TSTP Solution File: LAT399-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT399-1 : TPTP v8.1.2. Released v8.1.0.
% 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 : n002.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 06:29:04 EDT 2023
% Result : Unsatisfiable 152.18s 19.90s
% Output : Proof 152.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LAT399-1 : TPTP v8.1.2. Released v8.1.0.
% 0.14/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 08:46:16 EDT 2023
% 0.14/0.35 % CPUTime :
% 152.18/19.90 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 152.18/19.90
% 152.18/19.90 % SZS status Unsatisfiable
% 152.18/19.90
% 152.18/19.99 % SZS output start Proof
% 152.18/19.99 Axiom 1 (commutativity): meet(X, Y) = meet(Y, X).
% 152.18/19.99 Axiom 2 (commutativity_001): join(X, Y) = join(Y, X).
% 152.18/19.99 Axiom 3 (absorption_003): meet(X, join(X, Y)) = X.
% 152.18/19.99 Axiom 4 (definition_of_upme): upme(X, Y, Z) = meet(X, join(Y, Z)).
% 152.18/19.99 Axiom 5 (associativity): meet(X, meet(Y, Z)) = meet(meet(X, Y), Z).
% 152.18/19.99 Axiom 6 (absorption): join(X, meet(X, Y)) = X.
% 152.18/19.99 Axiom 7 (associativity_002): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 152.18/19.99 Axiom 8 (definition_of_lome): lome(X, Y, Z) = join(meet(X, Y), meet(X, Z)).
% 152.18/19.99 Axiom 9 (conjecture): join(upme(meet(a, X), Y, Z), meet(Y, Z)) = meet(join(meet(meet(a, X), Y), Z), join(meet(meet(a, X), Z), Y)).
% 152.18/19.99
% 152.18/19.99 Lemma 10: meet(X, X) = X.
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, X)
% 152.18/19.99 = { by axiom 6 (absorption) R->L }
% 152.18/19.99 meet(X, join(X, meet(X, Y)))
% 152.18/19.99 = { by axiom 3 (absorption_003) }
% 152.18/19.99 X
% 152.18/19.99
% 152.18/19.99 Lemma 11: upme(X, Y, X) = X.
% 152.18/19.99 Proof:
% 152.18/19.99 upme(X, Y, X)
% 152.18/19.99 = { by axiom 4 (definition_of_upme) }
% 152.18/19.99 meet(X, join(Y, X))
% 152.18/19.99 = { by axiom 2 (commutativity_001) R->L }
% 152.18/19.99 meet(X, join(X, Y))
% 152.18/19.99 = { by axiom 3 (absorption_003) }
% 152.18/19.99 X
% 152.18/19.99
% 152.18/19.99 Lemma 12: upme(X, Z, Y) = upme(X, Y, Z).
% 152.18/19.99 Proof:
% 152.18/19.99 upme(X, Z, Y)
% 152.18/19.99 = { by axiom 4 (definition_of_upme) }
% 152.18/19.99 meet(X, join(Z, Y))
% 152.18/19.99 = { by axiom 2 (commutativity_001) R->L }
% 152.18/19.99 meet(X, join(Y, Z))
% 152.18/19.99 = { by axiom 4 (definition_of_upme) R->L }
% 152.18/19.99 upme(X, Y, Z)
% 152.18/19.99
% 152.18/19.99 Lemma 13: lome(X, Z, Y) = lome(X, Y, Z).
% 152.18/19.99 Proof:
% 152.18/19.99 lome(X, Z, Y)
% 152.18/19.99 = { by axiom 8 (definition_of_lome) }
% 152.18/19.99 join(meet(X, Z), meet(X, Y))
% 152.18/19.99 = { by axiom 2 (commutativity_001) }
% 152.18/19.99 join(meet(X, Y), meet(X, Z))
% 152.18/19.99 = { by axiom 8 (definition_of_lome) R->L }
% 152.18/19.99 lome(X, Y, Z)
% 152.18/19.99
% 152.18/19.99 Lemma 14: upme(X, Y, meet(Y, Z)) = meet(X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 upme(X, Y, meet(Y, Z))
% 152.18/19.99 = { by axiom 4 (definition_of_upme) }
% 152.18/19.99 meet(X, join(Y, meet(Y, Z)))
% 152.18/19.99 = { by axiom 6 (absorption) }
% 152.18/19.99 meet(X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 15: meet(X, meet(X, Y)) = meet(X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, meet(X, Y))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 meet(meet(X, Y), X)
% 152.18/19.99 = { by lemma 14 R->L }
% 152.18/19.99 upme(meet(X, Y), X, meet(X, Y))
% 152.18/19.99 = { by lemma 11 }
% 152.18/19.99 meet(X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 16: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, meet(Y, Z))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 meet(meet(Y, Z), X)
% 152.18/19.99 = { by axiom 5 (associativity) R->L }
% 152.18/19.99 meet(Y, meet(Z, X))
% 152.18/19.99 = { by axiom 1 (commutativity) }
% 152.18/19.99 meet(Y, meet(X, Z))
% 152.18/19.99
% 152.18/19.99 Lemma 17: meet(Z, meet(X, Y)) = meet(X, meet(Y, Z)).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(Z, meet(X, Y))
% 152.18/19.99 = { by lemma 16 R->L }
% 152.18/19.99 meet(X, meet(Z, Y))
% 152.18/19.99 = { by axiom 1 (commutativity) }
% 152.18/19.99 meet(X, meet(Y, Z))
% 152.18/19.99
% 152.18/19.99 Lemma 18: meet(join(X, Y), Z) = upme(Z, X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(join(X, Y), Z)
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 meet(Z, join(X, Y))
% 152.18/19.99 = { by axiom 4 (definition_of_upme) R->L }
% 152.18/19.99 upme(Z, X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 19: join(X, meet(Y, X)) = X.
