TSTP Solution File: MVA011-1 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : MVA011-1 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n029.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 : Mon Jun 24 12:00:32 EDT 2024
% Result : Unsatisfiable 62.02s 8.22s
% Output : Proof 62.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MVA011-1 : TPTP v8.2.0. Released v8.1.0.
% 0.03/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Jun 18 16:39:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 62.02/8.21 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 62.02/8.21
% 62.02/8.22 % SZS status Unsatisfiable
% 62.02/8.22
% 62.84/8.28 % SZS output start Proof
% 62.84/8.28 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 62.84/8.28 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 62.84/8.28 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 62.84/8.28 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 62.84/8.28 Axiom 5 (right_monoid_unit): op(X, unit) = X.
% 62.84/8.28 Axiom 6 (left_monoid_unit): op(unit, X) = X.
% 62.84/8.28 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 62.84/8.28 Axiom 8 (absorption_a): join(meet(X, Y), X) = X.
% 62.84/8.28 Axiom 9 (absorption_b): meet(join(X, Y), X) = X.
% 62.84/8.28 Axiom 10 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 62.84/8.28 Axiom 11 (monoid_associativity): op(op(X, Y), Z) = op(X, op(Y, Z)).
% 62.84/8.28 Axiom 12 (generalized_mv_algebra_b): join(X, Y) = ld(rd(X, join(X, Y)), X).
% 62.84/8.28 Axiom 13 (residual_a): join(op(X, meet(ld(X, Y), Z)), Y) = Y.
% 62.84/8.28 Axiom 14 (residual_b): join(op(meet(X, rd(Y, Z)), Z), Y) = Y.
% 62.84/8.28 Axiom 15 (residual_c): meet(ld(X, join(op(X, Y), Z)), Y) = Y.
% 62.84/8.28 Axiom 16 (residual_d): meet(rd(join(op(X, Y), Z), Y), X) = X.
% 62.84/8.28 Axiom 17 (definition_of_at): at(X, Y) = op(op(X, ld(X, unit)), ld(ld(Y, unit), unit)).
% 62.84/8.28
% 62.84/8.28 Lemma 18: meet(X, ld(Y, join(op(Y, X), Z))) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, ld(Y, join(op(Y, X), Z)))
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.28 meet(ld(Y, join(op(Y, X), Z)), X)
% 62.84/8.28 = { by axiom 15 (residual_c) }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 19: meet(X, ld(Y, op(Y, X))) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, ld(Y, op(Y, X)))
% 62.84/8.28 = { by axiom 1 (idempotence_of_join) R->L }
% 62.84/8.28 meet(X, ld(Y, join(op(Y, X), op(Y, X))))
% 62.84/8.28 = { by lemma 18 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 20: join(X, op(Y, meet(ld(Y, X), Z))) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 join(X, op(Y, meet(ld(Y, X), Z)))
% 62.84/8.28 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.28 join(op(Y, meet(ld(Y, X), Z)), X)
% 62.84/8.28 = { by axiom 13 (residual_a) }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 21: join(X, op(Y, ld(Y, X))) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 join(X, op(Y, ld(Y, X)))
% 62.84/8.28 = { by axiom 3 (idempotence_of_meet) R->L }
% 62.84/8.28 join(X, op(Y, meet(ld(Y, X), ld(Y, X))))
% 62.84/8.28 = { by lemma 20 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 22: meet(X, join(X, Y)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, join(X, Y))
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.28 meet(join(X, Y), X)
% 62.84/8.28 = { by axiom 9 (absorption_b) }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 23: meet(X, join(Y, X)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, join(Y, X))
% 62.84/8.28 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.28 meet(X, join(X, Y))
% 62.84/8.28 = { by lemma 22 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 24: meet(X, op(Y, ld(Y, X))) = op(Y, ld(Y, X)).
