TSTP Solution File: LAT170-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT170-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n014.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 06:27:38 EDT 2023
% Result : Unsatisfiable 53.70s 7.29s
% Output : Proof 54.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT170-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 07:44:04 EDT 2023
% 0.20/0.35 % CPUTime :
% 53.70/7.29 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 53.70/7.29
% 53.70/7.29 % SZS status Unsatisfiable
% 53.70/7.29
% 54.57/7.39 % SZS output start Proof
% 54.57/7.39 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 54.57/7.39 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 54.57/7.39 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 54.57/7.39 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 54.57/7.39 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 54.57/7.39 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 54.57/7.39 Axiom 7 (absorption1): meet(X, join(X, Y)) = X.
% 54.57/7.39 Axiom 8 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 54.57/7.39 Axiom 9 (equation_H49_dual): join(X, meet(Y, join(Z, meet(X, W)))) = join(X, meet(Y, meet(join(X, Z), join(Z, meet(Y, W))))).
% 54.57/7.39
% 54.57/7.39 Lemma 10: meet(X, join(Y, X)) = X.
% 54.57/7.39 Proof:
% 54.57/7.39 meet(X, join(Y, X))
% 54.57/7.39 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.39 meet(X, join(X, Y))
% 54.57/7.39 = { by axiom 7 (absorption1) }
% 54.57/7.39 X
% 54.57/7.39
% 54.57/7.39 Lemma 11: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 54.57/7.39 Proof:
% 54.57/7.39 meet(Y, meet(X, Z))
% 54.57/7.39 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.39 meet(meet(X, Z), Y)
% 54.57/7.39 = { by axiom 8 (associativity_of_meet) }
% 54.57/7.39 meet(X, meet(Z, Y))
% 54.57/7.39 = { by axiom 4 (commutativity_of_meet) }
% 54.57/7.39 meet(X, meet(Y, Z))
% 54.57/7.39
% 54.57/7.39 Lemma 12: meet(Z, meet(X, Y)) = meet(X, meet(Y, Z)).
% 54.57/7.39 Proof:
% 54.57/7.39 meet(Z, meet(X, Y))
% 54.57/7.39 = { by lemma 11 }
% 54.57/7.39 meet(X, meet(Z, Y))
% 54.57/7.39 = { by axiom 4 (commutativity_of_meet) }
% 54.57/7.39 meet(X, meet(Y, Z))
% 54.57/7.39
% 54.57/7.39 Lemma 13: join(X, meet(Y, X)) = X.
% 54.57/7.39 Proof:
% 54.57/7.39 join(X, meet(Y, X))
% 54.57/7.39 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.39 join(X, meet(X, Y))
% 54.57/7.39 = { by axiom 5 (absorption2) }
% 54.57/7.39 X
% 54.57/7.39
% 54.57/7.39 Lemma 14: join(X, join(X, Y)) = join(X, Y).
% 54.57/7.39 Proof:
% 54.57/7.39 join(X, join(X, Y))
% 54.57/7.39 = { by axiom 6 (associativity_of_join) R->L }
% 54.57/7.39 join(join(X, X), Y)
% 54.57/7.39 = { by axiom 1 (idempotence_of_join) }
% 54.57/7.39 join(X, Y)
% 54.57/7.39
% 54.57/7.39 Lemma 15: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 54.57/7.39 Proof:
% 54.57/7.39 join(Y, join(X, Z))
% 54.57/7.39 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.39 join(join(X, Z), Y)
% 54.57/7.39 = { by axiom 6 (associativity_of_join) }
% 54.57/7.39 join(X, join(Z, Y))
% 54.57/7.39 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.39 join(X, join(Y, Z))
% 54.57/7.39
% 54.57/7.39 Lemma 16: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 54.57/7.39 Proof:
% 54.57/7.39 join(Y, join(Z, X))
% 54.57/7.39 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.39 join(join(Z, X), Y)
% 54.57/7.39 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.39 join(join(X, Z), Y)
% 54.57/7.39 = { by axiom 6 (associativity_of_join) }
% 54.57/7.39 join(X, join(Z, Y))
% 54.57/7.39 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.39 join(X, join(Y, Z))
% 54.57/7.39
% 54.57/7.39 Lemma 17: join(meet(X, Y), Y) = Y.
% 54.57/7.39 Proof:
% 54.57/7.39 join(meet(X, Y), Y)
% 54.57/7.39 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.39 join(Y, meet(X, Y))
% 54.57/7.39 = { by lemma 13 }
% 54.57/7.40 Y
% 54.57/7.40
% 54.57/7.40 Lemma 18: join(X, meet(join(X, join(Y, meet(Z, X))), W)) = join(X, meet(W, join(X, Y))).
