TSTP Solution File: MVA008-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MVA008-1 : 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 : n003.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 09:32:29 EDT 2023
% Result : Unsatisfiable 5.40s 1.13s
% Output : Proof 6.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : MVA008-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.18 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.39 % Computer : n003.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 05:32:10 EDT 2023
% 0.18/0.39 % CPUTime :
% 5.40/1.13 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 5.40/1.13
% 5.40/1.13 % SZS status Unsatisfiable
% 5.40/1.13
% 6.37/1.23 % SZS output start Proof
% 6.37/1.23 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 6.37/1.23 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 6.37/1.23 Axiom 3 (right_monoid_unit): op(X, unit) = X.
% 6.37/1.23 Axiom 4 (left_monoid_unit): op(unit, X) = X.
% 6.37/1.23 Axiom 5 (idempotence_of_meet): meet(X, X) = X.
% 6.37/1.23 Axiom 6 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 6.37/1.23 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 6.37/1.23 Axiom 8 (absorption_a): join(meet(X, Y), X) = X.
% 6.37/1.23 Axiom 9 (monoid_associativity): op(op(X, Y), Z) = op(X, op(Y, Z)).
% 6.37/1.23 Axiom 10 (absorption_b): meet(join(X, Y), X) = X.
% 6.37/1.23 Axiom 11 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 6.37/1.23 Axiom 12 (residual_a): join(op(X, meet(ld(X, Y), Z)), Y) = Y.
% 6.37/1.23 Axiom 13 (residual_c): meet(ld(X, join(op(X, Y), Z)), Y) = Y.
% 6.37/1.23 Axiom 14 (definition_of_at): at(X, Y) = op(op(X, ld(X, unit)), ld(ld(Y, unit), unit)).
% 6.37/1.23
% 6.37/1.23 Lemma 15: meet(X, ld(Y, join(op(Y, X), Z))) = X.
% 6.37/1.23 Proof:
% 6.37/1.23 meet(X, ld(Y, join(op(Y, X), Z)))
% 6.37/1.23 = { by axiom 6 (commutativity_of_meet) R->L }
% 6.37/1.23 meet(ld(Y, join(op(Y, X), Z)), X)
% 6.37/1.23 = { by axiom 13 (residual_c) }
% 6.37/1.23 X
% 6.37/1.23
% 6.37/1.23 Lemma 16: meet(X, ld(Y, op(Y, X))) = X.
% 6.37/1.23 Proof:
% 6.37/1.23 meet(X, ld(Y, op(Y, X)))
% 6.37/1.23 = { by axiom 1 (idempotence_of_join) R->L }
% 6.37/1.23 meet(X, ld(Y, join(op(Y, X), op(Y, X))))
% 6.37/1.23 = { by lemma 15 }
% 6.37/1.23 X
% 6.37/1.23
% 6.37/1.23 Lemma 17: meet(unit, ld(X, X)) = unit.
% 6.37/1.23 Proof:
% 6.37/1.23 meet(unit, ld(X, X))
% 6.37/1.23 = { by axiom 3 (right_monoid_unit) R->L }
% 6.37/1.23 meet(unit, ld(X, op(X, unit)))
% 6.37/1.23 = { by lemma 16 }
% 6.37/1.23 unit
% 6.37/1.23
% 6.37/1.23 Lemma 18: join(X, meet(Y, X)) = X.
% 6.37/1.23 Proof:
% 6.37/1.23 join(X, meet(Y, X))
% 6.37/1.23 = { by axiom 6 (commutativity_of_meet) R->L }
% 6.37/1.23 join(X, meet(X, Y))
% 6.37/1.23 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.23 join(meet(X, Y), X)
% 6.37/1.23 = { by axiom 8 (absorption_a) }
% 6.37/1.23 X
% 6.37/1.23
% 6.37/1.23 Lemma 19: join(unit, ld(X, X)) = ld(X, X).
% 6.37/1.23 Proof:
% 6.37/1.23 join(unit, ld(X, X))
% 6.37/1.23 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.23 join(ld(X, X), unit)
% 6.37/1.23 = { by lemma 17 R->L }
% 6.37/1.23 join(ld(X, X), meet(unit, ld(X, X)))
% 6.37/1.23 = { by lemma 18 }
% 6.37/1.23 ld(X, X)
% 6.37/1.23
% 6.37/1.23 Lemma 20: join(X, op(Y, meet(ld(Y, X), Z))) = X.