% 152.18/19.99 Proof:
% 152.18/19.99 join(X, meet(Y, X))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 join(X, meet(X, Y))
% 152.18/19.99 = { by axiom 6 (absorption) }
% 152.18/19.99 X
% 152.18/19.99
% 152.18/19.99 Lemma 20: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 152.18/19.99 Proof:
% 152.18/19.99 join(Y, join(X, Z))
% 152.18/19.99 = { by axiom 2 (commutativity_001) R->L }
% 152.18/19.99 join(join(X, Z), Y)
% 152.18/19.99 = { by axiom 7 (associativity_002) R->L }
% 152.18/19.99 join(X, join(Z, Y))
% 152.18/19.99 = { by axiom 2 (commutativity_001) }
% 152.18/19.99 join(X, join(Y, Z))
% 152.18/19.99
% 152.18/19.99 Lemma 21: meet(X, upme(Y, X, Z)) = meet(X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, upme(Y, X, Z))
% 152.18/19.99 = { by lemma 18 R->L }
% 152.18/19.99 meet(X, meet(join(X, Z), Y))
% 152.18/19.99 = { by axiom 5 (associativity) }
% 152.18/19.99 meet(meet(X, join(X, Z)), Y)
% 152.18/19.99 = { by axiom 3 (absorption_003) }
% 152.18/19.99 meet(X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 22: meet(X, meet(Y, lome(X, Y, Z))) = meet(X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, meet(Y, lome(X, Y, Z)))
% 152.18/19.99 = { by axiom 5 (associativity) }
% 152.18/19.99 meet(meet(X, Y), lome(X, Y, Z))
% 152.18/19.99 = { by axiom 8 (definition_of_lome) }
% 152.18/19.99 meet(meet(X, Y), join(meet(X, Y), meet(X, Z)))
% 152.18/19.99 = { by axiom 3 (absorption_003) }
% 152.18/19.99 meet(X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 23: meet(X, meet(Y, lome(Y, X, Z))) = meet(X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, meet(Y, lome(Y, X, Z)))
% 152.18/19.99 = { by lemma 16 R->L }
% 152.18/19.99 meet(Y, meet(X, lome(Y, X, Z)))
% 152.18/19.99 = { by lemma 22 }
% 152.18/19.99 meet(Y, X)
% 152.18/19.99 = { by axiom 1 (commutativity) }
% 152.18/19.99 meet(X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 24: join(meet(X, Y), meet(Z, X)) = lome(X, Y, Z).
% 152.18/19.99 Proof:
% 152.18/19.99 join(meet(X, Y), meet(Z, X))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 join(meet(X, Y), meet(X, Z))
% 152.18/19.99 = { by axiom 8 (definition_of_lome) R->L }
% 152.18/19.99 lome(X, Y, Z)
% 152.18/19.99
% 152.18/19.99 Lemma 25: join(meet(X, Y), meet(Y, Z)) = lome(Y, X, Z).
% 152.18/19.99 Proof:
% 152.18/19.99 join(meet(X, Y), meet(Y, Z))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 join(meet(Y, X), meet(Y, Z))
% 152.18/19.99 = { by axiom 8 (definition_of_lome) R->L }
% 152.18/19.99 lome(Y, X, Z)
% 152.18/19.99
% 152.18/19.99 Lemma 26: join(meet(X, Y), upme(X, Z, W)) = lome(X, Y, join(Z, W)).
% 152.18/19.99 Proof:
% 152.18/19.99 join(meet(X, Y), upme(X, Z, W))
% 152.18/19.99 = { by axiom 2 (commutativity_001) R->L }
% 152.18/19.99 join(upme(X, Z, W), meet(X, Y))
% 152.18/19.99 = { by axiom 4 (definition_of_upme) }
% 152.18/19.99 join(meet(X, join(Z, W)), meet(X, Y))
% 152.18/19.99 = { by axiom 8 (definition_of_lome) R->L }
% 152.18/19.99 lome(X, join(Z, W), Y)
% 152.18/19.99 = { by lemma 13 R->L }
% 152.18/19.99 lome(X, Y, join(Z, W))
% 152.18/19.99
% 152.18/19.99 Lemma 27: join(meet(X, Y), upme(Y, Z, W)) = lome(Y, X, join(Z, W)).
% 152.18/19.99 Proof:
% 152.18/19.99 join(meet(X, Y), upme(Y, Z, W))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 join(meet(Y, X), upme(Y, Z, W))
% 152.18/19.99 = { by lemma 26 }
% 152.18/19.99 lome(Y, X, join(Z, W))
% 152.18/19.99
% 152.18/19.99 Lemma 28: join(X, join(Y, upme(Z, X, Y))) = join(X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 join(X, join(Y, upme(Z, X, Y)))
% 152.18/19.99 = { by lemma 18 R->L }
% 152.18/19.99 join(X, join(Y, meet(join(X, Y), Z)))
% 152.18/19.99 = { by axiom 7 (associativity_002) }
% 152.18/19.99 join(join(X, Y), meet(join(X, Y), Z))
% 152.18/19.99 = { by axiom 6 (absorption) }
% 152.18/19.99 join(X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 29: meet(X, lome(X, Y, Z)) = lome(X, Y, Z).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, lome(X, Y, Z))
% 152.18/19.99 = { by lemma 19 R->L }
% 152.18/19.99 join(meet(X, lome(X, Y, Z)), meet(Y, meet(X, lome(X, Y, Z))))
% 152.18/19.99 = { by lemma 23 }
