) = meet(X, meet(join(X, Y), Z)).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(Z, join(X, meet(X, Y)))
% 39.14/5.52 = { by lemma 28 }
% 39.14/5.52 meet(X, join(Z, meet(Z, Y)))
% 39.14/5.52 = { by lemma 26 R->L }
% 39.14/5.52 meet(X, meet(join(X, Y), Z))
% 39.14/5.52
% 39.14/5.52 Lemma 31: meet(X, meet(Y, join(X, meet(X, Z)))) = meet(Y, join(X, meet(X, Z))).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(X, meet(Y, join(X, meet(X, Z))))
% 39.14/5.52 = { by axiom 1 (idempotence_of_join) R->L }
% 39.14/5.52 meet(join(X, X), meet(Y, join(X, meet(X, Z))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(join(X, X), meet(join(X, meet(X, Z)), Y))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.52 meet(meet(join(X, X), join(X, meet(X, Z))), Y)
% 39.14/5.52 = { by lemma 15 }
% 39.14/5.52 meet(join(X, meet(X, Z)), Y)
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(Y, join(X, meet(X, Z)))
% 39.14/5.52
% 39.14/5.52 Lemma 32: join(X, meet(Y, join(Z, meet(Z, X)))) = join(X, meet(Y, Z)).
% 39.14/5.52 Proof:
% 39.14/5.52 join(X, meet(Y, join(Z, meet(Z, X))))
% 39.14/5.52 = { by lemma 28 }
% 39.14/5.52 join(X, meet(Z, join(Y, meet(Y, X))))
% 39.14/5.52 = { by lemma 17 R->L }
% 39.14/5.52 join(X, meet(Z, meet(Y, join(Y, X))))
% 39.14/5.52 = { by lemma 29 R->L }
% 39.14/5.52 join(X, meet(Z, join(Y, meet(Y, join(X, Y)))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 join(X, meet(Z, join(Y, meet(join(X, Y), Y))))
% 39.14/5.52 = { by lemma 27 R->L }
% 39.14/5.52 join(X, meet(Z, meet(join(Z, join(X, Y)), Y)))
% 39.14/5.52 = { by lemma 30 R->L }
% 39.14/5.52 join(X, meet(Y, join(Z, meet(Z, join(X, Y)))))
% 39.14/5.52 = { by lemma 10 R->L }
% 39.14/5.52 join(X, meet(Y, join(Z, meet(Z, meet(Z, join(X, Y))))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 join(X, meet(Y, join(Z, meet(Z, meet(join(X, Y), Z)))))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.52 join(X, meet(Y, join(Z, meet(meet(Z, join(X, Y)), Z))))
% 39.14/5.52 = { by lemma 27 R->L }
% 39.14/5.52 join(X, meet(Y, meet(join(Y, meet(Z, join(X, Y))), Z)))
% 39.14/5.52 = { by lemma 30 R->L }
% 39.14/5.52 join(X, meet(Z, join(Y, meet(Y, meet(Z, join(X, Y))))))
% 39.14/5.52 = { by lemma 31 R->L }
% 39.14/5.52 join(X, meet(Y, meet(Z, join(Y, meet(Y, meet(Z, join(X, Y)))))))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.52 join(X, meet(Y, meet(Z, join(Y, meet(meet(Y, Z), join(X, Y))))))
% 39.14/5.52 = { by lemma 22 R->L }
% 39.14/5.52 join(X, meet(Y, meet(Z, join(meet(meet(Y, Z), join(X, Y)), meet(Y, Z)))))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.52 join(X, meet(meet(Y, Z), join(meet(meet(Y, Z), join(X, Y)), meet(Y, Z))))
% 39.14/5.52 = { by lemma 20 R->L }
% 39.14/5.52 join(X, meet(meet(Y, Z), meet(join(meet(meet(Y, Z), join(X, Y)), Y), join(meet(Y, Z), meet(meet(Y, Z), join(X, Y))))))