% 6.37/1.23 Proof:
% 6.37/1.23 join(X, op(Y, meet(ld(Y, X), Z)))
% 6.37/1.23 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.23 join(op(Y, meet(ld(Y, X), Z)), X)
% 6.37/1.23 = { by axiom 12 (residual_a) }
% 6.37/1.23 X
% 6.37/1.23
% 6.37/1.23 Lemma 21: join(X, op(Y, ld(Y, X))) = X.
% 6.37/1.23 Proof:
% 6.37/1.23 join(X, op(Y, ld(Y, X)))
% 6.37/1.23 = { by axiom 5 (idempotence_of_meet) R->L }
% 6.37/1.23 join(X, op(Y, meet(ld(Y, X), ld(Y, X))))
% 6.37/1.23 = { by lemma 20 }
% 6.37/1.23 X
% 6.37/1.23
% 6.37/1.23 Lemma 22: ld(unit, unit) = unit.
% 6.37/1.23 Proof:
% 6.37/1.23 ld(unit, unit)
% 6.37/1.23 = { by lemma 19 R->L }
% 6.37/1.23 join(unit, ld(unit, unit))
% 6.37/1.23 = { by axiom 4 (left_monoid_unit) R->L }
% 6.37/1.23 join(unit, op(unit, ld(unit, unit)))
% 6.37/1.23 = { by lemma 21 }
% 6.37/1.23 unit
% 6.37/1.23
% 6.37/1.23 Lemma 23: meet(X, join(Y, X)) = X.
% 6.37/1.23 Proof:
% 6.37/1.23 meet(X, join(Y, X))
% 6.37/1.23 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.23 meet(X, join(X, Y))
% 6.37/1.23 = { by axiom 6 (commutativity_of_meet) R->L }
% 6.37/1.23 meet(join(X, Y), X)
% 6.37/1.23 = { by axiom 10 (absorption_b) }
% 6.37/1.23 X
% 6.37/1.23
% 6.37/1.23 Lemma 24: op(X, op(ld(X, unit), ld(ld(Y, unit), unit))) = at(X, Y).
% 6.37/1.23 Proof:
% 6.37/1.23 op(X, op(ld(X, unit), ld(ld(Y, unit), unit)))
% 6.37/1.23 = { by axiom 9 (monoid_associativity) R->L }
% 6.37/1.23 op(op(X, ld(X, unit)), ld(ld(Y, unit), unit))
% 6.37/1.23 = { by axiom 14 (definition_of_at) R->L }
% 6.37/1.23 at(X, Y)
% 6.37/1.23
% 6.37/1.23 Lemma 25: op(X, ld(X, unit)) = at(X, unit).
% 6.37/1.23 Proof:
% 6.37/1.23 op(X, ld(X, unit))
% 6.37/1.23 = { by axiom 3 (right_monoid_unit) R->L }
% 6.37/1.23 op(X, op(ld(X, unit), unit))
% 6.37/1.23 = { by lemma 22 R->L }
% 6.37/1.23 op(X, op(ld(X, unit), ld(unit, unit)))
% 6.37/1.23 = { by lemma 22 R->L }
% 6.37/1.23 op(X, op(ld(X, unit), ld(ld(unit, unit), unit)))
% 6.37/1.23 = { by lemma 24 }
% 6.37/1.23 at(X, unit)
% 6.37/1.23
% 6.37/1.23 Lemma 26: join(unit, at(X, unit)) = unit.
% 6.37/1.23 Proof:
% 6.37/1.23 join(unit, at(X, unit))
% 6.37/1.23 = { by lemma 25 R->L }
% 6.37/1.23 join(unit, op(X, ld(X, unit)))
% 6.37/1.23 = { by lemma 21 }
% 6.37/1.23 unit
% 6.37/1.23
% 6.37/1.23 Lemma 27: meet(unit, ld(X, op(X, ld(Y, Y)))) = unit.