% 54.57/7.40 Proof:
% 54.57/7.40 join(X, meet(join(X, join(Y, meet(Z, X))), W))
% 54.57/7.40 = { by lemma 16 }
% 54.57/7.40 join(X, meet(join(meet(Z, X), join(X, Y)), W))
% 54.57/7.40 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.40 join(X, meet(W, join(meet(Z, X), join(X, Y))))
% 54.57/7.40 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.40 join(X, meet(W, join(join(X, Y), meet(Z, X))))
% 54.57/7.40 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.40 join(X, meet(W, join(join(X, Y), meet(X, Z))))
% 54.57/7.40 = { by axiom 9 (equation_H49_dual) }
% 54.57/7.40 join(X, meet(W, meet(join(X, join(X, Y)), join(join(X, Y), meet(W, Z)))))
% 54.57/7.40 = { by lemma 14 }
% 54.57/7.40 join(X, meet(W, meet(join(X, Y), join(join(X, Y), meet(W, Z)))))
% 54.57/7.40 = { by axiom 7 (absorption1) }
% 54.57/7.40 join(X, meet(W, join(X, Y)))
% 54.57/7.40
% 54.57/7.40 Lemma 19: join(X, join(Y, meet(Z, X))) = join(X, Y).
% 54.57/7.40 Proof:
% 54.57/7.40 join(X, join(Y, meet(Z, X)))
% 54.57/7.40 = { by lemma 14 R->L }
% 54.57/7.40 join(X, join(X, join(Y, meet(Z, X))))
% 54.57/7.40 = { by axiom 3 (idempotence_of_meet) R->L }
% 54.57/7.40 join(X, meet(join(X, join(Y, meet(Z, X))), join(X, join(Y, meet(Z, X)))))
% 54.57/7.40 = { by lemma 18 }
% 54.57/7.40 join(X, meet(join(X, join(Y, meet(Z, X))), join(X, Y)))
% 54.57/7.40 = { by lemma 18 }
% 54.57/7.40 join(X, meet(join(X, Y), join(X, Y)))
% 54.57/7.40 = { by axiom 3 (idempotence_of_meet) }
% 54.57/7.40 join(X, join(X, Y))
% 54.57/7.40 = { by lemma 14 }
% 54.57/7.40 join(X, Y)
% 54.57/7.40
% 54.57/7.40 Lemma 20: meet(join(X, Y), join(X, meet(Y, Z))) = join(X, meet(Y, Z)).
% 54.57/7.40 Proof:
% 54.57/7.40 meet(join(X, Y), join(X, meet(Y, Z)))
% 54.57/7.40 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.40 meet(join(Y, X), join(X, meet(Y, Z)))
% 54.57/7.40 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.40 meet(join(X, meet(Y, Z)), join(Y, X))
% 54.57/7.40 = { by axiom 5 (absorption2) R->L }
% 54.57/7.40 meet(join(X, meet(Y, Z)), join(join(Y, meet(Y, Z)), X))
% 54.57/7.40 = { by axiom 6 (associativity_of_join) }
% 54.57/7.40 meet(join(X, meet(Y, Z)), join(Y, join(meet(Y, Z), X)))
% 54.57/7.40 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.40 meet(join(X, meet(Y, Z)), join(Y, join(X, meet(Y, Z))))
% 54.57/7.40 = { by lemma 10 }
% 54.57/7.40 join(X, meet(Y, Z))
% 54.57/7.40
% 54.57/7.40 Lemma 21: meet(join(X, Y), join(Y, meet(X, Z))) = join(Y, meet(X, Z)).
% 54.57/7.40 Proof:
% 54.57/7.40 meet(join(X, Y), join(Y, meet(X, Z)))
% 54.57/7.40 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.40 meet(join(Y, X), join(Y, meet(X, Z)))
% 54.57/7.40 = { by lemma 20 }
% 54.57/7.40 join(Y, meet(X, Z))
% 54.57/7.40
% 54.57/7.40 Lemma 22: join(meet(X, join(Y, meet(join(Z, Y), join(W, meet(Z, Y))))), meet(X, join(Y, W))) = meet(X, join(Y, W)).