% 152.18/19.99 join(meet(X, lome(X, Y, Z)), meet(Y, X))
% 152.18/19.99 = { by lemma 24 }
% 152.18/19.99 lome(X, lome(X, Y, Z), Y)
% 152.18/19.99 = { by lemma 13 R->L }
% 152.18/19.99 lome(X, Y, lome(X, Y, Z))
% 152.18/19.99 = { by lemma 25 R->L }
% 152.18/19.99 lome(X, Y, join(meet(Y, X), meet(X, Z)))
% 152.18/19.99 = { by lemma 27 R->L }
% 152.18/19.99 join(meet(Y, X), upme(X, meet(Y, X), meet(X, Z)))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 join(meet(Y, X), upme(X, meet(Y, X), meet(Z, X)))
% 152.18/19.99 = { by lemma 19 R->L }
% 152.18/19.99 join(meet(Y, X), join(upme(X, meet(Y, X), meet(Z, X)), meet(Z, upme(X, meet(Y, X), meet(Z, X)))))
% 152.18/19.99 = { by lemma 12 }
% 152.18/19.99 join(meet(Y, X), join(upme(X, meet(Y, X), meet(Z, X)), meet(Z, upme(X, meet(Z, X), meet(Y, X)))))
% 152.18/19.99 = { by axiom 4 (definition_of_upme) }
% 152.18/19.99 join(meet(Y, X), join(upme(X, meet(Y, X), meet(Z, X)), meet(Z, meet(X, join(meet(Z, X), meet(Y, X))))))
% 152.18/19.99 = { by axiom 5 (associativity) }
% 152.18/19.99 join(meet(Y, X), join(upme(X, meet(Y, X), meet(Z, X)), meet(meet(Z, X), join(meet(Z, X), meet(Y, X)))))
% 152.18/19.99 = { by axiom 3 (absorption_003) }
% 152.18/19.99 join(meet(Y, X), join(upme(X, meet(Y, X), meet(Z, X)), meet(Z, X)))
% 152.18/19.99 = { by axiom 2 (commutativity_001) }
% 152.18/19.99 join(meet(Y, X), join(meet(Z, X), upme(X, meet(Y, X), meet(Z, X))))
% 152.18/19.99 = { by lemma 27 }
% 152.18/19.99 join(meet(Y, X), lome(X, Z, join(meet(Y, X), meet(Z, X))))
% 152.18/19.99 = { by axiom 1 (commutativity) }
% 152.18/19.99 join(meet(Y, X), lome(X, Z, join(meet(Y, X), meet(X, Z))))
% 152.18/19.99 = { by lemma 26 R->L }
% 152.18/19.99 join(meet(Y, X), join(meet(X, Z), upme(X, meet(Y, X), meet(X, Z))))
% 152.18/19.99 = { by lemma 28 }
% 152.18/19.99 join(meet(Y, X), meet(X, Z))
% 152.18/19.99 = { by lemma 25 }
% 152.18/19.99 lome(X, Y, Z)
% 152.18/19.99
% 152.18/19.99 Lemma 30: meet(X, lome(Y, X, Z)) = meet(X, Y).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(X, lome(Y, X, Z))
% 152.18/19.99 = { by lemma 29 R->L }
% 152.18/19.99 meet(X, meet(Y, lome(Y, X, Z)))
% 152.18/19.99 = { by lemma 16 R->L }
% 152.18/19.99 meet(Y, meet(X, lome(Y, X, Z)))
% 152.18/19.99 = { by lemma 22 }
% 152.18/19.99 meet(Y, X)
% 152.18/19.99 = { by axiom 1 (commutativity) }
% 152.18/19.99 meet(X, Y)
% 152.18/19.99
% 152.18/19.99 Lemma 31: meet(Y, upme(X, Z, W)) = meet(X, upme(Y, Z, W)).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(Y, upme(X, Z, W))
% 152.18/19.99 = { by lemma 12 }
% 152.18/19.99 meet(Y, upme(X, W, Z))
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 meet(upme(X, W, Z), Y)
% 152.18/19.99 = { by axiom 4 (definition_of_upme) }
% 152.18/19.99 meet(meet(X, join(W, Z)), Y)
% 152.18/19.99 = { by axiom 5 (associativity) R->L }
% 152.18/19.99 meet(X, meet(join(W, Z), Y))
% 152.18/19.99 = { by lemma 18 }
% 152.18/19.99 meet(X, upme(Y, W, Z))
% 152.18/19.99 = { by lemma 12 R->L }
% 152.18/19.99 meet(X, upme(Y, Z, W))
% 152.18/19.99
% 152.18/19.99 Lemma 32: meet(upme(X, Y, Z), W) = meet(X, upme(W, Y, Z)).
% 152.18/19.99 Proof:
% 152.18/19.99 meet(upme(X, Y, Z), W)
% 152.18/19.99 = { by axiom 1 (commutativity) R->L }
% 152.18/19.99 meet(W, upme(X, Y, Z))
% 152.18/19.99 = { by lemma 31 R->L }
% 152.18/19.99 meet(X, upme(W, Y, Z))
% 152.18/19.99
% 152.18/19.99 Lemma 33: join(X, upme(X, Y, Z)) = X.
% 152.18/19.99 Proof:
% 152.18/19.99 join(X, upme(X, Y, Z))
% 152.18/19.99 = { by axiom 4 (definition_of_upme) }
% 152.18/19.99 join(X, meet(X, join(Y, Z)))
% 152.18/19.99 = { by axiom 6 (absorption) }
% 152.18/19.99 X
% 152.18/19.99
% 152.18/19.99 Lemma 34: upme(meet(X, Y), Z, W) = meet(X, upme(Y, Z, W)).
% 152.18/19.99 Proof:
% 152.18/20.00 upme(meet(X, Y), Z, W)
% 152.18/20.00 = { by axiom 4 (definition_of_upme) }
% 152.18/20.01 meet(meet(X, Y), join(Z, W))
% 152.18/20.01 = { by axiom 5 (associativity) R->L }
% 152.18/20.01 meet(X, meet(Y, join(Z, W)))
% 152.18/20.01 = { by axiom 4 (definition_of_upme) R->L }
% 152.18/20.01 meet(X, upme(Y, Z, W))
% 152.18/20.01
% 152.18/20.01 Lemma 35: upme(join(Z, W), X, Y) = upme(join(X, Y), Z, W).
