TSTP Solution File: MVA009-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MVA009-1 : 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 : 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 09:32:29 EDT 2023
% Result : Unsatisfiable 37.08s 5.28s
% Output : Proof 38.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MVA009-1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 05:25:32 EDT 2023
% 0.15/0.34 % CPUTime :
% 37.08/5.28 Command-line arguments: --ground-connectedness --complete-subsets
% 37.08/5.28
% 37.08/5.28 % SZS status Unsatisfiable
% 37.08/5.28
% 37.08/5.35 % SZS output start Proof
% 37.08/5.35 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 38.50/5.36 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 38.50/5.36 Axiom 3 (right_monoid_unit): op(X, unit) = X.
% 38.50/5.36 Axiom 4 (left_monoid_unit): op(unit, X) = X.
% 38.50/5.36 Axiom 5 (idempotence_of_join): join(X, X) = X.
% 38.50/5.36 Axiom 6 (commutativity_of_join): join(X, Y) = join(Y, X).
% 38.50/5.36 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 38.50/5.36 Axiom 8 (absorption_b): meet(join(X, Y), X) = X.
% 38.50/5.36 Axiom 9 (monoid_associativity): op(op(X, Y), Z) = op(X, op(Y, Z)).
% 38.50/5.36 Axiom 10 (absorption_a): join(meet(X, Y), X) = X.
% 38.50/5.36 Axiom 11 (generalized_mv_algebra_a): join(X, Y) = rd(X, ld(join(X, Y), X)).
% 38.50/5.36 Axiom 12 (generalized_mv_algebra_b): join(X, Y) = ld(rd(X, join(X, Y)), X).
% 38.50/5.36 Axiom 13 (residual_d): meet(rd(join(op(X, Y), Z), Y), X) = X.
% 38.50/5.36 Axiom 14 (residual_c): meet(ld(X, join(op(X, Y), Z)), Y) = Y.
% 38.50/5.36 Axiom 15 (residual_a): join(op(X, meet(ld(X, Y), Z)), Y) = Y.
% 38.50/5.36 Axiom 16 (residual_b): join(op(meet(X, rd(Y, Z)), Z), Y) = Y.
% 38.50/5.36 Axiom 17 (definition_of_at): at(X, Y) = op(op(X, ld(X, unit)), ld(ld(Y, unit), unit)).
% 38.50/5.36
% 38.50/5.36 Lemma 18: join(X, meet(X, Y)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 join(X, meet(X, Y))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 join(meet(X, Y), X)
% 38.50/5.36 = { by axiom 10 (absorption_a) }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 19: join(X, meet(Y, X)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 join(X, meet(Y, X))
% 38.50/5.36 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.36 join(X, meet(X, Y))
% 38.50/5.36 = { by lemma 18 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 20: meet(X, ld(Y, join(op(Y, X), Z))) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, ld(Y, join(op(Y, X), Z)))
% 38.50/5.36 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.36 meet(ld(Y, join(op(Y, X), Z)), X)
% 38.50/5.36 = { by axiom 14 (residual_c) }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 21: meet(X, ld(Y, op(Y, X))) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, ld(Y, op(Y, X)))
% 38.50/5.36 = { by axiom 5 (idempotence_of_join) R->L }
% 38.50/5.36 meet(X, ld(Y, join(op(Y, X), op(Y, X))))
% 38.50/5.36 = { by lemma 20 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 22: join(X, op(Y, meet(ld(Y, X), Z))) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 join(X, op(Y, meet(ld(Y, X), Z)))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 join(op(Y, meet(ld(Y, X), Z)), X)
% 38.50/5.36 = { by axiom 15 (residual_a) }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 23: join(X, op(Y, ld(Y, X))) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 join(X, op(Y, ld(Y, X)))