% 6.37/1.23 Proof:
% 6.37/1.23 meet(unit, ld(X, op(X, ld(Y, Y))))
% 6.37/1.23 = { by lemma 17 R->L }
% 6.37/1.23 meet(meet(unit, ld(Y, Y)), ld(X, op(X, ld(Y, Y))))
% 6.37/1.23 = { by axiom 11 (associativity_of_meet) }
% 6.37/1.23 meet(unit, meet(ld(Y, Y), ld(X, op(X, ld(Y, Y)))))
% 6.37/1.23 = { by lemma 16 }
% 6.37/1.23 meet(unit, ld(Y, Y))
% 6.37/1.23 = { by lemma 17 }
% 6.37/1.23 unit
% 6.37/1.23
% 6.37/1.23 Lemma 28: meet(X, op(Y, meet(Z, ld(Y, X)))) = op(Y, meet(Z, ld(Y, X))).
% 6.37/1.23 Proof:
% 6.37/1.23 meet(X, op(Y, meet(Z, ld(Y, X))))
% 6.37/1.23 = { by axiom 6 (commutativity_of_meet) R->L }
% 6.37/1.23 meet(X, op(Y, meet(ld(Y, X), Z)))
% 6.37/1.23 = { by axiom 6 (commutativity_of_meet) R->L }
% 6.37/1.23 meet(op(Y, meet(ld(Y, X), Z)), X)
% 6.37/1.23 = { by lemma 20 R->L }
% 6.37/1.23 meet(op(Y, meet(ld(Y, X), Z)), join(X, op(Y, meet(ld(Y, X), Z))))
% 6.37/1.23 = { by lemma 23 }
% 6.37/1.23 op(Y, meet(ld(Y, X), Z))
% 6.37/1.23 = { by axiom 6 (commutativity_of_meet) }
% 6.37/1.23 op(Y, meet(Z, ld(Y, X)))
% 6.37/1.24
% 6.37/1.24 Lemma 29: op(X, ld(X, X)) = X.
% 6.37/1.24 Proof:
% 6.37/1.24 op(X, ld(X, X))
% 6.37/1.24 = { by lemma 23 R->L }
% 6.37/1.24 meet(op(X, ld(X, X)), join(X, op(X, ld(X, X))))
% 6.37/1.24 = { by lemma 21 }
% 6.37/1.24 meet(op(X, ld(X, X)), X)
% 6.37/1.24 = { by axiom 3 (right_monoid_unit) R->L }
% 6.37/1.24 meet(op(X, ld(X, X)), op(X, unit))
% 6.37/1.24 = { by lemma 27 R->L }
% 6.37/1.24 meet(op(X, ld(X, X)), op(X, meet(unit, ld(X, op(X, ld(X, X))))))
% 6.37/1.24 = { by lemma 28 }
% 6.37/1.24 op(X, meet(unit, ld(X, op(X, ld(X, X)))))
% 6.37/1.24 = { by lemma 27 }
% 6.37/1.24 op(X, unit)
% 6.37/1.24 = { by axiom 3 (right_monoid_unit) }
% 6.37/1.24 X
% 6.37/1.24
% 6.37/1.24 Lemma 30: join(X, join(op(Y, ld(Y, X)), Z)) = join(Z, X).
% 6.37/1.24 Proof:
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), Z))
% 6.37/1.24 = { by axiom 7 (associativity_of_join) R->L }
% 6.37/1.24 join(join(X, op(Y, ld(Y, X))), Z)
% 6.37/1.24 = { by lemma 21 }
% 6.37/1.24 join(X, Z)
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) }
% 6.37/1.24 join(Z, X)
% 6.37/1.24
% 6.37/1.24 Lemma 31: join(X, ld(Y, join(Z, op(Y, X)))) = ld(Y, join(Z, op(Y, X))).
% 6.37/1.24 Proof:
% 6.37/1.24 join(X, ld(Y, join(Z, op(Y, X))))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 join(X, ld(Y, join(op(Y, X), Z)))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 join(ld(Y, join(op(Y, X), Z)), X)
% 6.37/1.24 = { by lemma 15 R->L }
% 6.37/1.24 join(ld(Y, join(op(Y, X), Z)), meet(X, ld(Y, join(op(Y, X), Z))))
% 6.37/1.24 = { by lemma 18 }
% 6.37/1.24 ld(Y, join(op(Y, X), Z))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) }
% 6.37/1.24 ld(Y, join(Z, op(Y, X)))
% 6.37/1.24
% 6.37/1.24 Lemma 32: join(unit, op(X, ld(X, at(Y, unit)))) = unit.