% 152.18/20.01 Proof:
% 152.18/20.01 upme(join(Z, W), X, Y)
% 152.18/20.01 = { by axiom 2 (commutativity_001) R->L }
% 152.18/20.01 upme(join(W, Z), X, Y)
% 152.18/20.01 = { by lemma 12 }
% 152.18/20.01 upme(join(W, Z), Y, X)
% 152.18/20.01 = { by axiom 4 (definition_of_upme) }
% 152.18/20.01 meet(join(W, Z), join(Y, X))
% 152.18/20.01 = { by lemma 18 }
% 152.18/20.01 upme(join(Y, X), W, Z)
% 152.18/20.01 = { by lemma 12 R->L }
% 152.18/20.01 upme(join(Y, X), Z, W)
% 152.18/20.01 = { by axiom 2 (commutativity_001) }
% 152.18/20.01 upme(join(X, Y), Z, W)
% 152.18/20.01
% 152.18/20.01 Lemma 36: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 152.18/20.01 Proof:
% 152.18/20.01 join(X, join(Y, meet(X, Z)))
% 152.18/20.01 = { by axiom 2 (commutativity_001) R->L }
% 152.18/20.01 join(X, join(meet(X, Z), Y))
% 152.18/20.01 = { by axiom 7 (associativity_002) }
% 152.18/20.01 join(join(X, meet(X, Z)), Y)
% 152.18/20.01 = { by axiom 6 (absorption) }
% 152.18/20.01 join(X, Y)
% 152.18/20.01
% 152.18/20.01 Lemma 37: join(meet(X, Y), meet(Z, Y)) = lome(Y, X, Z).
% 152.18/20.01 Proof:
% 152.18/20.01 join(meet(X, Y), meet(Z, Y))
% 152.18/20.01 = { by axiom 1 (commutativity) R->L }
% 152.18/20.01 join(meet(X, Y), meet(Y, Z))
% 152.18/20.01 = { by lemma 25 }
% 152.18/20.01 lome(Y, X, Z)
% 152.18/20.01
% 152.18/20.01 Lemma 38: upme(X, Y, upme(Y, Z, W)) = meet(X, Y).
% 152.18/20.01 Proof:
% 152.18/20.01 upme(X, Y, upme(Y, Z, W))
% 152.18/20.01 = { by axiom 4 (definition_of_upme) }
% 152.18/20.01 meet(X, join(Y, upme(Y, Z, W)))
% 152.18/20.01 = { by lemma 33 }
% 152.18/20.01 meet(X, Y)
% 152.18/20.01
% 152.18/20.01 Lemma 39: lome(upme(X, Y, Z), W, X) = upme(X, Y, Z).
% 152.18/20.01 Proof:
% 152.18/20.01 lome(upme(X, Y, Z), W, X)
% 152.18/20.01 = { by lemma 13 }
% 152.18/20.01 lome(upme(X, Y, Z), X, W)
% 152.18/20.01 = { by lemma 33 R->L }
% 152.18/20.01 lome(upme(X, Y, Z), join(X, upme(X, Y, Z)), W)
% 152.18/20.01 = { by axiom 2 (commutativity_001) R->L }
% 152.18/20.01 lome(upme(X, Y, Z), join(upme(X, Y, Z), X), W)
% 152.18/20.01 = { by axiom 8 (definition_of_lome) }
% 152.18/20.01 join(meet(upme(X, Y, Z), join(upme(X, Y, Z), X)), meet(upme(X, Y, Z), W))
% 152.18/20.01 = { by axiom 3 (absorption_003) }
% 152.18/20.01 join(upme(X, Y, Z), meet(upme(X, Y, Z), W))
% 152.18/20.01 = { by axiom 6 (absorption) }
% 152.18/20.01 upme(X, Y, Z)
% 152.18/20.01
% 152.18/20.01 Lemma 40: upme(join(meet(a, meet(X, Y)), Z), meet(a, meet(X, Z)), Y) = join(meet(Y, Z), upme(meet(a, X), Y, Z)).
% 152.18/20.01 Proof:
% 152.18/20.01 upme(join(meet(a, meet(X, Y)), Z), meet(a, meet(X, Z)), Y)
% 152.18/20.01 = { by axiom 5 (associativity) }
% 152.18/20.01 upme(join(meet(a, meet(X, Y)), Z), meet(meet(a, X), Z), Y)
% 152.18/20.01 = { by axiom 5 (associativity) }
% 152.18/20.01 upme(join(meet(meet(a, X), Y), Z), meet(meet(a, X), Z), Y)
% 152.18/20.01 = { by axiom 4 (definition_of_upme) }
% 152.18/20.01 meet(join(meet(meet(a, X), Y), Z), join(meet(meet(a, X), Z), Y))
% 152.18/20.01 = { by axiom 9 (conjecture) R->L }
% 152.18/20.01 join(upme(meet(a, X), Y, Z), meet(Y, Z))
% 152.18/20.01 = { by axiom 2 (commutativity_001) }
% 152.18/20.01 join(meet(Y, Z), upme(meet(a, X), Y, Z))
% 152.18/20.01
% 152.18/20.01 Lemma 41: upme(join(meet(a, meet(X, Y)), Z), meet(a, meet(Y, Z)), X) = join(meet(X, Z), meet(Y, upme(a, X, Z))).
% 152.18/20.01 Proof:
% 152.18/20.01 upme(join(meet(a, meet(X, Y)), Z), meet(a, meet(Y, Z)), X)
% 152.18/20.01 = { by axiom 1 (commutativity) R->L }
% 152.18/20.01 upme(join(meet(a, meet(Y, X)), Z), meet(a, meet(Y, Z)), X)
% 152.18/20.01 = { by lemma 40 }
% 152.18/20.01 join(meet(X, Z), upme(meet(a, Y), X, Z))
% 152.18/20.01 = { by lemma 34 }
% 152.18/20.01 join(meet(X, Z), meet(a, upme(Y, X, Z)))
% 152.18/20.01 = { by lemma 31 R->L }
% 152.18/20.01 join(meet(X, Z), meet(Y, upme(a, X, Z)))
% 152.18/20.01
% 152.18/20.01 Lemma 42: upme(a, meet(a, X), upme(X, Y, Z)) = meet(a, X).