% 38.50/5.36 = { by axiom 1 (idempotence_of_meet) R->L }
% 38.50/5.36 join(X, op(Y, meet(ld(Y, X), ld(Y, X))))
% 38.50/5.36 = { by lemma 22 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 24: ld(unit, X) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 ld(unit, X)
% 38.50/5.36 = { by lemma 19 R->L }
% 38.50/5.36 join(ld(unit, X), meet(X, ld(unit, X)))
% 38.50/5.36 = { by axiom 4 (left_monoid_unit) R->L }
% 38.50/5.36 join(ld(unit, X), meet(X, ld(unit, op(unit, X))))
% 38.50/5.36 = { by lemma 21 }
% 38.50/5.36 join(ld(unit, X), X)
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) }
% 38.50/5.36 join(X, ld(unit, X))
% 38.50/5.36 = { by axiom 4 (left_monoid_unit) R->L }
% 38.50/5.36 join(X, op(unit, ld(unit, X)))
% 38.50/5.36 = { by lemma 23 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 25: meet(X, rd(join(op(X, Y), Z), Y)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, rd(join(op(X, Y), Z), Y))
% 38.50/5.36 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.36 meet(rd(join(op(X, Y), Z), Y), X)
% 38.50/5.36 = { by axiom 13 (residual_d) }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 26: meet(X, rd(op(X, Y), Y)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, rd(op(X, Y), Y))
% 38.50/5.36 = { by axiom 5 (idempotence_of_join) R->L }
% 38.50/5.36 meet(X, rd(join(op(X, Y), op(X, Y)), Y))
% 38.50/5.36 = { by lemma 25 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 27: join(X, op(meet(Y, rd(X, Z)), Z)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 join(X, op(meet(Y, rd(X, Z)), Z))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 join(op(meet(Y, rd(X, Z)), Z), X)
% 38.50/5.36 = { by axiom 16 (residual_b) }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 28: rd(X, unit) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 rd(X, unit)
% 38.50/5.36 = { by lemma 19 R->L }
% 38.50/5.36 join(rd(X, unit), meet(X, rd(X, unit)))
% 38.50/5.36 = { by axiom 3 (right_monoid_unit) R->L }
% 38.50/5.36 join(rd(X, unit), meet(X, rd(op(X, unit), unit)))
% 38.50/5.36 = { by lemma 26 }
% 38.50/5.36 join(rd(X, unit), X)
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) }
% 38.50/5.36 join(X, rd(X, unit))
% 38.50/5.36 = { by axiom 3 (right_monoid_unit) R->L }
% 38.50/5.36 join(X, op(rd(X, unit), unit))
% 38.50/5.36 = { by axiom 1 (idempotence_of_meet) R->L }
% 38.50/5.36 join(X, op(meet(rd(X, unit), rd(X, unit)), unit))
% 38.50/5.36 = { by lemma 27 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 29: meet(X, join(X, Y)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, join(X, Y))
% 38.50/5.36 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.36 meet(join(X, Y), X)
% 38.50/5.36 = { by axiom 8 (absorption_b) }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 30: join(unit, ld(X, X)) = ld(X, X).
% 38.50/5.36 Proof:
% 38.50/5.36 join(unit, ld(X, X))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 join(ld(X, X), unit)
% 38.50/5.36 = { by lemma 21 R->L }
% 38.50/5.36 join(ld(X, X), meet(unit, ld(X, op(X, unit))))
% 38.50/5.36 = { by axiom 3 (right_monoid_unit) }
% 38.50/5.36 join(ld(X, X), meet(unit, ld(X, X)))
% 38.50/5.36 = { by lemma 19 }
% 38.50/5.36 ld(X, X)
% 38.50/5.36
% 38.50/5.36 Lemma 31: ld(ld(X, unit), unit) = at(unit, X).