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, op(Y, ld(Y, X)))
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.28 meet(op(Y, ld(Y, X)), X)
% 62.84/8.28 = { by lemma 21 R->L }
% 62.84/8.28 meet(op(Y, ld(Y, X)), join(X, op(Y, ld(Y, X))))
% 62.84/8.28 = { by lemma 23 }
% 62.84/8.28 op(Y, ld(Y, X))
% 62.84/8.28
% 62.84/8.28 Lemma 25: join(X, op(meet(Y, rd(X, Z)), Z)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 join(X, op(meet(Y, rd(X, Z)), Z))
% 62.84/8.28 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.28 join(op(meet(Y, rd(X, Z)), Z), X)
% 62.84/8.28 = { by axiom 14 (residual_b) }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 26: join(X, op(rd(X, Y), Y)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 join(X, op(rd(X, Y), Y))
% 62.84/8.28 = { by axiom 3 (idempotence_of_meet) R->L }
% 62.84/8.28 join(X, op(meet(rd(X, Y), rd(X, Y)), Y))
% 62.84/8.28 = { by lemma 25 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 27: meet(X, rd(join(op(X, Y), Z), Y)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, rd(join(op(X, Y), Z), Y))
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.28 meet(rd(join(op(X, Y), Z), Y), X)
% 62.84/8.28 = { by axiom 16 (residual_d) }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 28: meet(X, rd(op(X, Y), Y)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, rd(op(X, Y), Y))
% 62.84/8.28 = { by axiom 1 (idempotence_of_join) R->L }
% 62.84/8.28 meet(X, rd(join(op(X, Y), op(X, Y)), Y))
% 62.84/8.28 = { by lemma 27 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 29: rd(X, unit) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 rd(X, unit)
% 62.84/8.28 = { by lemma 23 R->L }
% 62.84/8.28 meet(rd(X, unit), join(X, rd(X, unit)))
% 62.84/8.28 = { by axiom 5 (right_monoid_unit) R->L }
% 62.84/8.28 meet(rd(X, unit), join(X, op(rd(X, unit), unit)))
% 62.84/8.28 = { by lemma 26 }
% 62.84/8.28 meet(rd(X, unit), X)
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) }
% 62.84/8.28 meet(X, rd(X, unit))
% 62.84/8.28 = { by axiom 5 (right_monoid_unit) R->L }
% 62.84/8.28 meet(X, rd(op(X, unit), unit))
% 62.84/8.28 = { by lemma 28 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 30: join(X, meet(X, Y)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 join(X, meet(X, Y))
% 62.84/8.28 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.28 join(meet(X, Y), X)
% 62.84/8.28 = { by axiom 8 (absorption_a) }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 31: join(X, meet(Y, X)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 join(X, meet(Y, X))
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.28 join(X, meet(X, Y))
% 62.84/8.28 = { by lemma 30 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 32: meet(unit, ld(X, X)) = unit.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(unit, ld(X, X))
% 62.84/8.28 = { by axiom 5 (right_monoid_unit) R->L }
% 62.84/8.28 meet(unit, ld(X, op(X, unit)))
% 62.84/8.28 = { by lemma 19 }
% 62.84/8.28 unit
% 62.84/8.28
% 62.84/8.28 Lemma 33: meet(X, meet(join(X, Y), Z)) = meet(X, Z).
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, meet(join(X, Y), Z))
% 62.84/8.28 = { by axiom 10 (associativity_of_meet) R->L }
% 62.84/8.28 meet(meet(X, join(X, Y)), Z)
% 62.84/8.28 = { by lemma 22 }
% 62.84/8.28 meet(X, Z)
% 62.84/8.28
% 62.84/8.28 Lemma 34: meet(X, rd(join(Y, op(X, Z)), Z)) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, rd(join(Y, op(X, Z)), Z))
% 62.84/8.28 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.28 meet(X, rd(join(op(X, Z), Y), Z))
% 62.84/8.28 = { by lemma 27 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 35: meet(X, rd(Y, meet(Z, ld(X, Y)))) = X.
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, rd(Y, meet(Z, ld(X, Y))))
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.28 meet(X, rd(Y, meet(ld(X, Y), Z)))
% 62.84/8.28 = { by lemma 20 R->L }
% 62.84/8.28 meet(X, rd(join(Y, op(X, meet(ld(X, Y), Z))), meet(ld(X, Y), Z)))
% 62.84/8.28 = { by lemma 34 }
% 62.84/8.28 X
% 62.84/8.28
% 62.84/8.28 Lemma 36: meet(X, op(rd(X, Y), Y)) = op(rd(X, Y), Y).