% 152.18/20.01 Proof:
% 152.18/20.01 upme(a, meet(a, X), upme(X, Y, Z))
% 152.18/20.01 = { by lemma 18 R->L }
% 152.18/20.01 meet(join(meet(a, X), upme(X, Y, Z)), a)
% 152.18/20.01 = { by lemma 14 R->L }
% 152.18/20.01 upme(join(meet(a, X), upme(X, Y, Z)), a, meet(a, meet(upme(X, Y, Z), X)))
% 152.18/20.01 = { by lemma 16 }
% 152.18/20.01 upme(join(meet(a, X), upme(X, Y, Z)), a, meet(upme(X, Y, Z), meet(a, X)))
% 152.18/20.01 = { by lemma 12 }
% 152.18/20.01 upme(join(meet(a, X), upme(X, Y, Z)), meet(upme(X, Y, Z), meet(a, X)), a)
% 152.18/20.01 = { by lemma 17 }
% 152.18/20.01 upme(join(meet(a, X), upme(X, Y, Z)), meet(a, meet(X, upme(X, Y, Z))), a)
% 152.18/20.01 = { by lemma 15 R->L }
% 152.18/20.01 upme(join(meet(a, meet(a, X)), upme(X, Y, Z)), meet(a, meet(X, upme(X, Y, Z))), a)
% 152.18/20.01 = { by lemma 41 }
% 152.18/20.01 join(meet(a, upme(X, Y, Z)), meet(X, upme(a, a, upme(X, Y, Z))))
% 152.18/20.01 = { by axiom 4 (definition_of_upme) }
% 152.18/20.01 join(meet(a, upme(X, Y, Z)), meet(X, meet(a, join(a, upme(X, Y, Z)))))
% 152.18/20.01 = { by axiom 3 (absorption_003) }
% 152.18/20.01 join(meet(a, upme(X, Y, Z)), meet(X, a))
% 152.18/20.01 = { by lemma 24 }
% 152.18/20.01 lome(a, upme(X, Y, Z), X)
% 152.18/20.01 = { by lemma 13 }
% 152.18/20.01 lome(a, X, upme(X, Y, Z))
% 152.18/20.01 = { by axiom 8 (definition_of_lome) }
% 152.18/20.01 join(meet(a, X), meet(a, upme(X, Y, Z)))
% 152.18/20.01 = { by lemma 34 R->L }
% 152.18/20.01 join(meet(a, X), upme(meet(a, X), Y, Z))
% 152.18/20.01 = { by lemma 33 }
% 152.18/20.01 meet(a, X)
% 152.18/20.01
% 152.18/20.01 Lemma 43: join(meet(X, meet(Y, Z)), upme(Y, W, V)) = lome(Y, meet(X, Z), join(W, V)).
% 152.18/20.01 Proof:
% 152.18/20.01 join(meet(X, meet(Y, Z)), upme(Y, W, V))
% 152.18/20.01 = { by lemma 16 R->L }
% 152.18/20.01 join(meet(Y, meet(X, Z)), upme(Y, W, V))
% 152.18/20.01 = { by lemma 26 }
% 152.18/20.01 lome(Y, meet(X, Z), join(W, V))
% 152.18/20.01
% 152.18/20.01 Lemma 44: upme(join(X, meet(Y, meet(a, Z))), Y, meet(X, meet(a, Z))) = join(meet(X, Y), upme(meet(a, Z), X, Y)).
% 152.18/20.01 Proof:
% 152.18/20.01 upme(join(X, meet(Y, meet(a, Z))), Y, meet(X, meet(a, Z)))
% 152.18/20.01 = { by lemma 12 }
% 152.18/20.01 upme(join(X, meet(Y, meet(a, Z))), meet(X, meet(a, Z)), Y)
% 152.18/20.01 = { by lemma 35 }
% 152.18/20.01 upme(join(meet(X, meet(a, Z)), Y), X, meet(Y, meet(a, Z)))
% 152.18/20.01 = { by lemma 12 }
% 152.18/20.01 upme(join(meet(X, meet(a, Z)), Y), meet(Y, meet(a, Z)), X)
% 152.18/20.01 = { by lemma 35 }
% 152.18/20.01 upme(join(meet(Y, meet(a, Z)), X), meet(X, meet(a, Z)), Y)
% 152.18/20.01 = { by lemma 17 }
% 152.18/20.01 upme(join(meet(Y, meet(a, Z)), X), meet(a, meet(Z, X)), Y)
% 152.18/20.01 = { by lemma 16 R->L }
% 152.18/20.01 upme(join(meet(a, meet(Y, Z)), X), meet(a, meet(Z, X)), Y)
% 152.18/20.01 = { by lemma 41 }
% 152.18/20.01 join(meet(Y, X), meet(Z, upme(a, Y, X)))
% 152.18/20.01 = { by lemma 31 R->L }
% 152.18/20.01 join(meet(Y, X), meet(a, upme(Z, Y, X)))
% 152.18/20.01 = { by lemma 34 R->L }
% 152.18/20.01 join(meet(Y, X), upme(meet(a, Z), Y, X))
% 152.18/20.01 = { by axiom 1 (commutativity) }
% 152.18/20.01 join(meet(X, Y), upme(meet(a, Z), Y, X))
% 152.18/20.01 = { by lemma 12 R->L }
% 152.18/20.01 join(meet(X, Y), upme(meet(a, Z), X, Y))
% 152.18/20.01
% 152.18/20.01 Goal 1 (conjecture_1): upme(meet(a, z1), z2, z3) = lome(meet(a, z1), z2, z3).