% 54.57/7.40 Proof:
% 54.57/7.40 join(meet(X, join(Y, meet(join(Z, Y), join(W, meet(Z, Y))))), meet(X, join(Y, W)))
% 54.57/7.40 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, join(Y, meet(join(Z, Y), join(W, meet(Z, Y))))))
% 54.57/7.40 = { by lemma 10 R->L }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(W, join(Y, meet(join(Z, Y), join(W, meet(Z, Y))))))))
% 54.57/7.40 = { by lemma 15 }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, meet(join(Z, Y), join(W, meet(Z, Y))))))))
% 54.57/7.40 = { by axiom 5 (absorption2) R->L }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(join(Z, Y), join(W, meet(Z, Y))), meet(Z, Y))))))))
% 54.57/7.40 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), meet(join(Z, Y), join(W, meet(Z, Y))))))))))
% 54.57/7.40 = { by lemma 11 }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(join(Z, Y), meet(meet(Z, Y), join(W, meet(Z, Y))))))))))
% 54.57/7.40 = { by lemma 10 }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(join(Z, Y), meet(Z, Y))))))))
% 54.57/7.40 = { by axiom 4 (commutativity_of_meet) }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Z, Y))))))))
% 54.57/7.40 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, Z))))))))
% 54.57/7.40 = { by axiom 7 (absorption1) R->L }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(Z, join(Z, Y))))))))))
% 54.57/7.40 = { by axiom 5 (absorption2) R->L }
% 54.57/7.40 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), join(Z, Y))))))))))
% 54.57/7.41 = { by axiom 7 (absorption1) R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), meet(join(Z, Y), join(join(Z, Y), meet(join(Z, meet(Z, Y)), Z))))))))))))
% 54.57/7.41 = { by lemma 13 R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), meet(join(join(Z, Y), meet(Y, join(Z, Y))), join(join(Z, Y), meet(join(Z, meet(Z, Y)), Z))))))))))))
% 54.57/7.41 = { by lemma 10 }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), meet(join(join(Z, Y), Y), join(join(Z, Y), meet(join(Z, meet(Z, Y)), Z))))))))))))
% 54.57/7.41 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), meet(join(Y, join(Z, Y)), join(join(Z, Y), meet(join(Z, meet(Z, Y)), Z))))))))))))
% 54.57/7.41 = { by axiom 9 (equation_H49_dual) R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), join(join(Z, Y), meet(Y, Z)))))))))))
% 54.57/7.41 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), join(join(Z, Y), meet(Z, Y)))))))))))
% 54.57/7.41 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(Z, meet(Z, Y)), join(meet(Z, Y), join(Z, Y)))))))))))
% 54.57/7.41 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(meet(Z, Y), Z), join(meet(Z, Y), join(Z, Y)))))))))))
% 54.57/7.41 = { by lemma 16 }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, meet(join(meet(Z, Y), Z), join(Y, join(meet(Z, Y), Z)))))))))))
% 54.57/7.41 = { by lemma 10 }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(Y, join(meet(Z, Y), Z)))))))))
% 54.57/7.41 = { by lemma 16 R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(meet(Z, Y), join(meet(Z, Y), join(Z, Y)))))))))
% 54.57/7.41 = { by axiom 7 (absorption1) }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, join(meet(join(Z, Y), join(W, meet(Z, Y))), meet(Z, Y)))))))
% 54.57/7.41 = { by lemma 15 R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(meet(join(Z, Y), join(W, meet(Z, Y))), join(W, meet(Z, Y)))))))
% 54.57/7.41 = { by lemma 17 }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, join(W, meet(Z, Y))))))
% 54.57/7.41 = { by lemma 19 }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(X, meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), join(Y, W))))
% 54.57/7.41 = { by lemma 11 R->L }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(join(Y, meet(join(Z, Y), join(W, meet(Z, Y)))), meet(X, join(Y, W))))
% 54.57/7.41 = { by axiom 4 (commutativity_of_meet) }
% 54.57/7.41 join(meet(X, join(Y, W)), meet(meet(X, join(Y, W)), join(Y, meet(join(Z, Y), join(W, meet(Z, Y))))))
% 54.57/7.41 = { by axiom 5 (absorption2) }
% 54.57/7.41 meet(X, join(Y, W))
% 54.57/7.41
% 54.57/7.41 Lemma 23: join(meet(X, join(Y, Z)), meet(W, meet(X, join(Y, meet(join(V, Y), join(Z, meet(V, Y))))))) = meet(X, join(Y, Z)).