% 39.14/5.52 = { by lemma 31 }
% 39.14/5.52 join(X, meet(join(meet(meet(Y, Z), join(X, Y)), Y), join(meet(Y, Z), meet(meet(Y, Z), join(X, Y)))))
% 39.14/5.52 = { by lemma 20 }
% 39.14/5.52 join(X, join(meet(meet(Y, Z), join(X, Y)), meet(Y, Z)))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.52 join(X, join(meet(Y, meet(Z, join(X, Y))), meet(Y, Z)))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.52 join(X, join(meet(Y, Z), meet(Y, meet(Z, join(X, Y)))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 join(X, join(meet(Y, Z), meet(meet(Z, join(X, Y)), Y)))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.52 join(X, join(meet(Y, Z), meet(Z, meet(join(X, Y), Y))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 join(X, join(meet(Y, Z), meet(meet(join(X, Y), Y), Z)))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.52 join(X, join(meet(Y, Z), meet(join(X, Y), meet(Y, Z))))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.52 join(X, join(meet(join(X, Y), meet(Y, Z)), meet(Y, Z)))
% 39.14/5.52 = { by lemma 19 }
% 39.14/5.52 join(meet(join(X, Y), meet(Y, Z)), join(X, meet(Y, Z)))
% 39.14/5.52 = { by lemma 20 R->L }
% 39.14/5.52 join(meet(join(X, Y), meet(Y, Z)), meet(join(X, Y), join(meet(Y, Z), X)))
% 39.14/5.52 = { by lemma 12 }
% 39.14/5.52 meet(join(X, Y), join(meet(Y, Z), X))
% 39.14/5.52 = { by lemma 20 }
% 39.14/5.52 join(X, meet(Y, Z))
% 39.14/5.52
% 39.14/5.52 Lemma 33: join(X, join(meet(X, Y), meet(Y, Z))) = join(X, meet(Y, Z)).
% 39.14/5.52 Proof:
% 39.14/5.52 join(X, join(meet(X, Y), meet(Y, Z)))
% 39.14/5.52 = { by lemma 18 R->L }
% 39.14/5.52 join(X, join(X, join(meet(X, Y), meet(Y, Z))))
% 39.14/5.52 = { by axiom 5 (associativity_of_join) R->L }
% 39.14/5.52 join(X, join(join(X, meet(X, Y)), meet(Y, Z)))
% 39.14/5.52 = { by lemma 17 R->L }
% 39.14/5.52 join(X, join(meet(X, join(X, Y)), meet(Y, Z)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 join(X, join(meet(join(X, Y), X), meet(Y, Z)))
% 39.14/5.52 = { by lemma 19 }
% 39.14/5.52 join(meet(join(X, Y), X), join(X, meet(Y, Z)))
% 39.14/5.52 = { by lemma 15 R->L }
% 39.14/5.52 join(meet(join(X, Y), X), meet(join(X, Y), join(X, meet(Y, Z))))
% 39.14/5.52 = { by lemma 12 }
% 39.14/5.52 meet(join(X, Y), join(X, meet(Y, Z)))
% 39.14/5.52 = { by lemma 15 }
% 39.14/5.52 join(X, meet(Y, Z))
% 39.14/5.52
% 39.14/5.52 Lemma 34: join(X, join(meet(Y, Z), meet(X, Y))) = join(X, meet(Y, Z)).
% 39.14/5.52 Proof:
% 39.14/5.52 join(X, join(meet(Y, Z), meet(X, Y)))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.52 join(X, join(meet(X, Y), meet(Y, Z)))
% 39.14/5.52 = { by lemma 33 }
% 39.14/5.52 join(X, meet(Y, Z))
% 39.14/5.52
% 39.14/5.52 Lemma 35: meet(X, join(Y, meet(X, Z))) = join(meet(Y, X), meet(X, Z)).