% 152.18/20.01 Proof:
% 152.18/20.01 upme(meet(a, z1), z2, z3)
% 152.18/20.01 = { by lemma 39 R->L }
% 152.18/20.01 lome(upme(meet(a, z1), z2, z3), z2, meet(a, z1))
% 152.18/20.01 = { by lemma 42 R->L }
% 152.18/20.01 lome(upme(meet(a, z1), z2, z3), z2, upme(a, meet(a, z1), upme(z1, X, Y)))
% 152.18/20.01 = { by lemma 13 }
% 152.18/20.01 lome(upme(meet(a, z1), z2, z3), upme(a, meet(a, z1), upme(z1, X, Y)), z2)
% 152.18/20.01 = { by lemma 24 R->L }
% 152.18/20.01 join(meet(upme(meet(a, z1), z2, z3), upme(a, meet(a, z1), upme(z1, X, Y))), meet(z2, upme(meet(a, z1), z2, z3)))
% 152.18/20.01 = { by lemma 38 R->L }
% 152.18/20.01 join(meet(upme(meet(a, z1), z2, z3), upme(a, meet(a, z1), upme(z1, X, Y))), upme(z2, upme(meet(a, z1), z2, z3), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))))
% 152.18/20.01 = { by lemma 32 R->L }
% 152.18/20.01 join(meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a), upme(z2, upme(meet(a, z1), z2, z3), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))))
% 152.18/20.01 = { by lemma 12 }
% 152.18/20.01 join(meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a), upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)))
% 152.18/20.01 = { by axiom 1 (commutativity) R->L }
% 152.18/20.01 join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)))
% 152.18/20.01 = { by axiom 2 (commutativity_001) R->L }
% 152.18/20.01 join(upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))))
% 152.18/20.01 = { by axiom 3 (absorption_003) R->L }
% 152.18/20.01 join(upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(z2, upme(meet(a, z1), z2, z3))))))
% 152.18/20.01 = { by lemma 20 R->L }
% 152.18/20.01 join(upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(z2, join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3))))))
% 152.18/20.01 = { by axiom 4 (definition_of_upme) R->L }
% 152.18/20.01 join(upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), meet(a, upme(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2, join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)))))
% 152.18/20.02 = { by lemma 12 R->L }
% 152.18/20.02 join(upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), meet(a, upme(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), z2)))
% 152.18/20.02 = { by lemma 34 R->L }
% 152.18/20.02 join(upme(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), upme(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), z2))
% 152.18/20.02 = { by lemma 18 R->L }
% 152.18/20.02 join(meet(join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), z2), upme(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)), z2))
% 152.18/20.02 = { by lemma 40 R->L }
% 152.18/20.02 upme(join(meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)))), z2), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2)), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)))
% 152.18/20.02 = { by axiom 3 (absorption_003) }
% 152.18/20.02 upme(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2)), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3)))
% 152.18/20.02 = { by axiom 4 (definition_of_upme) }
% 152.18/20.02 meet(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), join(meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2)), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), upme(meet(a, z1), z2, z3))))
% 152.18/20.02 = { by lemma 20 R->L }
% 152.18/20.02 meet(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2)), upme(meet(a, z1), z2, z3))))
% 152.18/20.02 = { by axiom 4 (definition_of_upme) R->L }
% 152.82/20.02 upme(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2)), upme(meet(a, z1), z2, z3)))
% 152.82/20.02 = { by axiom 2 (commutativity_001) R->L }
% 152.82/20.02 upme(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), join(upme(meet(a, z1), z2, z3), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2))))
% 152.82/20.02 = { by lemma 12 }
% 152.82/20.02 upme(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), join(upme(meet(a, z1), z2, z3), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2))), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)))
% 152.82/20.02 = { by axiom 4 (definition_of_upme) }
% 152.82/20.02 meet(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), join(join(upme(meet(a, z1), z2, z3), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2))), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))))
% 152.82/20.02 = { by axiom 7 (associativity_002) R->L }
% 152.82/20.02 meet(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), join(upme(meet(a, z1), z2, z3), join(meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2)), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)))))
% 152.82/20.02 = { by axiom 4 (definition_of_upme) R->L }
% 152.82/20.02 upme(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), upme(meet(a, z1), z2, z3), join(meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2)), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))))
% 152.82/20.02 = { by axiom 2 (commutativity_001) }
% 152.82/20.02 upme(join(meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2), upme(meet(a, z1), z2, z3), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2))))
% 152.82/20.02 = { by axiom 2 (commutativity_001) }
% 152.82/20.02 upme(join(z2, meet(a, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)))), upme(meet(a, z1), z2, z3), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2))))
% 152.82/20.02 = { by axiom 1 (commutativity) }
% 152.82/20.02 upme(join(z2, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a)), upme(meet(a, z1), z2, z3), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), meet(a, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), z2))))
% 152.82/20.02 = { by axiom 1 (commutativity) R->L }
% 152.82/20.02 upme(join(z2, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a)), upme(meet(a, z1), z2, z3), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), meet(a, meet(z2, upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))))))
% 152.82/20.02 = { by axiom 5 (associativity) }
% 152.82/20.02 upme(join(z2, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a)), upme(meet(a, z1), z2, z3), join(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), meet(meet(a, z2), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)))))