% 38.50/5.36 Proof:
% 38.50/5.36 ld(ld(X, unit), unit)
% 38.50/5.36 = { by axiom 4 (left_monoid_unit) R->L }
% 38.50/5.36 op(unit, ld(ld(X, unit), unit))
% 38.50/5.36 = { by axiom 4 (left_monoid_unit) R->L }
% 38.50/5.36 op(unit, op(unit, ld(ld(X, unit), unit)))
% 38.50/5.36 = { by lemma 24 R->L }
% 38.50/5.36 op(unit, op(ld(unit, unit), ld(ld(X, unit), unit)))
% 38.50/5.36 = { by axiom 9 (monoid_associativity) R->L }
% 38.50/5.36 op(op(unit, ld(unit, unit)), ld(ld(X, unit), unit))
% 38.50/5.36 = { by axiom 17 (definition_of_at) R->L }
% 38.50/5.36 at(unit, X)
% 38.50/5.36
% 38.50/5.36 Lemma 32: meet(X, meet(join(X, Y), Z)) = meet(X, Z).
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, meet(join(X, Y), Z))
% 38.50/5.36 = { by axiom 7 (associativity_of_meet) R->L }
% 38.50/5.36 meet(meet(X, join(X, Y)), Z)
% 38.50/5.36 = { by lemma 29 }
% 38.50/5.36 meet(X, Z)
% 38.50/5.36
% 38.50/5.36 Lemma 33: meet(X, op(Y, ld(Y, X))) = op(Y, ld(Y, X)).
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, op(Y, ld(Y, X)))
% 38.50/5.36 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.36 meet(op(Y, ld(Y, X)), X)
% 38.50/5.36 = { by lemma 23 R->L }
% 38.50/5.36 meet(op(Y, ld(Y, X)), join(X, op(Y, ld(Y, X))))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 meet(op(Y, ld(Y, X)), join(op(Y, ld(Y, X)), X))
% 38.50/5.36 = { by lemma 29 }
% 38.50/5.36 op(Y, ld(Y, X))
% 38.50/5.36
% 38.50/5.36 Lemma 34: meet(unit, ld(X, join(X, Y))) = unit.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(unit, ld(X, join(X, Y)))
% 38.50/5.36 = { by axiom 3 (right_monoid_unit) R->L }
% 38.50/5.36 meet(unit, ld(X, join(op(X, unit), Y)))
% 38.50/5.36 = { by lemma 20 }
% 38.50/5.36 unit
% 38.50/5.36
% 38.50/5.36 Lemma 35: join(X, ld(Y, op(Y, X))) = ld(Y, op(Y, X)).
% 38.50/5.36 Proof:
% 38.50/5.36 join(X, ld(Y, op(Y, X)))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 join(ld(Y, op(Y, X)), X)
% 38.50/5.36 = { by lemma 21 R->L }
% 38.50/5.36 join(ld(Y, op(Y, X)), meet(X, ld(Y, op(Y, X))))
% 38.50/5.36 = { by lemma 19 }
% 38.50/5.36 ld(Y, op(Y, X))
% 38.50/5.36
% 38.50/5.36 Lemma 36: join(op(X, ld(X, Y)), Y) = Y.
% 38.50/5.36 Proof:
% 38.50/5.36 join(op(X, ld(X, Y)), Y)
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 join(Y, op(X, ld(X, Y)))
% 38.50/5.36 = { by lemma 23 }
% 38.50/5.36 Y
% 38.50/5.36
% 38.50/5.36 Lemma 37: meet(X, rd(op(X, join(Y, Z)), Y)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, rd(op(X, join(Y, Z)), Y))
% 38.50/5.36 = { by lemma 29 R->L }
% 38.50/5.36 meet(X, rd(op(X, join(Y, Z)), meet(Y, join(Y, Z))))
% 38.50/5.36 = { by lemma 21 R->L }
% 38.50/5.36 meet(X, rd(op(X, join(Y, Z)), meet(Y, meet(join(Y, Z), ld(X, op(X, join(Y, Z)))))))
% 38.50/5.36 = { by lemma 32 }
% 38.50/5.36 meet(X, rd(op(X, join(Y, Z)), meet(Y, ld(X, op(X, join(Y, Z))))))
% 38.50/5.36 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.36 meet(X, rd(op(X, join(Y, Z)), meet(ld(X, op(X, join(Y, Z))), Y)))
% 38.50/5.36 = { by lemma 22 R->L }
% 38.50/5.36 meet(X, rd(join(op(X, join(Y, Z)), op(X, meet(ld(X, op(X, join(Y, Z))), Y))), meet(ld(X, op(X, join(Y, Z))), Y)))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 meet(X, rd(join(op(X, meet(ld(X, op(X, join(Y, Z))), Y)), op(X, join(Y, Z))), meet(ld(X, op(X, join(Y, Z))), Y)))
% 38.50/5.36 = { by lemma 25 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 38: op(op(X, Y), ld(Y, Y)) = op(X, Y).