% 39.14/5.52 Proof:
% 39.14/5.52 meet(X, join(Y, meet(X, Z)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(X, join(Y, meet(Z, X)))
% 39.14/5.52 = { by lemma 32 R->L }
% 39.14/5.52 meet(X, join(Y, meet(Z, join(X, meet(X, Y)))))
% 39.14/5.52 = { by lemma 23 }
% 39.14/5.52 meet(X, join(Y, meet(X, meet(Z, join(X, Y)))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(X, join(Y, meet(meet(Z, join(X, Y)), X)))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.52 meet(X, join(Y, meet(Z, meet(join(X, Y), X))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(X, join(Y, meet(Z, meet(X, join(X, Y)))))
% 39.14/5.52 = { by lemma 34 R->L }
% 39.14/5.52 meet(X, join(Y, join(meet(Z, meet(X, join(X, Y))), meet(Y, Z))))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) R->L }
% 39.14/5.52 meet(X, join(Y, join(meet(meet(Z, X), join(X, Y)), meet(Y, Z))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(X, join(Y, join(meet(meet(Z, X), join(X, Y)), meet(Z, Y))))
% 39.14/5.52 = { by axiom 5 (associativity_of_join) R->L }
% 39.14/5.52 meet(X, join(join(Y, meet(meet(Z, X), join(X, Y))), meet(Z, Y)))
% 39.14/5.52 = { by lemma 34 R->L }
% 39.14/5.52 meet(X, join(join(Y, meet(meet(Z, X), join(X, Y))), join(meet(Z, Y), meet(join(Y, meet(meet(Z, X), join(X, Y))), Z))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(X, join(join(Y, meet(meet(Z, X), join(X, Y))), join(meet(Z, Y), meet(Z, join(Y, meet(meet(Z, X), join(X, Y)))))))
% 39.14/5.52 = { by lemma 12 }
% 39.14/5.52 meet(X, join(join(Y, meet(meet(Z, X), join(X, Y))), meet(Z, join(Y, meet(meet(Z, X), join(X, Y))))))
% 39.14/5.52 = { by lemma 24 }
% 39.14/5.52 meet(join(Y, meet(meet(Z, X), join(X, Y))), meet(X, join(join(Y, meet(meet(Z, X), join(X, Y))), Z)))
% 39.14/5.52 = { by lemma 25 }
% 39.14/5.52 meet(join(Y, meet(meet(Z, X), join(X, Y))), join(X, meet(X, Z)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(join(Y, meet(meet(Z, X), join(X, Y))), join(X, meet(Z, X)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 meet(join(X, meet(Z, X)), join(Y, meet(meet(Z, X), join(X, Y))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(join(X, meet(Z, X)), join(Y, meet(join(X, Y), meet(Z, X))))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.52 meet(join(meet(Z, X), X), join(Y, meet(join(X, Y), meet(Z, X))))
% 39.14/5.52 = { by lemma 14 }
% 39.14/5.52 join(meet(meet(Z, X), X), meet(Y, join(meet(X, Y), meet(Z, X))))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.52 join(meet(meet(Z, X), X), meet(Y, join(meet(Z, X), meet(X, Y))))
% 39.14/5.52 = { by axiom 6 (associativity_of_meet) }
% 39.14/5.52 join(meet(Z, meet(X, X)), meet(Y, join(meet(Z, X), meet(X, Y))))
% 39.14/5.52 = { by axiom 3 (idempotence_of_meet) }
% 39.14/5.52 join(meet(Z, X), meet(Y, join(meet(Z, X), meet(X, Y))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 join(meet(Z, X), meet(Y, join(meet(Z, X), meet(Y, X))))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.52 join(meet(Z, X), meet(Y, join(meet(Y, X), meet(Z, X))))
% 39.14/5.52 = { by lemma 12 R->L }
% 39.14/5.52 join(meet(Z, X), join(meet(Y, meet(Y, X)), meet(Y, join(meet(Y, X), meet(Z, X)))))
% 39.14/5.52 = { by lemma 10 }
% 39.14/5.52 join(meet(Z, X), join(meet(Y, X), meet(Y, join(meet(Y, X), meet(Z, X)))))
% 39.14/5.52 = { by lemma 19 }
% 39.14/5.52 join(meet(Y, X), join(meet(Z, X), meet(Y, join(meet(Y, X), meet(Z, X)))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 join(meet(Y, X), join(meet(Z, X), meet(join(meet(Y, X), meet(Z, X)), Y)))