% 54.57/7.41 Proof:
% 54.57/7.41 join(meet(X, join(Y, Z)), meet(W, meet(X, join(Y, meet(join(V, Y), join(Z, meet(V, Y)))))))
% 54.57/7.41 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.41 join(meet(X, join(Y, Z)), meet(meet(X, join(Y, meet(join(V, Y), join(Z, meet(V, Y))))), W))
% 54.57/7.41 = { by lemma 21 R->L }
% 54.57/7.41 meet(join(meet(X, join(Y, meet(join(V, Y), join(Z, meet(V, Y))))), meet(X, join(Y, Z))), join(meet(X, join(Y, Z)), meet(meet(X, join(Y, meet(join(V, Y), join(Z, meet(V, Y))))), W)))
% 54.57/7.41 = { by lemma 22 }
% 54.57/7.41 meet(meet(X, join(Y, Z)), join(meet(X, join(Y, Z)), meet(meet(X, join(Y, meet(join(V, Y), join(Z, meet(V, Y))))), W)))
% 54.57/7.41 = { by axiom 7 (absorption1) }
% 54.57/7.41 meet(X, join(Y, Z))
% 54.57/7.41
% 54.57/7.41 Goal 1 (prove_H58): meet(a, join(b, c)) = meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))).
% 54.57/7.41 Proof:
% 54.57/7.41 meet(a, join(b, c))
% 54.57/7.41 = { by lemma 22 R->L }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, c)))
% 54.57/7.41 = { by lemma 10 R->L }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(meet(a, join(b, c)), join(b, meet(a, join(b, c)))))
% 54.57/7.41 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(join(b, meet(a, join(b, c))), meet(a, join(b, c))))
% 54.57/7.41 = { by lemma 12 }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, meet(join(b, c), join(b, meet(a, join(b, c))))))
% 54.57/7.41 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, meet(join(b, c), join(meet(a, join(b, c)), b))))
% 54.57/7.41 = { by axiom 7 (absorption1) R->L }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, meet(join(b, c), join(meet(a, join(b, c)), meet(b, join(b, c))))))
% 54.57/7.41 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, meet(join(b, c), join(meet(a, join(b, c)), meet(join(b, c), b)))))
% 54.57/7.41 = { by lemma 17 R->L }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, meet(join(meet(a, join(b, c)), join(b, c)), join(meet(a, join(b, c)), meet(join(b, c), b)))))
% 54.57/7.41 = { by lemma 20 }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(meet(a, join(b, c)), meet(join(b, c), b))))
% 54.57/7.41 = { by axiom 4 (commutativity_of_meet) }
% 54.57/7.41 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(meet(a, join(b, c)), meet(b, join(b, c)))))
% 54.57/7.41 = { by axiom 7 (absorption1) }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(meet(a, join(b, c)), b)))
% 54.57/7.42 = { by axiom 2 (commutativity_of_join) }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(a, join(b, c)))))
% 54.57/7.42 = { by axiom 7 (absorption1) R->L }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(b, c)), join(meet(a, join(b, c)), join(b, c))))))
% 54.57/7.42 = { by lemma 17 }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(b, c)), join(b, c)))))
% 54.57/7.42 = { by lemma 19 R->L }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(b, c)), join(b, join(c, meet(a, b)))))))
% 54.57/7.42 = { by lemma 23 R->L }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(b, join(c, meet(a, b)))))))
% 54.57/7.42 = { by axiom 2 (commutativity_of_join) R->L }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), b)))))
% 54.57/7.42 = { by axiom 3 (idempotence_of_meet) R->L }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(b, b))))))
% 54.57/7.42 = { by axiom 9 (equation_H49_dual) }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), meet(join(b, join(c, meet(a, b))), join(join(c, meet(a, b)), meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), b)))))))
% 54.57/7.42 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.57/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), meet(join(b, join(c, meet(a, b))), join(join(c, meet(a, b)), meet(b, join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))))))))))
% 54.84/7.42 = { by lemma 21 }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(b, join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b)))))))))))))
% 54.84/7.42 = { by axiom 2 (commutativity_of_join) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(b, join(meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b)))))), meet(a, join(b, c)))))))))
% 54.84/7.42 = { by lemma 21 R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(b, meet(join(a, meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b)))))), meet(a, join(b, c))))))))))
% 54.84/7.42 = { by axiom 5 (absorption2) }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(b, meet(a, join(meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b)))))), meet(a, join(b, c))))))))))
% 54.84/7.42 = { by axiom 2 (commutativity_of_join) }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(b, meet(a, join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))))))))))
% 54.84/7.42 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), a)))))))