% 38.50/5.36 Proof:
% 38.50/5.36 op(op(X, Y), ld(Y, Y))
% 38.50/5.36 = { by axiom 9 (monoid_associativity) }
% 38.50/5.36 op(X, op(Y, ld(Y, Y)))
% 38.50/5.36 = { by lemma 33 R->L }
% 38.50/5.36 op(X, meet(Y, op(Y, ld(Y, Y))))
% 38.50/5.36 = { by lemma 28 R->L }
% 38.50/5.36 op(X, meet(Y, rd(op(Y, ld(Y, Y)), unit)))
% 38.50/5.36 = { by lemma 30 R->L }
% 38.50/5.36 op(X, meet(Y, rd(op(Y, join(unit, ld(Y, Y))), unit)))
% 38.50/5.36 = { by lemma 37 }
% 38.50/5.36 op(X, Y)
% 38.50/5.36
% 38.50/5.36 Lemma 39: meet(X, ld(meet(Y, rd(Z, X)), Z)) = X.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(X, ld(meet(Y, rd(Z, X)), Z))
% 38.50/5.36 = { by lemma 27 R->L }
% 38.50/5.36 meet(X, ld(meet(Y, rd(Z, X)), join(Z, op(meet(Y, rd(Z, X)), X))))
% 38.50/5.36 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.36 meet(X, ld(meet(Y, rd(Z, X)), join(op(meet(Y, rd(Z, X)), X), Z)))
% 38.50/5.36 = { by lemma 20 }
% 38.50/5.36 X
% 38.50/5.36
% 38.50/5.36 Lemma 40: meet(unit, ld(op(X, ld(X, Y)), Y)) = unit.
% 38.50/5.36 Proof:
% 38.50/5.36 meet(unit, ld(op(X, ld(X, Y)), Y))
% 38.50/5.36 = { by lemma 36 R->L }
% 38.50/5.36 meet(unit, ld(op(X, ld(X, Y)), join(op(X, ld(X, Y)), Y)))
% 38.50/5.36 = { by lemma 34 }
% 38.50/5.36 unit
% 38.50/5.36
% 38.50/5.37 Lemma 41: join(unit, ld(op(X, ld(X, Y)), Y)) = ld(op(X, ld(X, Y)), Y).
% 38.50/5.37 Proof:
% 38.50/5.37 join(unit, ld(op(X, ld(X, Y)), Y))
% 38.50/5.37 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.37 join(ld(op(X, ld(X, Y)), Y), unit)
% 38.50/5.37 = { by lemma 40 R->L }
% 38.50/5.37 join(ld(op(X, ld(X, Y)), Y), meet(unit, ld(op(X, ld(X, Y)), Y)))
% 38.50/5.37 = { by lemma 19 }
% 38.50/5.37 ld(op(X, ld(X, Y)), Y)
% 38.50/5.37
% 38.50/5.37 Lemma 42: rd(unit, at(unit, op(X, ld(X, unit)))) = ld(op(X, ld(X, unit)), unit).