% 39.14/5.52 = { by axiom 5 (associativity_of_join) R->L }
% 39.14/5.52 join(join(meet(Y, X), meet(Z, X)), meet(join(meet(Y, X), meet(Z, X)), Y))
% 39.14/5.52 = { by lemma 17 R->L }
% 39.14/5.52 meet(join(meet(Y, X), meet(Z, X)), join(join(meet(Y, X), meet(Z, X)), Y))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.52 meet(join(meet(Y, X), meet(Z, X)), join(Y, join(meet(Y, X), meet(Z, X))))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 meet(join(Y, join(meet(Y, X), meet(Z, X))), join(meet(Y, X), meet(Z, X)))
% 39.14/5.52 = { by lemma 18 R->L }
% 39.14/5.52 meet(join(Y, join(meet(Y, X), meet(Z, X))), join(meet(Y, X), join(meet(Y, X), meet(Z, X))))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.52 meet(join(Y, join(meet(Y, X), meet(Z, X))), join(join(meet(Y, X), meet(Z, X)), meet(Y, X)))
% 39.14/5.52 = { by lemma 16 }
% 39.14/5.52 join(join(meet(Y, X), meet(Z, X)), meet(Y, X))
% 39.14/5.52 = { by axiom 5 (associativity_of_join) }
% 39.14/5.52 join(meet(Y, X), join(meet(Z, X), meet(Y, X)))
% 39.14/5.52 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.52 join(meet(Y, X), join(meet(Y, X), meet(Z, X)))
% 39.14/5.52 = { by lemma 18 }
% 39.14/5.52 join(meet(Y, X), meet(Z, X))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.52 join(meet(Y, X), meet(X, Z))
% 39.14/5.52
% 39.14/5.52 Lemma 36: join(X, join(meet(X, Y), meet(Z, Y))) = join(X, meet(Y, Z)).
% 39.14/5.52 Proof:
% 39.14/5.52 join(X, join(meet(X, Y), meet(Z, Y)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 join(X, join(meet(X, Y), meet(Y, Z)))
% 39.14/5.52 = { by lemma 33 }
% 39.14/5.52 join(X, meet(Y, Z))
% 39.14/5.52
% 39.14/5.52 Lemma 37: join(meet(X, Y), meet(Y, join(X, Z))) = meet(Y, join(X, Z)).
% 39.14/5.52 Proof:
% 39.14/5.52 join(meet(X, Y), meet(Y, join(X, Z)))
% 39.14/5.52 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.52 join(meet(Y, X), meet(Y, join(X, Z)))
% 39.14/5.52 = { by lemma 12 }
% 39.14/5.53 meet(Y, join(X, Z))
% 39.14/5.53
% 39.14/5.53 Lemma 38: meet(join(X, Y), join(X, meet(Z, join(X, Y)))) = join(X, meet(Z, join(X, Y))).
% 39.14/5.53 Proof:
% 39.14/5.53 meet(join(X, Y), join(X, meet(Z, join(X, Y))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.53 meet(join(X, Y), join(X, meet(join(X, Y), Z)))
% 39.14/5.53 = { by lemma 18 R->L }
% 39.14/5.53 meet(join(X, join(X, Y)), join(X, meet(join(X, Y), Z)))
% 39.14/5.53 = { by lemma 15 }
% 39.14/5.53 join(X, meet(join(X, Y), Z))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.53 join(X, meet(Z, join(X, Y)))
% 39.14/5.53
% 39.14/5.53 Lemma 39: meet(join(X, Y), join(Z, meet(X, join(Z, Y)))) = join(meet(X, Y), join(meet(X, Z), meet(Y, Z))).
% 39.14/5.53 Proof:
% 39.14/5.53 meet(join(X, Y), join(Z, meet(X, join(Z, Y))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.53 meet(join(X, Y), join(Z, meet(join(Z, Y), X)))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 meet(join(X, Y), join(Z, meet(join(Y, Z), X)))
% 39.14/5.53 = { by lemma 14 }
% 39.14/5.53 join(meet(X, Y), meet(Z, join(meet(Y, Z), X)))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 join(meet(X, Y), meet(Z, join(X, meet(Y, Z))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.53 join(meet(X, Y), meet(Z, join(X, meet(Z, Y))))
% 39.14/5.53 = { by lemma 35 }
% 39.14/5.53 join(meet(X, Y), join(meet(X, Z), meet(Z, Y)))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.53 join(meet(X, Y), join(meet(X, Z), meet(Y, Z)))
% 39.14/5.53
% 39.14/5.53 Goal 1 (prove_distributivity): meet(a, join(b, c)) = join(meet(a, b), meet(a, c)).
