TSTP Solution File: GRP689-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP689-1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n019.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 01:19:43 EDT 2023
% Result : Unsatisfiable 39.56s 5.49s
% Output : Proof 43.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP689-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.34 % Computer : n019.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Mon Aug 28 20:02:28 EDT 2023
% 0.18/0.34 % CPUTime :
% 39.56/5.49 Command-line arguments: --flatten
% 39.56/5.49
% 39.56/5.49 % SZS status Unsatisfiable
% 39.56/5.49
% 42.24/5.82 % SZS output start Proof
% 42.24/5.82 Axiom 1 (c05): mult(X, unit) = X.
% 42.24/5.82 Axiom 2 (c06): mult(unit, X) = X.
% 42.24/5.82 Axiom 3 (c02): ld(X, mult(X, Y)) = Y.
% 42.24/5.82 Axiom 4 (c04): rd(mult(X, Y), Y) = X.
% 42.24/5.82 Axiom 5 (c01): mult(X, ld(X, Y)) = Y.
% 42.24/5.82 Axiom 6 (c09): i(mult(X, Y)) = mult(i(X), i(Y)).
% 42.24/5.82 Axiom 7 (c03): mult(rd(X, Y), Y) = X.
% 42.24/5.82 Axiom 8 (c08): mult(i(X), mult(X, Y)) = Y.
% 42.24/5.82 Axiom 9 (c10): mult(op_c, mult(op_c, mult(op_c, op_c))) = unit.
% 42.24/5.82 Axiom 10 (c07): mult(X, mult(Y, mult(X, Z))) = mult(mult(X, mult(Y, X)), Z).
% 42.24/5.82 Axiom 11 (c11): mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))) = unit.
% 42.24/5.82
% 42.24/5.82 Lemma 12: mult(X, mult(op_c, mult(op_c, mult(op_c, op_c)))) = X.
% 42.24/5.82 Proof:
% 42.24/5.82 mult(X, mult(op_c, mult(op_c, mult(op_c, op_c))))
% 42.24/5.82 = { by axiom 9 (c10) }
% 42.24/5.82 mult(X, unit)
% 42.24/5.82 = { by axiom 1 (c05) }
% 42.24/5.82 X
% 42.24/5.82
% 42.24/5.82 Lemma 13: mult(op_c, mult(op_c, mult(op_c, op_c))) = mult(i(X), X).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(op_c, mult(op_c, mult(op_c, op_c)))
% 42.24/5.82 = { by axiom 9 (c10) }
% 42.24/5.82 unit
% 42.24/5.82 = { by axiom 8 (c08) R->L }
% 42.24/5.82 mult(i(X), mult(X, unit))
% 42.24/5.82 = { by axiom 1 (c05) }
% 42.24/5.82 mult(i(X), X)
% 42.24/5.82
% 42.24/5.82 Lemma 14: i(i(X)) = X.
% 42.24/5.82 Proof:
% 42.24/5.82 i(i(X))
% 42.24/5.82 = { by lemma 12 R->L }
% 42.24/5.82 mult(i(i(X)), mult(op_c, mult(op_c, mult(op_c, op_c))))
% 42.24/5.82 = { by lemma 13 }
% 42.24/5.82 mult(i(i(X)), mult(i(X), X))
% 42.24/5.82 = { by axiom 8 (c08) }
% 42.24/5.82 X
% 42.24/5.82
% 42.24/5.82 Lemma 15: ld(i(X), Y) = mult(X, Y).
% 42.24/5.82 Proof:
% 42.24/5.82 ld(i(X), Y)
% 42.24/5.82 = { by axiom 8 (c08) R->L }
% 42.24/5.82 ld(i(X), mult(i(X), mult(X, Y)))
% 42.24/5.82 = { by axiom 3 (c02) }
% 42.24/5.82 mult(X, Y)
% 42.24/5.82
% 42.24/5.82 Lemma 16: mult(i(X), Y) = ld(X, Y).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(i(X), Y)
% 42.24/5.82 = { by axiom 5 (c01) R->L }
% 42.24/5.82 mult(i(X), mult(X, ld(X, Y)))
% 42.24/5.82 = { by axiom 8 (c08) }
% 42.24/5.82 ld(X, Y)
% 42.24/5.82
% 42.24/5.82 Lemma 17: i(mult(X, Y)) = ld(X, i(Y)).