% 6.37/1.24 Proof:
% 6.37/1.24 join(unit, op(X, ld(X, at(Y, unit))))
% 6.37/1.24 = { by lemma 26 R->L }
% 6.37/1.24 join(join(unit, at(Y, unit)), op(X, ld(X, at(Y, unit))))
% 6.37/1.24 = { by axiom 7 (associativity_of_join) }
% 6.37/1.24 join(unit, join(at(Y, unit), op(X, ld(X, at(Y, unit)))))
% 6.37/1.24 = { by lemma 21 }
% 6.37/1.24 join(unit, at(Y, unit))
% 6.37/1.24 = { by lemma 26 }
% 6.37/1.24 unit
% 6.37/1.24
% 6.37/1.24 Lemma 33: join(ld(X, unit), ld(X, at(Y, unit))) = ld(X, unit).
% 6.37/1.24 Proof:
% 6.37/1.24 join(ld(X, unit), ld(X, at(Y, unit)))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 join(ld(X, at(Y, unit)), ld(X, unit))
% 6.37/1.24 = { by lemma 32 R->L }
% 6.37/1.24 join(ld(X, at(Y, unit)), ld(X, join(unit, op(X, ld(X, at(Y, unit))))))
% 6.37/1.24 = { by lemma 31 }
% 6.37/1.24 ld(X, join(unit, op(X, ld(X, at(Y, unit)))))
% 6.37/1.24 = { by lemma 32 }
% 6.37/1.24 ld(X, unit)
% 6.37/1.24
% 6.37/1.24 Lemma 34: join(X, op(op(Y, ld(Y, X)), at(Z, unit))) = X.
% 6.37/1.24 Proof:
% 6.37/1.24 join(X, op(op(Y, ld(Y, X)), at(Z, unit)))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 join(op(op(Y, ld(Y, X)), at(Z, unit)), X)
% 6.37/1.24 = { by lemma 30 R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), at(Z, unit))))
% 6.37/1.24 = { by lemma 23 R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))), at(Z, unit))))))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(at(Z, unit), ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))))))))
% 6.37/1.24 = { by lemma 25 R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(op(Z, ld(Z, unit)), ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))))))))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))), op(Z, ld(Z, unit)))))))
% 6.37/1.24 = { by lemma 19 R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(join(unit, ld(op(Y, ld(Y, X)), op(Y, ld(Y, X)))), op(Z, ld(Z, unit)))))))
% 6.37/1.24 = { by axiom 7 (associativity_of_join) }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(unit, join(ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))), op(Z, ld(Z, unit))))))))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(unit, join(op(Z, ld(Z, unit)), ld(op(Y, ld(Y, X)), op(Y, ld(Y, X)))))))))
% 6.37/1.24 = { by axiom 7 (associativity_of_join) R->L }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(join(unit, op(Z, ld(Z, unit))), ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))))))))
% 6.37/1.24 = { by lemma 21 }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), join(unit, ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))))))))
% 6.37/1.24 = { by lemma 19 }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(at(Z, unit), ld(op(Y, ld(Y, X)), op(Y, ld(Y, X)))))))
% 6.37/1.24 = { by axiom 6 (commutativity_of_meet) }
% 6.37/1.24 join(X, join(op(Y, ld(Y, X)), op(op(Y, ld(Y, X)), meet(ld(op(Y, ld(Y, X)), op(Y, ld(Y, X))), at(Z, unit)))))
% 6.37/1.24 = { by lemma 20 }
% 6.37/1.24 join(X, op(Y, ld(Y, X)))
% 6.37/1.24 = { by lemma 21 }
% 6.37/1.24 X
% 6.37/1.24
% 6.37/1.24 Lemma 35: meet(unit, ld(op(op(X, ld(X, unit)), at(Y, unit)), at(op(X, ld(X, unit)), unit))) = unit.