% 38.50/5.37 Proof:
% 38.50/5.37 rd(unit, at(unit, op(X, ld(X, unit))))
% 38.50/5.37 = { by lemma 31 R->L }
% 38.50/5.37 rd(unit, ld(ld(op(X, ld(X, unit)), unit), unit))
% 38.50/5.37 = { by lemma 40 R->L }
% 38.50/5.37 rd(unit, ld(ld(op(X, ld(X, unit)), unit), meet(unit, ld(op(X, ld(X, unit)), unit))))
% 38.50/5.37 = { by lemma 40 R->L }
% 38.50/5.37 rd(meet(unit, ld(op(X, ld(X, unit)), unit)), ld(ld(op(X, ld(X, unit)), unit), meet(unit, ld(op(X, ld(X, unit)), unit))))
% 38.50/5.37 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.37 rd(meet(unit, ld(op(X, ld(X, unit)), unit)), ld(ld(op(X, ld(X, unit)), unit), meet(ld(op(X, ld(X, unit)), unit), unit)))
% 38.50/5.37 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.37 rd(meet(ld(op(X, ld(X, unit)), unit), unit), ld(ld(op(X, ld(X, unit)), unit), meet(ld(op(X, ld(X, unit)), unit), unit)))
% 38.50/5.37 = { by lemma 18 R->L }
% 38.50/5.37 rd(meet(ld(op(X, ld(X, unit)), unit), unit), ld(join(ld(op(X, ld(X, unit)), unit), meet(ld(op(X, ld(X, unit)), unit), unit)), meet(ld(op(X, ld(X, unit)), unit), unit)))
% 38.50/5.37 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.37 rd(meet(ld(op(X, ld(X, unit)), unit), unit), ld(join(meet(ld(op(X, ld(X, unit)), unit), unit), ld(op(X, ld(X, unit)), unit)), meet(ld(op(X, ld(X, unit)), unit), unit)))
% 38.50/5.37 = { by axiom 11 (generalized_mv_algebra_a) R->L }
% 38.50/5.37 join(meet(ld(op(X, ld(X, unit)), unit), unit), ld(op(X, ld(X, unit)), unit))
% 38.50/5.37 = { by axiom 6 (commutativity_of_join) }
% 38.50/5.37 join(ld(op(X, ld(X, unit)), unit), meet(ld(op(X, ld(X, unit)), unit), unit))
% 38.50/5.37 = { by lemma 18 }
% 38.50/5.37 ld(op(X, ld(X, unit)), unit)
% 38.50/5.37
% 38.50/5.37 Lemma 43: meet(X, rd(Y, op(Z, ld(op(X, Z), Y)))) = X.
% 38.50/5.37 Proof:
% 38.50/5.37 meet(X, rd(Y, op(Z, ld(op(X, Z), Y))))
% 38.50/5.37 = { by lemma 23 R->L }
% 38.50/5.37 meet(X, rd(join(Y, op(op(X, Z), ld(op(X, Z), Y))), op(Z, ld(op(X, Z), Y))))
% 38.50/5.37 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.37 meet(X, rd(join(op(op(X, Z), ld(op(X, Z), Y)), Y), op(Z, ld(op(X, Z), Y))))
% 38.50/5.37 = { by axiom 9 (monoid_associativity) }
% 38.50/5.37 meet(X, rd(join(op(X, op(Z, ld(op(X, Z), Y))), Y), op(Z, ld(op(X, Z), Y))))
% 38.50/5.37 = { by lemma 25 }
% 38.50/5.37 X
% 38.50/5.37
% 38.50/5.37 Lemma 44: ld(op(X, ld(X, unit)), op(X, ld(X, unit))) = unit.
% 38.50/5.37 Proof:
% 38.50/5.37 ld(op(X, ld(X, unit)), op(X, ld(X, unit)))
% 38.50/5.37 = { by lemma 28 R->L }
% 38.50/5.37 ld(rd(op(X, ld(X, unit)), unit), op(X, ld(X, unit)))
% 38.50/5.37 = { by lemma 36 R->L }
% 38.50/5.37 ld(rd(op(X, ld(X, unit)), join(op(X, ld(X, unit)), unit)), op(X, ld(X, unit)))
% 38.50/5.37 = { by axiom 12 (generalized_mv_algebra_b) R->L }
% 38.50/5.37 join(op(X, ld(X, unit)), unit)
% 38.50/5.37 = { by lemma 36 }
% 38.50/5.37 unit
% 38.50/5.37
% 38.50/5.37 Lemma 45: meet(X, op(rd(unit, at(unit, op(Y, ld(Y, unit)))), X)) = X.