% 42.24/5.82 Proof:
% 42.24/5.82 i(mult(X, Y))
% 42.24/5.82 = { by axiom 6 (c09) }
% 42.24/5.82 mult(i(X), i(Y))
% 42.24/5.82 = { by lemma 16 }
% 42.24/5.82 ld(X, i(Y))
% 42.24/5.82
% 42.24/5.82 Lemma 18: mult(X, i(Y)) = i(ld(X, Y)).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(X, i(Y))
% 42.24/5.82 = { by lemma 15 R->L }
% 42.24/5.82 ld(i(X), i(Y))
% 42.24/5.82 = { by lemma 17 R->L }
% 42.24/5.82 i(mult(i(X), Y))
% 42.24/5.82 = { by lemma 16 }
% 42.24/5.82 i(ld(X, Y))
% 42.24/5.82
% 42.24/5.82 Lemma 19: mult(op_c, mult(op_c, mult(op_c, op_c))) = ld(X, X).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(op_c, mult(op_c, mult(op_c, op_c)))
% 42.24/5.82 = { by axiom 9 (c10) }
% 42.24/5.82 unit
% 42.24/5.82 = { by axiom 3 (c02) R->L }
% 42.24/5.82 ld(X, mult(X, unit))
% 42.24/5.82 = { by axiom 1 (c05) }
% 42.24/5.82 ld(X, X)
% 42.24/5.82
% 42.24/5.82 Lemma 20: mult(op_c, mult(op_c, mult(op_c, op_c))) = mult(X, i(X)).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(op_c, mult(op_c, mult(op_c, op_c)))
% 42.24/5.82 = { by lemma 19 }
% 42.24/5.82 ld(i(X), i(X))
% 42.24/5.82 = { by lemma 15 }
% 42.24/5.82 mult(X, i(X))
% 42.24/5.82
% 42.24/5.82 Lemma 21: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(mult(X, X), Y)
% 42.24/5.82 = { by axiom 2 (c06) R->L }
% 42.24/5.82 mult(mult(X, mult(unit, X)), Y)
% 42.24/5.82 = { by axiom 10 (c07) R->L }
% 42.24/5.82 mult(X, mult(unit, mult(X, Y)))
% 42.24/5.82 = { by axiom 2 (c06) }
% 42.24/5.82 mult(X, mult(X, Y))
% 42.24/5.82
% 42.24/5.82 Lemma 22: rd(mult(X, mult(X, Y)), Y) = mult(X, X).
% 42.24/5.82 Proof:
% 42.24/5.82 rd(mult(X, mult(X, Y)), Y)
% 42.24/5.82 = { by lemma 21 R->L }
% 42.24/5.82 rd(mult(mult(X, X), Y), Y)
% 42.24/5.82 = { by axiom 4 (c04) }
% 42.24/5.82 mult(X, X)
% 42.24/5.82
% 42.24/5.82 Lemma 23: rd(X, i(X)) = mult(X, X).
% 42.24/5.82 Proof:
% 42.24/5.82 rd(X, i(X))
% 42.24/5.82 = { by lemma 12 R->L }
% 42.24/5.82 rd(mult(X, mult(op_c, mult(op_c, mult(op_c, op_c)))), i(X))
% 42.24/5.82 = { by lemma 20 }
% 42.24/5.82 rd(mult(X, mult(X, i(X))), i(X))
% 42.24/5.82 = { by lemma 22 }
% 42.24/5.82 mult(X, X)
% 42.24/5.82
% 42.24/5.82 Lemma 24: ld(rd(X, Y), i(Y)) = i(X).
% 42.24/5.82 Proof:
% 42.24/5.82 ld(rd(X, Y), i(Y))
% 42.24/5.82 = { by lemma 17 R->L }
% 42.24/5.82 i(mult(rd(X, Y), Y))
% 42.24/5.82 = { by axiom 7 (c03) }
% 42.24/5.82 i(X)
% 42.24/5.82
% 42.24/5.82 Lemma 25: rd(X, ld(Y, X)) = Y.
% 42.24/5.82 Proof:
% 42.24/5.82 rd(X, ld(Y, X))
% 42.24/5.82 = { by axiom 5 (c01) R->L }
% 42.24/5.82 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 42.24/5.82 = { by axiom 4 (c04) }
% 42.24/5.82 Y
% 42.24/5.82
% 42.24/5.82 Lemma 26: rd(i(X), i(Y)) = rd(Y, X).