% 6.37/1.24 Proof:
% 6.37/1.24 meet(unit, ld(op(op(X, ld(X, unit)), at(Y, unit)), at(op(X, ld(X, unit)), unit)))
% 6.37/1.24 = { by lemma 23 R->L }
% 6.37/1.24 meet(unit, ld(op(op(X, ld(X, unit)), meet(at(Y, unit), join(ld(op(X, ld(X, unit)), unit), at(Y, unit)))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.24 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.24 meet(unit, ld(op(op(X, ld(X, unit)), meet(at(Y, unit), join(at(Y, unit), ld(op(X, ld(X, unit)), unit)))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.24 = { by lemma 34 R->L }
% 6.37/1.24 meet(unit, ld(op(op(X, ld(X, unit)), meet(at(Y, unit), join(at(Y, unit), ld(op(X, ld(X, unit)), join(unit, op(op(X, ld(X, unit)), at(Y, unit))))))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.24 = { by lemma 31 }
% 6.37/1.24 meet(unit, ld(op(op(X, ld(X, unit)), meet(at(Y, unit), ld(op(X, ld(X, unit)), join(unit, op(op(X, ld(X, unit)), at(Y, unit)))))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.24 = { by lemma 34 }
% 6.37/1.24 meet(unit, ld(op(op(X, ld(X, unit)), meet(at(Y, unit), ld(op(X, ld(X, unit)), unit))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.25 = { by axiom 6 (commutativity_of_meet) }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), unit), at(Y, unit))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.25 = { by lemma 33 R->L }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(join(ld(op(X, ld(X, unit)), unit), ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit))), at(Y, unit))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.25 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(join(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), ld(op(X, ld(X, unit)), unit)), at(Y, unit))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.25 = { by lemma 16 R->L }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(join(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), meet(ld(op(X, ld(X, unit)), unit), ld(op(X, ld(X, unit)), op(op(X, ld(X, unit)), ld(op(X, ld(X, unit)), unit))))), at(Y, unit))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.25 = { by lemma 25 }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(join(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), meet(ld(op(X, ld(X, unit)), unit), ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)))), at(Y, unit))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.25 = { by lemma 18 }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), at(Y, unit))), at(op(X, ld(X, unit)), unit)))
% 6.37/1.25 = { by lemma 20 R->L }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), at(Y, unit))), join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), at(Y, unit))))))
% 6.37/1.25 = { by axiom 2 (commutativity_of_join) R->L }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), at(Y, unit))), join(op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), at(Y, unit))), at(op(X, ld(X, unit)), unit))))
% 6.37/1.25 = { by axiom 3 (right_monoid_unit) R->L }
% 6.37/1.25 meet(unit, ld(op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), at(Y, unit))), join(op(op(op(X, ld(X, unit)), meet(ld(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)), at(Y, unit))), unit), at(op(X, ld(X, unit)), unit))))
% 6.37/1.25 = { by lemma 15 }
% 6.37/1.25 unit
% 6.37/1.25
% 6.37/1.25 Lemma 36: join(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)) = at(op(X, ld(X, unit)), unit).
% 6.37/1.25 Proof:
% 6.37/1.25 join(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit))
% 6.37/1.25 = { by axiom 2 (commutativity_of_join) R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(X, ld(X, unit)))
% 6.68/1.25 = { by lemma 25 }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), at(X, unit))
% 6.68/1.25 = { by lemma 24 R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(X, op(ld(X, unit), ld(ld(unit, unit), unit))))
% 6.68/1.25 = { by axiom 9 (monoid_associativity) R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), ld(ld(unit, unit), unit)))
% 6.68/1.25 = { by axiom 4 (left_monoid_unit) R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), op(unit, ld(ld(unit, unit), unit))))