% 38.50/5.37 Proof:
% 38.50/5.37 meet(X, op(rd(unit, at(unit, op(Y, ld(Y, unit)))), X))
% 38.50/5.37 = { by lemma 42 }
% 38.50/5.37 meet(X, op(ld(op(Y, ld(Y, unit)), unit), X))
% 38.50/5.37 = { by lemma 24 R->L }
% 38.50/5.37 meet(X, ld(unit, op(ld(op(Y, ld(Y, unit)), unit), X)))
% 38.50/5.37 = { by lemma 41 R->L }
% 38.50/5.37 meet(X, ld(unit, op(join(unit, ld(op(Y, ld(Y, unit)), unit)), X)))
% 38.50/5.37 = { by lemma 29 R->L }
% 38.50/5.37 meet(X, ld(meet(unit, join(unit, ld(op(Y, ld(Y, unit)), unit))), op(join(unit, ld(op(Y, ld(Y, unit)), unit)), X)))
% 38.50/5.37 = { by lemma 26 R->L }
% 38.50/5.37 meet(X, ld(meet(unit, meet(join(unit, ld(op(Y, ld(Y, unit)), unit)), rd(op(join(unit, ld(op(Y, ld(Y, unit)), unit)), X), X))), op(join(unit, ld(op(Y, ld(Y, unit)), unit)), X)))
% 38.50/5.37 = { by lemma 32 }
% 38.50/5.37 meet(X, ld(meet(unit, rd(op(join(unit, ld(op(Y, ld(Y, unit)), unit)), X), X)), op(join(unit, ld(op(Y, ld(Y, unit)), unit)), X)))
% 38.50/5.37 = { by lemma 39 }
% 38.50/5.37 X
% 38.50/5.37
% 38.50/5.37 Goal 1 (goal): at(unit, op(x, ld(x, unit))) = unit.
% 38.50/5.37 Proof:
% 38.50/5.37 at(unit, op(x, ld(x, unit)))
% 38.50/5.37 = { by lemma 31 R->L }
% 38.50/5.37 ld(ld(op(x, ld(x, unit)), unit), unit)
% 38.50/5.37 = { by lemma 42 R->L }
% 38.50/5.37 ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit)
% 38.50/5.37 = { by lemma 45 R->L }
% 38.50/5.37 meet(ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit), op(rd(unit, at(unit, op(x, ld(x, unit)))), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit)))
% 38.50/5.37 = { by axiom 2 (commutativity_of_meet) R->L }
% 38.50/5.37 meet(op(rd(unit, at(unit, op(x, ld(x, unit)))), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit)), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit))
% 38.50/5.37 = { by lemma 33 R->L }
% 38.50/5.37 meet(meet(unit, op(rd(unit, at(unit, op(x, ld(x, unit)))), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit))), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit))
% 38.50/5.37 = { by axiom 7 (associativity_of_meet) }
% 38.50/5.37 meet(unit, meet(op(rd(unit, at(unit, op(x, ld(x, unit)))), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit)), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit)))
% 38.50/5.37 = { by axiom 2 (commutativity_of_meet) }
% 38.50/5.37 meet(unit, meet(ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit), op(rd(unit, at(unit, op(x, ld(x, unit)))), ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit))))
% 38.50/5.37 = { by lemma 45 }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), unit))
% 38.50/5.37 = { by lemma 44 R->L }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(op(x, ld(x, unit)), op(x, ld(x, unit)))))
% 38.50/5.37 = { by lemma 38 R->L }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(op(x, ld(x, unit)), op(op(x, ld(x, unit)), ld(ld(x, unit), ld(x, unit))))))
% 38.50/5.37 = { by lemma 35 R->L }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), join(ld(ld(x, unit), ld(x, unit)), ld(op(x, ld(x, unit)), op(op(x, ld(x, unit)), ld(ld(x, unit), ld(x, unit)))))))
% 38.50/5.37 = { by lemma 38 }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), join(ld(ld(x, unit), ld(x, unit)), ld(op(x, ld(x, unit)), op(x, ld(x, unit))))))