% 54.84/7.42 = { by lemma 12 }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), meet(a, b)))))))
% 54.84/7.42 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(join(c, meet(a, b)), meet(meet(a, b), join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b)))))))))))))
% 54.84/7.42 = { by axiom 2 (commutativity_of_join) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(meet(meet(a, b), join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b)))))))), join(c, meet(a, b)))))))
% 54.84/7.42 = { by lemma 16 R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(c, join(meet(a, b), meet(meet(a, b), join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))))))))))
% 54.84/7.42 = { by axiom 5 (absorption2) }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(meet(a, join(b, c)), meet(a, meet(a, join(b, meet(join(X, b), join(c, meet(X, b))))))), join(c, meet(a, b))))))
% 54.84/7.42 = { by lemma 23 }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(b, c)), join(c, meet(a, b))))))
% 54.84/7.42 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(c, meet(a, b)), meet(a, join(b, c))))))
% 54.84/7.42 = { by lemma 11 }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(a, meet(join(c, meet(a, b)), join(b, c))))))
% 54.84/7.42 = { by axiom 8 (associativity_of_meet) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, c)))))
% 54.84/7.42 = { by lemma 19 R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, meet(a, b)))))))
% 54.84/7.42 = { by lemma 13 R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(join(c, meet(a, b)), meet(a, join(c, meet(a, b)))))))))
% 54.84/7.42 = { by axiom 2 (commutativity_of_join) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(meet(a, join(c, meet(a, b))), join(c, meet(a, b))))))))
% 54.84/7.42 = { by lemma 16 R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, join(meet(a, b), meet(a, join(c, meet(a, b))))))))))
% 54.84/7.42 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, join(meet(a, b), meet(join(c, meet(a, b)), a))))))))
% 54.84/7.42 = { by axiom 2 (commutativity_of_join) R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, join(meet(join(c, meet(a, b)), a), meet(a, b))))))))
% 54.84/7.42 = { by lemma 10 R->L }
% 54.84/7.42 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, join(meet(join(c, meet(a, b)), a), meet(meet(a, b), join(c, meet(a, b))))))))))
% 54.84/7.43 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, join(meet(join(c, meet(a, b)), a), meet(join(c, meet(a, b)), meet(a, b)))))))))
% 54.84/7.43 = { by lemma 12 R->L }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, join(meet(join(c, meet(a, b)), a), meet(b, meet(join(c, meet(a, b)), a)))))))))
% 54.84/7.43 = { by lemma 13 }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, meet(join(c, meet(a, b)), a)))))))
% 54.84/7.43 = { by axiom 4 (commutativity_of_meet) }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(b, join(c, meet(a, join(c, meet(a, b)))))))))
% 54.84/7.43 = { by lemma 16 }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(meet(a, join(c, meet(a, b))), join(b, c))))))
% 54.84/7.43 = { by axiom 2 (commutativity_of_join) }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(c, meet(a, b))), join(join(b, c), meet(a, join(c, meet(a, b))))))))
% 54.84/7.43 = { by lemma 10 }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(a, join(c, meet(a, b))))))
% 54.84/7.43 = { by axiom 7 (absorption1) R->L }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(a, join(a, b)), join(c, meet(a, b))))))
% 54.84/7.43 = { by axiom 8 (associativity_of_meet) }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(a, meet(join(a, b), join(c, meet(a, b)))))))
% 54.84/7.43 = { by axiom 4 (commutativity_of_meet) R->L }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(meet(join(a, b), join(c, meet(a, b))), a))))
% 54.84/7.43 = { by lemma 20 R->L }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, meet(join(b, meet(join(a, b), join(c, meet(a, b)))), join(b, meet(meet(join(a, b), join(c, meet(a, b))), a)))))
% 54.84/7.43 = { by axiom 4 (commutativity_of_meet) }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(a, meet(join(b, meet(join(a, b), join(c, meet(a, b)))), join(b, meet(a, meet(join(a, b), join(c, meet(a, b))))))))
% 54.84/7.43 = { by lemma 12 R->L }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(join(b, meet(a, meet(join(a, b), join(c, meet(a, b))))), meet(a, join(b, meet(join(a, b), join(c, meet(a, b)))))))
% 54.84/7.43 = { by axiom 4 (commutativity_of_meet) }
% 54.84/7.43 join(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), meet(meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))), join(b, meet(a, meet(join(a, b), join(c, meet(a, b)))))))
% 54.84/7.43 = { by axiom 5 (absorption2) }
% 54.84/7.43 meet(a, join(b, meet(join(a, b), join(c, meet(a, b)))))
% 54.84/7.43 % SZS output end Proof
% 54.84/7.43
% 54.84/7.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------