% 6.68/1.25 = { by axiom 4 (left_monoid_unit) R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), op(unit, op(unit, ld(ld(unit, unit), unit)))))
% 6.68/1.25 = { by lemma 22 R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), op(unit, op(ld(unit, unit), ld(ld(unit, unit), unit)))))
% 6.68/1.25 = { by lemma 24 }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), at(unit, unit)))
% 6.68/1.25 = { by axiom 3 (right_monoid_unit) R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), op(at(unit, unit), unit)))
% 6.68/1.25 = { by lemma 35 R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), op(at(unit, unit), meet(unit, ld(op(op(X, ld(X, unit)), at(unit, unit)), at(op(X, ld(X, unit)), unit))))))
% 6.68/1.25 = { by axiom 9 (monoid_associativity) R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), op(op(op(X, ld(X, unit)), at(unit, unit)), meet(unit, ld(op(op(X, ld(X, unit)), at(unit, unit)), at(op(X, ld(X, unit)), unit)))))
% 6.68/1.25 = { by lemma 28 R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(op(op(X, ld(X, unit)), at(unit, unit)), meet(unit, ld(op(op(X, ld(X, unit)), at(unit, unit)), at(op(X, ld(X, unit)), unit))))))
% 6.68/1.25 = { by lemma 35 }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(op(op(X, ld(X, unit)), at(unit, unit)), unit)))
% 6.68/1.25 = { by axiom 9 (monoid_associativity) }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), op(at(unit, unit), unit))))
% 6.68/1.25 = { by axiom 3 (right_monoid_unit) }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), at(unit, unit))))
% 6.68/1.25 = { by lemma 25 R->L }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), op(unit, ld(unit, unit)))))
% 6.68/1.25 = { by axiom 4 (left_monoid_unit) }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), ld(unit, unit))))
% 6.68/1.25 = { by lemma 22 }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(op(X, ld(X, unit)), unit)))
% 6.68/1.25 = { by axiom 3 (right_monoid_unit) }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(at(op(X, ld(X, unit)), unit), op(X, ld(X, unit))))
% 6.68/1.25 = { by axiom 6 (commutativity_of_meet) }
% 6.68/1.25 join(at(op(X, ld(X, unit)), unit), meet(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)))
% 6.68/1.25 = { by lemma 18 }
% 6.68/1.25 at(op(X, ld(X, unit)), unit)
% 6.68/1.25
% 6.68/1.25 Lemma 37: ld(X, at(op(X, ld(X, unit)), unit)) = ld(X, unit).
% 6.68/1.25 Proof:
% 6.68/1.25 ld(X, at(op(X, ld(X, unit)), unit))
% 6.68/1.25 = { by lemma 36 R->L }
% 6.68/1.25 ld(X, join(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit)))
% 6.68/1.25 = { by axiom 2 (commutativity_of_join) R->L }
% 6.68/1.25 ld(X, join(at(op(X, ld(X, unit)), unit), op(X, ld(X, unit))))
% 6.68/1.25 = { by lemma 31 R->L }
% 6.68/1.25 join(ld(X, unit), ld(X, join(at(op(X, ld(X, unit)), unit), op(X, ld(X, unit)))))
% 6.68/1.25 = { by axiom 2 (commutativity_of_join) }
% 6.68/1.25 join(ld(X, unit), ld(X, join(op(X, ld(X, unit)), at(op(X, ld(X, unit)), unit))))
% 6.68/1.25 = { by lemma 36 }
% 6.68/1.25 join(ld(X, unit), ld(X, at(op(X, ld(X, unit)), unit)))
% 6.68/1.25 = { by lemma 33 }
% 6.68/1.26 ld(X, unit)
% 6.68/1.26
% 6.68/1.26 Lemma 38: join(X, op(Y, ld(Y, op(Z, ld(Z, X))))) = X.
% 6.68/1.26 Proof:
% 6.68/1.26 join(X, op(Y, ld(Y, op(Z, ld(Z, X)))))
% 6.68/1.26 = { by axiom 2 (commutativity_of_join) R->L }
% 6.68/1.26 join(op(Y, ld(Y, op(Z, ld(Z, X)))), X)
% 6.68/1.26 = { by lemma 30 R->L }
% 6.68/1.26 join(X, join(op(Z, ld(Z, X)), op(Y, ld(Y, op(Z, ld(Z, X))))))
% 6.68/1.26 = { by lemma 21 }
% 6.68/1.26 join(X, op(Z, ld(Z, X)))
% 6.68/1.26 = { by lemma 21 }
% 6.68/1.26 X
% 6.68/1.26
% 6.68/1.26 Lemma 39: join(ld(X, Y), ld(X, op(Z, ld(Z, Y)))) = ld(X, Y).
% 6.68/1.26 Proof:
% 6.68/1.26 join(ld(X, Y), ld(X, op(Z, ld(Z, Y))))
% 6.68/1.26 = { by axiom 2 (commutativity_of_join) R->L }
% 6.68/1.26 join(ld(X, op(Z, ld(Z, Y))), ld(X, Y))
% 6.68/1.26 = { by lemma 38 R->L }
% 6.68/1.26 join(ld(X, op(Z, ld(Z, Y))), ld(X, join(Y, op(X, ld(X, op(Z, ld(Z, Y)))))))
% 6.68/1.26 = { by lemma 31 }
% 6.68/1.26 ld(X, join(Y, op(X, ld(X, op(Z, ld(Z, Y))))))
% 6.68/1.26 = { by lemma 38 }
% 6.68/1.26 ld(X, Y)
% 6.68/1.26
% 6.68/1.26 Lemma 40: join(op(X, Y), ld(Z, op(op(Z, X), Y))) = ld(Z, op(op(Z, X), Y)).