% 42.24/5.82 Proof:
% 42.24/5.82 rd(i(X), i(Y))
% 42.24/5.82 = { by lemma 24 R->L }
% 42.24/5.82 rd(i(X), ld(rd(Y, X), i(X)))
% 42.24/5.82 = { by lemma 25 }
% 42.24/5.82 rd(Y, X)
% 42.24/5.82
% 42.24/5.82 Lemma 27: rd(X, i(Y)) = rd(Y, i(X)).
% 42.24/5.82 Proof:
% 42.24/5.82 rd(X, i(Y))
% 42.24/5.82 = { by lemma 26 R->L }
% 42.24/5.82 rd(i(i(Y)), i(X))
% 42.24/5.82 = { by lemma 14 }
% 42.24/5.82 rd(Y, i(X))
% 42.24/5.82
% 42.24/5.82 Lemma 28: ld(X, mult(op_c, mult(op_c, mult(op_c, op_c)))) = i(X).
% 42.24/5.82 Proof:
% 42.24/5.82 ld(X, mult(op_c, mult(op_c, mult(op_c, op_c))))
% 42.24/5.82 = { by axiom 9 (c10) }
% 42.24/5.82 ld(X, unit)
% 42.24/5.82 = { by lemma 16 R->L }
% 42.24/5.82 mult(i(X), unit)
% 42.24/5.82 = { by axiom 1 (c05) }
% 42.24/5.82 i(X)
% 42.24/5.82
% 42.24/5.82 Lemma 29: rd(i(X), X) = ld(X, i(X)).
% 42.24/5.82 Proof:
% 42.24/5.82 rd(i(X), X)
% 42.24/5.82 = { by lemma 28 R->L }
% 42.24/5.82 rd(ld(X, mult(op_c, mult(op_c, mult(op_c, op_c)))), X)
% 42.24/5.82 = { by lemma 16 R->L }
% 42.24/5.82 rd(mult(i(X), mult(op_c, mult(op_c, mult(op_c, op_c)))), X)
% 42.24/5.82 = { by lemma 13 }
% 42.24/5.82 rd(mult(i(X), mult(i(X), X)), X)
% 42.24/5.82 = { by lemma 22 }
% 42.24/5.82 mult(i(X), i(X))
% 42.24/5.82 = { by axiom 6 (c09) R->L }
% 42.24/5.82 i(mult(X, X))
% 42.24/5.82 = { by lemma 17 }
% 42.24/5.82 ld(X, i(X))
% 42.24/5.82
% 42.24/5.82 Lemma 30: rd(mult(op_c, mult(op_c, mult(op_c, op_c))), X) = i(X).
% 42.24/5.82 Proof:
% 42.24/5.82 rd(mult(op_c, mult(op_c, mult(op_c, op_c))), X)
% 42.24/5.82 = { by lemma 13 }
% 42.24/5.82 rd(mult(i(X), X), X)
% 42.24/5.82 = { by axiom 4 (c04) }
% 42.24/5.82 i(X)
% 42.24/5.82
% 42.24/5.82 Lemma 31: i(mult(op_c, mult(op_c, op_c))) = op_c.
% 42.24/5.82 Proof:
% 42.24/5.82 i(mult(op_c, mult(op_c, op_c)))
% 42.24/5.82 = { by lemma 30 R->L }
% 42.24/5.82 rd(mult(op_c, mult(op_c, mult(op_c, op_c))), mult(op_c, mult(op_c, op_c)))
% 42.24/5.82 = { by axiom 4 (c04) }
% 42.24/5.82 op_c
% 42.24/5.82
% 42.24/5.82 Lemma 32: mult(op_c, mult(op_c, op_c)) = i(op_c).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(op_c, mult(op_c, op_c))
% 42.24/5.82 = { by lemma 14 R->L }
% 42.24/5.82 i(i(mult(op_c, mult(op_c, op_c))))
% 42.24/5.82 = { by lemma 31 }
% 42.24/5.82 i(op_c)
% 42.24/5.82
% 42.24/5.82 Lemma 33: i(mult(op_c, op_c)) = mult(op_c, op_c).
% 42.24/5.82 Proof:
% 42.24/5.82 i(mult(op_c, op_c))
% 42.24/5.82 = { by lemma 17 }
% 42.24/5.82 ld(op_c, i(op_c))
% 42.24/5.82 = { by lemma 32 R->L }
% 42.24/5.82 ld(op_c, mult(op_c, mult(op_c, op_c)))
% 42.24/5.82 = { by axiom 3 (c02) }
% 42.24/5.82 mult(op_c, op_c)
% 42.24/5.82
% 42.24/5.82 Lemma 34: i(rd(X, Y)) = rd(Y, X).