% 152.82/20.02 = { by lemma 19 }
% 152.82/20.02 upme(join(z2, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a)), upme(meet(a, z1), z2, z3), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)))
% 152.82/20.02 = { by lemma 35 R->L }
% 152.82/20.02 upme(join(upme(meet(a, z1), z2, z3), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y))), z2, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a))
% 152.82/20.02 = { by lemma 33 }
% 152.82/20.02 upme(upme(meet(a, z1), z2, z3), z2, meet(upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(z1, X, Y)), a))
% 152.82/20.02 = { by lemma 32 }
% 152.82/20.02 upme(upme(meet(a, z1), z2, z3), z2, meet(upme(meet(a, z1), z2, z3), upme(a, meet(a, z1), upme(z1, X, Y))))
% 152.82/20.02 = { by lemma 42 }
% 152.82/20.02 upme(upme(meet(a, z1), z2, z3), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by axiom 6 (absorption) R->L }
% 152.82/20.02 upme(join(upme(meet(a, z1), z2, z3), meet(upme(meet(a, z1), z2, z3), z2)), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by axiom 2 (commutativity_001) R->L }
% 152.82/20.02 upme(join(meet(upme(meet(a, z1), z2, z3), z2), upme(meet(a, z1), z2, z3)), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by axiom 3 (absorption_003) R->L }
% 152.82/20.02 upme(join(meet(upme(meet(a, z1), z2, z3), z2), meet(upme(meet(a, z1), z2, z3), join(upme(meet(a, z1), z2, z3), meet(a, z1)))), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by axiom 8 (definition_of_lome) R->L }
% 152.82/20.02 upme(lome(upme(meet(a, z1), z2, z3), z2, join(upme(meet(a, z1), z2, z3), meet(a, z1))), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by lemma 27 R->L }
% 152.82/20.02 upme(join(meet(z2, upme(meet(a, z1), z2, z3)), upme(upme(meet(a, z1), z2, z3), upme(meet(a, z1), z2, z3), meet(a, z1))), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by lemma 21 }
% 152.82/20.02 upme(join(meet(z2, meet(a, z1)), upme(upme(meet(a, z1), z2, z3), upme(meet(a, z1), z2, z3), meet(a, z1))), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by lemma 12 R->L }
% 152.82/20.02 upme(join(meet(z2, meet(a, z1)), upme(upme(meet(a, z1), z2, z3), meet(a, z1), upme(meet(a, z1), z2, z3))), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by lemma 38 }
% 152.82/20.02 upme(join(meet(z2, meet(a, z1)), meet(upme(meet(a, z1), z2, z3), meet(a, z1))), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by lemma 37 }
% 152.82/20.02 upme(lome(meet(a, z1), z2, upme(meet(a, z1), z2, z3)), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by lemma 13 }
% 152.82/20.02 upme(lome(meet(a, z1), upme(meet(a, z1), z2, z3), z2), z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1)))
% 152.82/20.02 = { by lemma 10 R->L }
% 152.82/20.02 upme(lome(meet(a, z1), upme(meet(a, z1), z2, z3), z2), z2, meet(upme(meet(a, z1), z2, z3), meet(meet(a, z1), meet(a, z1))))
% 152.82/20.02 = { by axiom 5 (associativity) }
% 152.82/20.02 upme(lome(meet(a, z1), upme(meet(a, z1), z2, z3), z2), z2, meet(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), meet(a, z1)))
% 152.82/20.02 = { by lemma 37 R->L }
% 152.82/20.02 upme(join(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), meet(z2, meet(a, z1))), z2, meet(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), meet(a, z1)))
% 152.82/20.02 = { by lemma 44 }
% 152.82/20.02 join(meet(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2), upme(meet(a, z1), meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by axiom 5 (associativity) R->L }
% 152.82/20.02 join(meet(upme(meet(a, z1), z2, z3), meet(meet(a, z1), z2)), upme(meet(a, z1), meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by lemma 43 }
% 152.82/20.02 lome(meet(a, z1), meet(upme(meet(a, z1), z2, z3), z2), join(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by axiom 1 (commutativity) }
% 152.82/20.02 lome(meet(a, z1), meet(z2, upme(meet(a, z1), z2, z3)), join(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by axiom 2 (commutativity_001) }
% 152.82/20.02 lome(meet(a, z1), meet(z2, upme(meet(a, z1), z2, z3)), join(z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1))))
% 152.82/20.02 = { by lemma 21 }
% 152.82/20.02 lome(meet(a, z1), meet(z2, meet(a, z1)), join(z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1))))
% 152.82/20.02 = { by lemma 30 R->L }
% 152.82/20.02 lome(meet(a, z1), meet(z2, lome(meet(a, z1), z2, Z)), join(z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1))))
% 152.82/20.02 = { by axiom 2 (commutativity_001) R->L }
% 152.82/20.02 lome(meet(a, z1), meet(z2, lome(meet(a, z1), z2, Z)), join(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by lemma 43 R->L }
% 152.82/20.02 join(meet(z2, meet(meet(a, z1), lome(meet(a, z1), z2, Z))), upme(meet(a, z1), meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by lemma 23 }
% 152.82/20.02 join(meet(z2, meet(a, z1)), upme(meet(a, z1), meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by lemma 27 }
% 152.82/20.02 lome(meet(a, z1), z2, join(meet(upme(meet(a, z1), z2, z3), meet(a, z1)), z2))
% 152.82/20.02 = { by axiom 2 (commutativity_001) }
% 152.82/20.02 lome(meet(a, z1), z2, join(z2, meet(upme(meet(a, z1), z2, z3), meet(a, z1))))
% 152.82/20.02 = { by axiom 1 (commutativity) }
% 152.82/20.02 lome(meet(a, z1), z2, join(z2, meet(meet(a, z1), upme(meet(a, z1), z2, z3))))
% 152.82/20.02 = { by lemma 34 R->L }
% 152.82/20.02 lome(meet(a, z1), z2, join(z2, upme(meet(meet(a, z1), meet(a, z1)), z2, z3)))
% 152.82/20.03 = { by lemma 10 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, upme(meet(a, z1), z2, z3)))
% 152.82/20.03 = { by lemma 39 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, lome(upme(meet(a, z1), z2, z3), a, meet(a, z1))))
% 152.82/20.03 = { by axiom 8 (definition_of_lome) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(upme(meet(a, z1), z2, z3), a), meet(upme(meet(a, z1), z2, z3), meet(a, z1)))))
% 152.82/20.03 = { by axiom 5 (associativity) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(upme(meet(a, z1), z2, z3), a), meet(meet(upme(meet(a, z1), z2, z3), a), z1))))
% 152.82/20.03 = { by axiom 6 (absorption) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(upme(meet(a, z1), z2, z3), a)))
% 152.82/20.03 = { by axiom 1 (commutativity) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(a, upme(meet(a, z1), z2, z3))))