% 6.68/1.26 Proof:
% 6.68/1.26 join(op(X, Y), ld(Z, op(op(Z, X), Y)))
% 6.68/1.26 = { by axiom 2 (commutativity_of_join) R->L }
% 6.68/1.26 join(ld(Z, op(op(Z, X), Y)), op(X, Y))
% 6.68/1.26 = { by lemma 16 R->L }
% 6.68/1.26 join(ld(Z, op(op(Z, X), Y)), meet(op(X, Y), ld(Z, op(Z, op(X, Y)))))
% 6.68/1.26 = { by axiom 9 (monoid_associativity) R->L }
% 6.68/1.26 join(ld(Z, op(op(Z, X), Y)), meet(op(X, Y), ld(Z, op(op(Z, X), Y))))
% 6.68/1.26 = { by lemma 18 }
% 6.68/1.26 ld(Z, op(op(Z, X), Y))
% 6.68/1.26
% 6.68/1.26 Lemma 41: ld(op(X, ld(X, Y)), op(X, ld(X, Y))) = ld(ld(X, Y), ld(X, Y)).
% 6.68/1.26 Proof:
% 6.68/1.26 ld(op(X, ld(X, Y)), op(X, ld(X, Y)))
% 6.68/1.26 = { by lemma 15 R->L }
% 6.68/1.26 meet(ld(op(X, ld(X, Y)), op(X, ld(X, Y))), ld(ld(X, Y), join(op(ld(X, Y), ld(op(X, ld(X, Y)), op(X, ld(X, Y)))), ld(X, op(op(X, ld(X, Y)), ld(op(X, ld(X, Y)), op(X, ld(X, Y))))))))
% 6.68/1.26 = { by lemma 40 }
% 6.68/1.26 meet(ld(op(X, ld(X, Y)), op(X, ld(X, Y))), ld(ld(X, Y), ld(X, op(op(X, ld(X, Y)), ld(op(X, ld(X, Y)), op(X, ld(X, Y)))))))
% 6.68/1.26 = { by lemma 29 }
% 6.68/1.26 meet(ld(op(X, ld(X, Y)), op(X, ld(X, Y))), ld(ld(X, Y), ld(X, op(X, ld(X, Y)))))
% 6.68/1.26 = { by lemma 18 R->L }
% 6.68/1.26 meet(ld(op(X, ld(X, Y)), op(X, ld(X, Y))), ld(ld(X, Y), join(ld(X, op(X, ld(X, Y))), meet(ld(X, Y), ld(X, op(X, ld(X, Y)))))))
% 6.68/1.26 = { by lemma 16 }
% 6.68/1.26 meet(ld(op(X, ld(X, Y)), op(X, ld(X, Y))), ld(ld(X, Y), join(ld(X, op(X, ld(X, Y))), ld(X, Y))))
% 6.68/1.26 = { by axiom 2 (commutativity_of_join) }
% 6.68/1.26 meet(ld(op(X, ld(X, Y)), op(X, ld(X, Y))), ld(ld(X, Y), join(ld(X, Y), ld(X, op(X, ld(X, Y))))))
% 6.68/1.26 = { by lemma 39 }
% 6.68/1.26 meet(ld(op(X, ld(X, Y)), op(X, ld(X, Y))), ld(ld(X, Y), ld(X, Y)))
% 6.68/1.26 = { by axiom 6 (commutativity_of_meet) R->L }
% 6.68/1.26 meet(ld(ld(X, Y), ld(X, Y)), ld(op(X, ld(X, Y)), op(X, ld(X, Y))))
% 6.68/1.26 = { by lemma 29 R->L }
% 6.68/1.26 meet(ld(ld(X, Y), ld(X, Y)), ld(op(X, ld(X, Y)), op(X, op(ld(X, Y), ld(ld(X, Y), ld(X, Y))))))
% 6.68/1.26 = { by axiom 9 (monoid_associativity) R->L }
% 6.68/1.26 meet(ld(ld(X, Y), ld(X, Y)), ld(op(X, ld(X, Y)), op(op(X, ld(X, Y)), ld(ld(X, Y), ld(X, Y)))))
% 6.68/1.26 = { by lemma 16 }
% 6.68/1.26 ld(ld(X, Y), ld(X, Y))
% 6.68/1.26
% 6.68/1.26 Lemma 42: join(ld(X, unit), op(ld(X, unit), ld(op(X, ld(X, unit)), unit))) = ld(X, unit).