% 62.84/8.28 Proof:
% 62.84/8.28 meet(X, op(rd(X, Y), Y))
% 62.84/8.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.28 meet(op(rd(X, Y), Y), X)
% 62.84/8.28 = { by lemma 26 R->L }
% 62.84/8.29 meet(op(rd(X, Y), Y), join(X, op(rd(X, Y), Y)))
% 62.84/8.29 = { by lemma 23 }
% 62.84/8.29 op(rd(X, Y), Y)
% 62.84/8.29
% 62.84/8.29 Lemma 37: ld(X, X) = unit.
% 62.84/8.29 Proof:
% 62.84/8.29 ld(X, X)
% 62.84/8.29 = { by lemma 19 R->L }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(op(rd(unit, X), X), ld(X, X))))
% 62.84/8.29 = { by axiom 11 (monoid_associativity) }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), op(X, ld(X, X)))))
% 62.84/8.29 = { by lemma 24 R->L }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, op(X, ld(X, X))))))
% 62.84/8.29 = { by lemma 29 R->L }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, rd(op(X, ld(X, X)), unit)))))
% 62.84/8.29 = { by lemma 31 R->L }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, rd(op(X, join(ld(X, X), meet(unit, ld(X, X)))), unit)))))
% 62.84/8.29 = { by lemma 32 }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, rd(op(X, join(ld(X, X), unit)), unit)))))
% 62.84/8.29 = { by axiom 2 (commutativity_of_join) }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, rd(op(X, join(unit, ld(X, X))), unit)))))
% 62.84/8.29 = { by lemma 22 R->L }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, rd(op(X, join(unit, ld(X, X))), meet(unit, join(unit, ld(X, X))))))))
% 62.84/8.29 = { by lemma 19 R->L }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, rd(op(X, join(unit, ld(X, X))), meet(unit, meet(join(unit, ld(X, X)), ld(X, op(X, join(unit, ld(X, X)))))))))))
% 62.84/8.29 = { by lemma 33 }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), meet(X, rd(op(X, join(unit, ld(X, X))), meet(unit, ld(X, op(X, join(unit, ld(X, X))))))))))
% 62.84/8.29 = { by lemma 35 }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), op(rd(unit, X), X)))
% 62.84/8.29 = { by lemma 36 R->L }
% 62.84/8.29 meet(ld(X, X), ld(op(rd(unit, X), X), meet(unit, op(rd(unit, X), X))))
% 62.84/8.29 = { by lemma 36 R->L }
% 62.84/8.29 meet(ld(X, X), ld(meet(unit, op(rd(unit, X), X)), meet(unit, op(rd(unit, X), X))))
% 62.84/8.29 = { by lemma 29 R->L }
% 62.84/8.29 meet(ld(X, X), ld(rd(meet(unit, op(rd(unit, X), X)), unit), meet(unit, op(rd(unit, X), X))))
% 62.84/8.29 = { by lemma 30 R->L }
% 62.84/8.29 meet(ld(X, X), ld(rd(meet(unit, op(rd(unit, X), X)), join(unit, meet(unit, op(rd(unit, X), X)))), meet(unit, op(rd(unit, X), X))))
% 62.84/8.29 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.29 meet(ld(X, X), ld(rd(meet(unit, op(rd(unit, X), X)), join(meet(unit, op(rd(unit, X), X)), unit)), meet(unit, op(rd(unit, X), X))))
% 62.84/8.29 = { by axiom 12 (generalized_mv_algebra_b) R->L }
% 62.84/8.29 meet(ld(X, X), join(meet(unit, op(rd(unit, X), X)), unit))
% 62.84/8.29 = { by axiom 2 (commutativity_of_join) }
% 62.84/8.29 meet(ld(X, X), join(unit, meet(unit, op(rd(unit, X), X))))
% 62.84/8.29 = { by lemma 30 }
% 62.84/8.29 meet(ld(X, X), unit)
% 62.84/8.29 = { by axiom 4 (commutativity_of_meet) }
% 62.84/8.29 meet(unit, ld(X, X))
% 62.84/8.29 = { by lemma 32 }
% 62.84/8.29 unit
% 62.84/8.29
% 62.84/8.29 Lemma 38: ld(ld(X, unit), unit) = at(unit, X).