% 39.14/5.53 Proof:
% 39.14/5.53 meet(a, join(b, c))
% 39.14/5.53 = { by lemma 37 R->L }
% 39.14/5.53 join(meet(b, a), meet(a, join(b, c)))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 join(meet(a, join(b, c)), meet(b, a))
% 39.14/5.53 = { by lemma 20 R->L }
% 39.14/5.53 meet(join(meet(a, join(b, c)), b), join(meet(b, a), meet(a, join(b, c))))
% 39.14/5.53 = { by lemma 37 }
% 39.14/5.53 meet(join(meet(a, join(b, c)), b), meet(a, join(b, c)))
% 39.14/5.53 = { by lemma 11 }
% 39.14/5.53 meet(a, meet(join(meet(a, join(b, c)), b), join(b, c)))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.53 meet(a, meet(join(b, c), join(meet(a, join(b, c)), b)))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 meet(a, meet(join(b, c), join(b, meet(a, join(b, c)))))
% 39.14/5.53 = { by lemma 38 }
% 39.14/5.53 meet(a, join(b, meet(a, join(b, c))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), b))
% 39.14/5.53 = { by axiom 3 (idempotence_of_meet) R->L }
% 39.14/5.53 meet(a, meet(join(meet(a, join(b, c)), b), join(meet(a, join(b, c)), b)))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 meet(a, meet(join(meet(a, join(b, c)), b), join(b, meet(a, join(b, c)))))
% 39.14/5.53 = { by lemma 13 R->L }
% 39.14/5.53 meet(a, join(meet(join(meet(a, join(b, c)), b), b), meet(join(meet(a, join(b, c)), b), join(meet(a, join(b, c)), b))))
% 39.14/5.53 = { by axiom 3 (idempotence_of_meet) }
% 39.14/5.53 meet(a, join(meet(join(meet(a, join(b, c)), b), b), join(meet(a, join(b, c)), b)))
% 39.14/5.53 = { by lemma 19 R->L }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), join(meet(join(meet(a, join(b, c)), b), b), b)))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), join(b, meet(join(meet(a, join(b, c)), b), b))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), join(b, meet(b, join(meet(a, join(b, c)), b)))))
% 39.14/5.53 = { by lemma 29 }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), meet(b, join(b, meet(a, join(b, c))))))
% 39.14/5.53 = { by lemma 38 R->L }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), meet(b, meet(join(b, c), join(b, meet(a, join(b, c)))))))
% 39.14/5.53 = { by lemma 21 R->L }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), meet(join(b, meet(b, meet(a, join(b, c)))), join(b, c))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), meet(join(b, c), join(b, meet(b, meet(a, join(b, c)))))))
% 39.14/5.53 = { by lemma 32 }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), meet(join(b, c), b)))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), meet(b, join(b, c))))
% 39.14/5.53 = { by lemma 17 }
% 39.14/5.53 meet(a, join(meet(a, join(b, c)), join(b, meet(b, c))))
% 39.14/5.53 = { by lemma 19 R->L }
% 39.14/5.53 meet(a, join(b, join(meet(a, join(b, c)), meet(b, c))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 meet(a, join(b, join(meet(b, c), meet(a, join(b, c)))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 meet(a, join(b, join(meet(b, c), meet(a, join(c, b)))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 meet(a, join(b, join(meet(a, join(c, b)), meet(b, c))))
% 39.14/5.53 = { by lemma 13 R->L }
% 39.14/5.53 meet(a, join(b, join(join(meet(a, c), meet(a, join(b, c))), meet(b, c))))
% 39.14/5.53 = { by axiom 5 (associativity_of_join) }
% 39.14/5.53 meet(a, join(b, join(meet(a, c), join(meet(a, join(b, c)), meet(b, c)))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 meet(a, join(b, join(meet(a, c), join(meet(b, c), meet(a, join(b, c))))))