% 6.68/1.26 Proof:
% 6.68/1.26 join(ld(X, unit), op(ld(X, unit), ld(op(X, ld(X, unit)), unit)))
% 6.68/1.26 = { by lemma 37 R->L }
% 6.68/1.26 join(ld(X, at(op(X, ld(X, unit)), unit)), op(ld(X, unit), ld(op(X, ld(X, unit)), unit)))
% 6.68/1.26 = { by axiom 2 (commutativity_of_join) R->L }
% 6.68/1.26 join(op(ld(X, unit), ld(op(X, ld(X, unit)), unit)), ld(X, at(op(X, ld(X, unit)), unit)))
% 6.68/1.26 = { by lemma 25 R->L }
% 6.68/1.26 join(op(ld(X, unit), ld(op(X, ld(X, unit)), unit)), ld(X, op(op(X, ld(X, unit)), ld(op(X, ld(X, unit)), unit))))
% 6.68/1.26 = { by lemma 40 }
% 6.68/1.26 ld(X, op(op(X, ld(X, unit)), ld(op(X, ld(X, unit)), unit)))
% 6.68/1.26 = { by lemma 25 }
% 6.68/1.26 ld(X, at(op(X, ld(X, unit)), unit))
% 6.68/1.26 = { by lemma 37 }
% 6.68/1.26 ld(X, unit)
% 6.68/1.26
% 6.68/1.26 Goal 1 (goal): at(op(x, ld(x, unit)), unit) = op(x, ld(x, unit)).
% 6.68/1.26 Proof:
% 6.68/1.26 at(op(x, ld(x, unit)), unit)
% 6.68/1.26 = { by lemma 36 R->L }
% 6.68/1.26 join(op(x, ld(x, unit)), at(op(x, ld(x, unit)), unit))
% 6.68/1.26 = { by lemma 25 R->L }
% 6.68/1.26 join(op(x, ld(x, unit)), op(op(x, ld(x, unit)), ld(op(x, ld(x, unit)), unit)))
% 6.68/1.26 = { by lemma 39 R->L }
% 6.68/1.26 join(op(x, ld(x, unit)), op(op(x, ld(x, unit)), join(ld(op(x, ld(x, unit)), unit), ld(op(x, ld(x, unit)), op(x, ld(x, unit))))))
% 6.68/1.26 = { by lemma 41 }
% 6.68/1.26 join(op(x, ld(x, unit)), op(op(x, ld(x, unit)), join(ld(op(x, ld(x, unit)), unit), ld(ld(x, unit), ld(x, unit)))))
% 6.68/1.26 = { by lemma 42 R->L }
% 6.68/1.26 join(op(x, ld(x, unit)), op(op(x, ld(x, unit)), join(ld(op(x, ld(x, unit)), unit), ld(ld(x, unit), join(ld(x, unit), op(ld(x, unit), ld(op(x, ld(x, unit)), unit)))))))
% 6.68/1.26 = { by lemma 31 }
% 6.68/1.26 join(op(x, ld(x, unit)), op(op(x, ld(x, unit)), ld(ld(x, unit), join(ld(x, unit), op(ld(x, unit), ld(op(x, ld(x, unit)), unit))))))
% 6.68/1.26 = { by lemma 42 }
% 6.68/1.26 join(op(x, ld(x, unit)), op(op(x, ld(x, unit)), ld(ld(x, unit), ld(x, unit))))
% 6.68/1.26 = { by lemma 41 R->L }
% 6.68/1.26 join(op(x, ld(x, unit)), op(op(x, ld(x, unit)), ld(op(x, ld(x, unit)), op(x, ld(x, unit)))))
% 6.68/1.26 = { by lemma 21 }
% 6.68/1.26 op(x, ld(x, unit))
% 6.68/1.26 % SZS output end Proof
% 6.68/1.26
% 6.68/1.26 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------