% 62.84/8.29 Proof:
% 62.84/8.29 ld(ld(X, unit), unit)
% 62.84/8.29 = { by axiom 6 (left_monoid_unit) R->L }
% 62.84/8.29 op(unit, ld(ld(X, unit), unit))
% 62.84/8.29 = { by axiom 6 (left_monoid_unit) R->L }
% 62.84/8.29 op(unit, op(unit, ld(ld(X, unit), unit)))
% 62.84/8.29 = { by lemma 19 R->L }
% 62.84/8.29 op(unit, op(meet(unit, ld(unit, op(unit, unit))), ld(ld(X, unit), unit)))
% 62.84/8.29 = { by axiom 6 (left_monoid_unit) }
% 62.84/8.29 op(unit, op(meet(unit, ld(unit, unit)), ld(ld(X, unit), unit)))
% 62.84/8.29 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.29 op(unit, op(meet(ld(unit, unit), unit), ld(ld(X, unit), unit)))
% 62.84/8.29 = { by lemma 21 R->L }
% 62.84/8.29 op(unit, op(meet(ld(unit, unit), join(unit, op(unit, ld(unit, unit)))), ld(ld(X, unit), unit)))
% 62.84/8.29 = { by axiom 6 (left_monoid_unit) }
% 62.84/8.29 op(unit, op(meet(ld(unit, unit), join(unit, ld(unit, unit))), ld(ld(X, unit), unit)))
% 62.84/8.29 = { by lemma 23 }
% 62.84/8.29 op(unit, op(ld(unit, unit), ld(ld(X, unit), unit)))
% 62.84/8.29 = { by axiom 11 (monoid_associativity) R->L }
% 62.84/8.29 op(op(unit, ld(unit, unit)), ld(ld(X, unit), unit))
% 62.84/8.29 = { by axiom 17 (definition_of_at) R->L }
% 62.84/8.29 at(unit, X)
% 62.84/8.29
% 62.84/8.29 Lemma 39: meet(X, rd(Y, ld(X, Y))) = X.
% 62.84/8.29 Proof:
% 62.84/8.29 meet(X, rd(Y, ld(X, Y)))
% 62.84/8.29 = { by lemma 21 R->L }
% 62.84/8.29 meet(X, rd(join(Y, op(X, ld(X, Y))), ld(X, Y)))
% 62.84/8.29 = { by lemma 34 }
% 62.84/8.29 X
% 62.84/8.29
% 62.84/8.29 Lemma 40: meet(unit, rd(X, X)) = unit.
% 62.84/8.29 Proof:
% 62.84/8.29 meet(unit, rd(X, X))
% 62.84/8.29 = { by axiom 6 (left_monoid_unit) R->L }
% 62.84/8.29 meet(unit, rd(op(unit, X), X))
% 62.84/8.29 = { by lemma 28 }
% 62.84/8.29 unit
% 62.84/8.29
% 62.84/8.29 Lemma 41: join(X, op(rd(unit, Y), op(Y, X))) = X.
% 62.84/8.29 Proof:
% 62.84/8.29 join(X, op(rd(unit, Y), op(Y, X)))
% 62.84/8.29 = { by axiom 11 (monoid_associativity) R->L }
% 62.84/8.29 join(X, op(op(rd(unit, Y), Y), X))
% 62.84/8.29 = { by lemma 23 R->L }
% 62.84/8.29 join(X, op(meet(op(rd(unit, Y), Y), join(join(rd(X, X), unit), op(rd(unit, Y), Y))), X))
% 62.84/8.29 = { by axiom 7 (associativity_of_join) }
% 62.84/8.29 join(X, op(meet(op(rd(unit, Y), Y), join(rd(X, X), join(unit, op(rd(unit, Y), Y)))), X))
% 62.84/8.29 = { by lemma 26 }
% 62.84/8.29 join(X, op(meet(op(rd(unit, Y), Y), join(rd(X, X), unit)), X))
% 62.84/8.29 = { by axiom 4 (commutativity_of_meet) }
% 62.84/8.29 join(X, op(meet(join(rd(X, X), unit), op(rd(unit, Y), Y)), X))
% 62.84/8.29 = { by lemma 40 R->L }
% 62.84/8.29 join(X, op(meet(join(rd(X, X), meet(unit, rd(X, X))), op(rd(unit, Y), Y)), X))
% 62.84/8.29 = { by lemma 31 }
% 62.84/8.29 join(X, op(meet(rd(X, X), op(rd(unit, Y), Y)), X))
% 62.84/8.29 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.29 join(X, op(meet(op(rd(unit, Y), Y), rd(X, X)), X))
% 62.84/8.29 = { by lemma 25 }
% 62.84/8.29 X
% 62.84/8.29
% 62.84/8.29 Lemma 42: meet(ld(X, unit), rd(unit, X)) = rd(unit, X).