% 38.50/5.37 = { by lemma 44 }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), join(ld(ld(x, unit), ld(x, unit)), unit)))
% 38.50/5.37 = { by axiom 6 (commutativity_of_join) }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), join(unit, ld(ld(x, unit), ld(x, unit)))))
% 38.50/5.37 = { by lemma 30 }
% 38.50/5.37 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), ld(x, unit))))
% 38.50/5.38 = { by lemma 43 R->L }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), ld(meet(x, rd(unit, op(ld(x, unit), ld(op(x, ld(x, unit)), unit)))), unit))))
% 38.50/5.38 = { by lemma 19 R->L }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(ld(meet(x, rd(unit, op(ld(x, unit), ld(op(x, ld(x, unit)), unit)))), unit), meet(op(ld(x, unit), ld(op(x, ld(x, unit)), unit)), ld(meet(x, rd(unit, op(ld(x, unit), ld(op(x, ld(x, unit)), unit)))), unit))))))
% 38.50/5.38 = { by lemma 39 }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(ld(meet(x, rd(unit, op(ld(x, unit), ld(op(x, ld(x, unit)), unit)))), unit), op(ld(x, unit), ld(op(x, ld(x, unit)), unit))))))
% 38.50/5.38 = { by axiom 6 (commutativity_of_join) }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(op(ld(x, unit), ld(op(x, ld(x, unit)), unit)), ld(meet(x, rd(unit, op(ld(x, unit), ld(op(x, ld(x, unit)), unit)))), unit)))))
% 38.50/5.38 = { by lemma 43 }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(op(ld(x, unit), ld(op(x, ld(x, unit)), unit)), ld(x, unit)))))
% 38.50/5.38 = { by axiom 6 (commutativity_of_join) }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(ld(x, unit), op(ld(x, unit), ld(op(x, ld(x, unit)), unit))))))
% 38.50/5.38 = { by lemma 42 R->L }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(ld(x, unit), op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit)))))))))
% 38.50/5.38 = { by axiom 6 (commutativity_of_join) R->L }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit))))), ld(x, unit)))))
% 38.50/5.38 = { by lemma 37 R->L }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit))))), meet(ld(x, unit), rd(op(ld(x, unit), join(unit, ld(op(x, ld(x, unit)), unit))), unit))))))
% 38.50/5.38 = { by lemma 41 }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit))))), meet(ld(x, unit), rd(op(ld(x, unit), ld(op(x, ld(x, unit)), unit)), unit))))))
% 38.50/5.38 = { by lemma 28 }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit))))), meet(ld(x, unit), op(ld(x, unit), ld(op(x, ld(x, unit)), unit)))))))
% 38.50/5.38 = { by lemma 42 R->L }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), join(op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit))))), meet(ld(x, unit), op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit))))))))))
% 38.50/5.38 = { by lemma 19 }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit))))))))
% 38.50/5.38 = { by lemma 35 R->L }
% 38.50/5.38 meet(unit, ld(rd(unit, at(unit, op(x, ld(x, unit)))), join(rd(unit, at(unit, op(x, ld(x, unit)))), ld(ld(x, unit), op(ld(x, unit), rd(unit, at(unit, op(x, ld(x, unit)))))))))
% 38.50/5.38 = { by lemma 34 }
% 38.50/5.38 unit
% 38.50/5.38 % SZS output end Proof
% 38.50/5.38
% 38.50/5.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------