% 152.82/20.03 = { by lemma 31 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(meet(a, z1), upme(a, z2, z3))))
% 152.82/20.03 = { by lemma 12 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(meet(a, z1), upme(a, z3, z2))))
% 152.82/20.03 = { by lemma 34 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, upme(meet(meet(a, z1), a), z3, z2)))
% 152.82/20.03 = { by lemma 19 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(upme(meet(meet(a, z1), a), z3, z2), meet(z3, upme(meet(meet(a, z1), a), z3, z2)))))
% 152.82/20.03 = { by lemma 21 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(upme(meet(meet(a, z1), a), z3, z2), meet(z3, meet(meet(a, z1), a)))))
% 152.82/20.03 = { by axiom 2 (commutativity_001) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(z3, meet(meet(a, z1), a)), upme(meet(meet(a, z1), a), z3, z2))))
% 152.82/20.03 = { by axiom 1 (commutativity) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(meet(meet(a, z1), a), z3), upme(meet(meet(a, z1), a), z3, z2))))
% 152.82/20.03 = { by lemma 26 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, lome(meet(meet(a, z1), a), z3, join(z3, z2))))
% 152.82/20.03 = { by axiom 2 (commutativity_001) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, lome(meet(meet(a, z1), a), z3, join(z2, z3))))
% 152.82/20.03 = { by lemma 26 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(meet(meet(a, z1), a), z3), upme(meet(meet(a, z1), a), z2, z3))))
% 152.82/20.03 = { by axiom 5 (associativity) R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(meet(a, z1), meet(a, z3)), upme(meet(meet(a, z1), a), z2, z3))))
% 152.82/20.03 = { by lemma 34 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(meet(a, z1), meet(a, z3)), meet(meet(a, z1), upme(a, z2, z3)))))
% 152.82/20.03 = { by axiom 8 (definition_of_lome) R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, lome(meet(a, z1), meet(a, z3), upme(a, z2, z3))))
% 152.82/20.03 = { by axiom 2 (commutativity_001) R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(lome(meet(a, z1), meet(a, z3), upme(a, z2, z3)), z2))
% 152.82/20.03 = { by axiom 8 (definition_of_lome) }
% 152.82/20.03 lome(meet(a, z1), z2, join(join(meet(meet(a, z1), meet(a, z3)), meet(meet(a, z1), upme(a, z2, z3))), z2))
% 152.82/20.03 = { by axiom 7 (associativity_002) R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(meet(meet(a, z1), meet(a, z3)), join(meet(meet(a, z1), upme(a, z2, z3)), z2)))
% 152.82/20.03 = { by axiom 2 (commutativity_001) }
% 152.82/20.03 lome(meet(a, z1), z2, join(meet(meet(a, z1), meet(a, z3)), join(z2, meet(meet(a, z1), upme(a, z2, z3)))))
% 152.82/20.03 = { by lemma 16 }
% 152.82/20.03 lome(meet(a, z1), z2, join(meet(a, meet(meet(a, z1), z3)), join(z2, meet(meet(a, z1), upme(a, z2, z3)))))
% 152.82/20.03 = { by lemma 36 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(meet(a, meet(meet(a, z1), z3)), join(z2, join(meet(meet(a, z1), upme(a, z2, z3)), meet(z2, z3)))))
% 152.82/20.03 = { by axiom 2 (commutativity_001) }
% 152.82/20.03 lome(meet(a, z1), z2, join(meet(a, meet(meet(a, z1), z3)), join(z2, join(meet(z2, z3), meet(meet(a, z1), upme(a, z2, z3))))))
% 152.82/20.03 = { by lemma 41 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(meet(a, meet(meet(a, z1), z3)), join(z2, upme(join(meet(a, meet(z2, meet(a, z1))), z3), meet(a, meet(meet(a, z1), z3)), z2))))
% 152.82/20.03 = { by lemma 28 }
% 152.82/20.03 lome(meet(a, z1), z2, join(meet(a, meet(meet(a, z1), z3)), z2))
% 152.82/20.03 = { by axiom 2 (commutativity_001) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(a, meet(meet(a, z1), z3))))
% 152.82/20.03 = { by lemma 16 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(meet(a, z1), meet(a, z3))))
% 152.82/20.03 = { by axiom 1 (commutativity) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(meet(a, z1), meet(z3, a))))
% 152.82/20.03 = { by lemma 16 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(z3, meet(meet(a, z1), a))))
% 152.82/20.03 = { by axiom 1 (commutativity) }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(z3, meet(a, meet(a, z1)))))
% 152.82/20.03 = { by lemma 15 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(z3, meet(a, z1))))
% 152.82/20.03 = { by axiom 1 (commutativity) R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, meet(meet(a, z1), z3)))
% 152.82/20.03 = { by lemma 36 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, join(meet(meet(a, z1), z3), meet(z2, meet(a, z1)))))
% 152.82/20.03 = { by lemma 24 }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, lome(meet(a, z1), z3, z2)))
% 152.82/20.03 = { by lemma 13 R->L }
% 152.82/20.03 lome(meet(a, z1), z2, join(z2, lome(meet(a, z1), z2, z3)))
% 152.82/20.03 = { by lemma 27 R->L }
% 152.82/20.03 join(meet(z2, meet(a, z1)), upme(meet(a, z1), z2, lome(meet(a, z1), z2, z3)))
% 152.82/20.03 = { by lemma 30 R->L }
% 152.82/20.03 join(meet(z2, lome(meet(a, z1), z2, z3)), upme(meet(a, z1), z2, lome(meet(a, z1), z2, z3)))
% 152.82/20.03 = { by lemma 44 R->L }
% 152.82/20.03 upme(join(z2, meet(lome(meet(a, z1), z2, z3), meet(a, z1))), lome(meet(a, z1), z2, z3), meet(z2, meet(a, z1)))
% 152.82/20.03 = { by axiom 1 (commutativity) }
% 152.82/20.03 upme(join(z2, meet(meet(a, z1), lome(meet(a, z1), z2, z3))), lome(meet(a, z1), z2, z3), meet(z2, meet(a, z1)))
% 152.82/20.03 = { by lemma 30 R->L }
% 152.82/20.03 upme(join(z2, meet(meet(a, z1), lome(meet(a, z1), z2, z3))), lome(meet(a, z1), z2, z3), meet(z2, lome(meet(a, z1), z2, z3)))
% 152.82/20.03 = { by axiom 1 (commutativity) R->L }
% 152.82/20.03 upme(join(z2, meet(meet(a, z1), lome(meet(a, z1), z2, z3))), lome(meet(a, z1), z2, z3), meet(lome(meet(a, z1), z2, z3), z2))
% 152.82/20.03 = { by lemma 14 }
% 152.82/20.03 meet(join(z2, meet(meet(a, z1), lome(meet(a, z1), z2, z3))), lome(meet(a, z1), z2, z3))
% 152.82/20.03 = { by lemma 18 }
% 152.82/20.03 upme(lome(meet(a, z1), z2, z3), z2, meet(meet(a, z1), lome(meet(a, z1), z2, z3)))
% 152.82/20.03 = { by lemma 29 }
% 152.82/20.03 upme(lome(meet(a, z1), z2, z3), z2, lome(meet(a, z1), z2, z3))
% 152.82/20.03 = { by lemma 11 }
% 152.82/20.03 lome(meet(a, z1), z2, z3)
% 152.82/20.03 % SZS output end Proof
% 152.82/20.03
% 152.82/20.03 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------