% 62.84/8.29 Proof:
% 62.84/8.29 meet(ld(X, unit), rd(unit, X))
% 62.84/8.29 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.29 meet(rd(unit, X), ld(X, unit))
% 62.84/8.29 = { by lemma 37 R->L }
% 62.84/8.29 meet(rd(unit, X), ld(X, ld(rd(unit, X), rd(unit, X))))
% 62.84/8.29 = { by lemma 41 R->L }
% 62.84/8.29 meet(rd(unit, X), ld(X, ld(rd(unit, X), join(rd(unit, X), op(rd(unit, X), op(X, rd(unit, X)))))))
% 62.84/8.29 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.29 meet(rd(unit, X), ld(X, ld(rd(unit, X), join(op(rd(unit, X), op(X, rd(unit, X))), rd(unit, X)))))
% 62.84/8.29 = { by lemma 31 R->L }
% 62.84/8.29 meet(rd(unit, X), ld(X, join(ld(rd(unit, X), join(op(rd(unit, X), op(X, rd(unit, X))), rd(unit, X))), meet(op(X, rd(unit, X)), ld(rd(unit, X), join(op(rd(unit, X), op(X, rd(unit, X))), rd(unit, X)))))))
% 62.84/8.29 = { by lemma 18 }
% 62.84/8.29 meet(rd(unit, X), ld(X, join(ld(rd(unit, X), join(op(rd(unit, X), op(X, rd(unit, X))), rd(unit, X))), op(X, rd(unit, X)))))
% 62.84/8.29 = { by axiom 2 (commutativity_of_join) }
% 62.84/8.29 meet(rd(unit, X), ld(X, join(op(X, rd(unit, X)), ld(rd(unit, X), join(op(rd(unit, X), op(X, rd(unit, X))), rd(unit, X))))))
% 62.84/8.29 = { by axiom 2 (commutativity_of_join) }
% 62.84/8.29 meet(rd(unit, X), ld(X, join(op(X, rd(unit, X)), ld(rd(unit, X), join(rd(unit, X), op(rd(unit, X), op(X, rd(unit, X))))))))
% 62.84/8.29 = { by lemma 41 }
% 62.84/8.29 meet(rd(unit, X), ld(X, join(op(X, rd(unit, X)), ld(rd(unit, X), rd(unit, X)))))
% 62.84/8.29 = { by lemma 18 }
% 62.84/8.29 rd(unit, X)
% 62.84/8.29
% 62.84/8.29 Lemma 43: meet(X, at(unit, X)) = X.
% 62.84/8.29 Proof:
% 62.84/8.29 meet(X, at(unit, X))
% 62.84/8.29 = { by lemma 38 R->L }
% 62.84/8.29 meet(X, ld(ld(X, unit), unit))
% 62.84/8.29 = { by lemma 39 R->L }
% 62.84/8.29 meet(meet(X, rd(unit, ld(X, unit))), ld(ld(X, unit), unit))
% 62.84/8.29 = { by axiom 10 (associativity_of_meet) }
% 62.84/8.29 meet(X, meet(rd(unit, ld(X, unit)), ld(ld(X, unit), unit)))
% 62.84/8.29 = { by axiom 4 (commutativity_of_meet) }
% 62.84/8.29 meet(X, meet(ld(ld(X, unit), unit), rd(unit, ld(X, unit))))
% 62.84/8.29 = { by lemma 42 }
% 62.84/8.29 meet(X, rd(unit, ld(X, unit)))
% 62.84/8.29 = { by lemma 39 }
% 62.84/8.30 X
% 62.84/8.30
% 62.84/8.30 Lemma 44: join(op(ld(X, unit), Y), ld(X, Y)) = ld(X, Y).