% 39.14/5.53 = { by axiom 5 (associativity_of_join) R->L }
% 39.14/5.53 meet(a, join(b, join(join(meet(a, c), meet(b, c)), meet(a, join(b, c)))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 meet(a, join(b, join(meet(a, join(b, c)), join(meet(a, c), meet(b, c)))))
% 39.14/5.53 = { by lemma 12 R->L }
% 39.14/5.53 meet(a, join(b, join(join(meet(a, b), meet(a, join(b, c))), join(meet(a, c), meet(b, c)))))
% 39.14/5.53 = { by axiom 5 (associativity_of_join) }
% 39.14/5.53 meet(a, join(b, join(meet(a, b), join(meet(a, join(b, c)), join(meet(a, c), meet(b, c))))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 meet(a, join(b, join(meet(a, b), join(join(meet(a, c), meet(b, c)), meet(a, join(b, c))))))
% 39.14/5.53 = { by axiom 5 (associativity_of_join) R->L }
% 39.14/5.53 meet(a, join(b, join(join(meet(a, b), join(meet(a, c), meet(b, c))), meet(a, join(b, c)))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) R->L }
% 39.14/5.53 meet(a, join(b, join(join(meet(a, b), join(meet(a, c), meet(b, c))), meet(a, join(c, b)))))
% 39.14/5.53 = { by lemma 37 R->L }
% 39.14/5.53 meet(a, join(b, join(join(meet(a, b), join(meet(a, c), meet(b, c))), join(meet(c, a), meet(a, join(c, b))))))
% 39.14/5.53 = { by lemma 19 R->L }
% 39.14/5.53 meet(a, join(b, join(meet(c, a), join(join(meet(a, b), join(meet(a, c), meet(b, c))), meet(a, join(c, b))))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 meet(a, join(b, join(meet(c, a), join(meet(a, join(c, b)), join(meet(a, b), join(meet(a, c), meet(b, c)))))))
% 39.14/5.53 = { by axiom 5 (associativity_of_join) R->L }
% 39.14/5.53 meet(a, join(b, join(join(meet(c, a), meet(a, join(c, b))), join(meet(a, b), join(meet(a, c), meet(b, c))))))
% 39.14/5.53 = { by lemma 35 R->L }
% 39.14/5.53 meet(a, join(b, join(meet(a, join(c, meet(a, join(c, b)))), join(meet(a, b), join(meet(a, c), meet(b, c))))))
% 39.14/5.53 = { by lemma 39 R->L }
% 39.14/5.53 meet(a, join(b, join(meet(a, join(c, meet(a, join(c, b)))), meet(join(a, b), join(c, meet(a, join(c, b)))))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.53 meet(a, join(b, join(meet(a, join(c, meet(a, join(c, b)))), meet(join(c, meet(a, join(c, b))), join(a, b)))))
% 39.14/5.53 = { by lemma 37 }
% 39.14/5.53 meet(a, join(b, meet(join(c, meet(a, join(c, b))), join(a, b))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.53 meet(a, join(b, meet(join(a, b), join(c, meet(a, join(c, b))))))
% 39.14/5.53 = { by lemma 39 }
% 39.14/5.53 meet(a, join(b, join(meet(a, b), join(meet(a, c), meet(b, c)))))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) }
% 39.14/5.53 meet(a, join(b, join(meet(b, a), join(meet(a, c), meet(b, c)))))
% 39.14/5.53 = { by axiom 2 (commutativity_of_join) }
% 39.14/5.53 meet(a, join(b, join(meet(b, a), join(meet(b, c), meet(a, c)))))
% 39.14/5.53 = { by lemma 19 }
% 39.14/5.53 meet(a, join(meet(b, a), join(b, join(meet(b, c), meet(a, c)))))
% 39.14/5.53 = { by lemma 36 }
% 39.14/5.53 meet(a, join(meet(b, a), join(b, meet(c, a))))
% 39.14/5.53 = { by lemma 19 R->L }
% 39.14/5.53 meet(a, join(b, join(meet(b, a), meet(c, a))))
% 39.14/5.53 = { by lemma 36 }
% 39.14/5.53 meet(a, join(b, meet(a, c)))
% 39.14/5.53 = { by lemma 35 }
% 39.14/5.53 join(meet(b, a), meet(a, c))
% 39.14/5.53 = { by axiom 4 (commutativity_of_meet) R->L }
% 39.14/5.53 join(meet(a, b), meet(a, c))
% 39.14/5.53 % SZS output end Proof
% 39.14/5.53
% 39.14/5.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------