% 62.84/8.30 Proof:
% 62.84/8.30 join(op(ld(X, unit), Y), ld(X, Y))
% 62.84/8.30 = { by axiom 2 (commutativity_of_join) R->L }
% 62.84/8.30 join(ld(X, Y), op(ld(X, unit), Y))
% 62.84/8.30 = { by lemma 18 R->L }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(op(X, op(ld(X, unit), Y)), Y))))
% 62.84/8.30 = { by axiom 2 (commutativity_of_join) }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(X, op(ld(X, unit), Y))))))
% 62.84/8.30 = { by axiom 11 (monoid_associativity) R->L }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(op(X, ld(X, unit)), Y)))))
% 62.84/8.30 = { by lemma 24 R->L }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(meet(unit, op(X, ld(X, unit))), Y)))))
% 62.84/8.30 = { by lemma 40 R->L }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(meet(meet(unit, rd(Y, Y)), op(X, ld(X, unit))), Y)))))
% 62.84/8.30 = { by axiom 10 (associativity_of_meet) }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(meet(unit, meet(rd(Y, Y), op(X, ld(X, unit)))), Y)))))
% 62.84/8.30 = { by axiom 4 (commutativity_of_meet) R->L }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(meet(unit, meet(op(X, ld(X, unit)), rd(Y, Y))), Y)))))
% 62.84/8.30 = { by axiom 10 (associativity_of_meet) R->L }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(meet(meet(unit, op(X, ld(X, unit))), rd(Y, Y)), Y)))))
% 62.84/8.30 = { by lemma 24 }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, join(Y, op(meet(op(X, ld(X, unit)), rd(Y, Y)), Y)))))
% 62.84/8.30 = { by lemma 25 }
% 62.84/8.30 join(ld(X, Y), meet(op(ld(X, unit), Y), ld(X, Y)))
% 62.84/8.30 = { by lemma 31 }
% 62.84/8.30 ld(X, Y)
% 62.84/8.30
% 62.84/8.30 Goal 1 (goal): at(unit, ld(x, unit)) = ld(x, unit).
% 62.84/8.30 Proof:
% 62.84/8.30 at(unit, ld(x, unit))
% 62.84/8.30 = { by lemma 35 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, ld(at(unit, ld(x, unit)), unit))))
% 62.84/8.30 = { by lemma 38 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, ld(ld(ld(ld(x, unit), unit), unit), unit))))
% 62.84/8.30 = { by lemma 38 }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, at(unit, ld(ld(x, unit), unit)))))
% 62.84/8.30 = { by lemma 37 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, at(unit, ld(ld(x, unit), ld(x, x))))))
% 62.84/8.30 = { by lemma 31 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, at(unit, join(ld(ld(x, unit), ld(x, x)), meet(x, ld(ld(x, unit), ld(x, x))))))))
% 62.84/8.30 = { by lemma 44 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, at(unit, join(ld(ld(x, unit), ld(x, x)), meet(x, ld(ld(x, unit), join(op(ld(x, unit), x), ld(x, x)))))))))
% 62.84/8.30 = { by lemma 18 }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, at(unit, join(ld(ld(x, unit), ld(x, x)), x)))))
% 62.84/8.30 = { by axiom 2 (commutativity_of_join) }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, at(unit, join(x, ld(ld(x, unit), ld(x, x)))))))
% 62.84/8.30 = { by lemma 37 }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, at(unit, join(x, ld(ld(x, unit), unit))))))
% 62.84/8.30 = { by lemma 33 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, meet(join(x, ld(ld(x, unit), unit)), at(unit, join(x, ld(ld(x, unit), unit)))))))
% 62.84/8.30 = { by lemma 43 }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, meet(x, join(x, ld(ld(x, unit), unit)))))
% 62.84/8.30 = { by lemma 22 }
% 62.84/8.30 meet(at(unit, ld(x, unit)), rd(unit, x))
% 62.84/8.30 = { by lemma 42 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), meet(ld(x, unit), rd(unit, x)))
% 62.84/8.30 = { by lemma 37 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), meet(ld(x, unit), rd(ld(x, x), x)))
% 62.84/8.30 = { by lemma 44 R->L }
% 62.84/8.30 meet(at(unit, ld(x, unit)), meet(ld(x, unit), rd(join(op(ld(x, unit), x), ld(x, x)), x)))
% 62.84/8.30 = { by lemma 27 }
% 62.84/8.30 meet(at(unit, ld(x, unit)), ld(x, unit))
% 62.84/8.30 = { by axiom 4 (commutativity_of_meet) }
% 62.84/8.30 meet(ld(x, unit), at(unit, ld(x, unit)))
% 62.84/8.30 = { by lemma 43 }
% 62.84/8.30 ld(x, unit)
% 62.84/8.30 % SZS output end Proof
% 62.84/8.30
% 62.84/8.30 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------