% 42.24/5.82 Proof:
% 42.24/5.82 i(rd(X, Y))
% 42.24/5.82 = { by axiom 4 (c04) R->L }
% 42.24/5.82 rd(mult(i(rd(X, Y)), mult(rd(X, Y), Y)), mult(rd(X, Y), Y))
% 42.24/5.82 = { by axiom 8 (c08) }
% 42.24/5.82 rd(Y, mult(rd(X, Y), Y))
% 42.24/5.82 = { by axiom 7 (c03) }
% 42.24/5.82 rd(Y, X)
% 42.24/5.82
% 42.24/5.82 Lemma 35: ld(mult(X, X), Y) = ld(X, ld(X, Y)).
% 42.24/5.82 Proof:
% 42.24/5.82 ld(mult(X, X), Y)
% 42.24/5.82 = { by lemma 16 R->L }
% 42.24/5.82 mult(i(mult(X, X)), Y)
% 42.24/5.82 = { by axiom 6 (c09) }
% 42.24/5.82 mult(mult(i(X), i(X)), Y)
% 42.24/5.82 = { by lemma 21 }
% 42.24/5.82 mult(i(X), mult(i(X), Y))
% 42.24/5.82 = { by lemma 16 }
% 42.24/5.82 ld(X, mult(i(X), Y))
% 42.24/5.82 = { by lemma 16 }
% 42.24/5.82 ld(X, ld(X, Y))
% 42.24/5.82
% 42.24/5.82 Lemma 36: mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))) = mult(op_c, mult(op_c, mult(op_c, op_c))).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.82 = { by axiom 11 (c11) }
% 42.24/5.82 unit
% 42.24/5.82 = { by axiom 9 (c10) R->L }
% 42.24/5.82 mult(op_c, mult(op_c, mult(op_c, op_c)))
% 42.24/5.82
% 42.24/5.82 Lemma 37: i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))) = op_d.
% 42.24/5.82 Proof:
% 42.24/5.82 i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.82 = { by lemma 30 R->L }
% 42.24/5.82 rd(mult(op_c, mult(op_c, mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.82 = { by lemma 36 R->L }
% 42.24/5.82 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.82 = { by axiom 4 (c04) }
% 42.24/5.82 op_d
% 42.24/5.82
% 42.24/5.82 Lemma 38: mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))) = i(op_d).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.82 = { by lemma 14 R->L }
% 42.24/5.82 i(i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.24/5.82 = { by lemma 37 }
% 42.24/5.82 i(op_d)
% 42.24/5.82
% 42.24/5.82 Lemma 39: mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))) = i(mult(op_d, op_d)).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.82 = { by axiom 3 (c02) R->L }
% 42.24/5.82 ld(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.82 = { by lemma 38 }
% 42.24/5.82 ld(op_d, i(op_d))
% 42.24/5.82 = { by lemma 17 R->L }
% 42.24/5.82 i(mult(op_d, op_d))
% 42.24/5.82
% 42.24/5.82 Lemma 40: mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X) = ld(mult(op_d, op_d), X).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)
% 42.24/5.82 = { by lemma 39 }
% 42.24/5.82 mult(i(mult(op_d, op_d)), X)
% 42.24/5.82 = { by lemma 16 }
% 42.24/5.82 ld(mult(op_d, op_d), X)
% 42.24/5.82
% 42.24/5.82 Lemma 41: mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, X)) = X.
% 42.24/5.82 Proof:
% 42.24/5.82 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, X))
% 42.24/5.82 = { by lemma 38 }
% 42.24/5.82 mult(i(op_d), mult(op_d, X))
% 42.24/5.82 = { by axiom 8 (c08) }
% 42.24/5.82 X
% 42.24/5.82
% 42.24/5.82 Lemma 42: mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X) = ld(op_d, X).
% 42.24/5.82 Proof:
% 42.24/5.82 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)
% 42.24/5.82 = { by lemma 15 R->L }
% 42.24/5.83 ld(i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), X)
% 42.24/5.83 = { by lemma 37 }
% 42.24/5.83 ld(op_d, X)
% 42.24/5.83
% 42.24/5.83 Lemma 43: ld(mult(op_d, op_d), X) = ld(op_d, ld(op_d, X)).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_d, op_d), X)
% 42.24/5.83 = { by lemma 40 R->L }
% 42.24/5.83 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)
% 42.24/5.83 = { by lemma 41 R->L }
% 42.24/5.83 mult(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), X)
% 42.24/5.83 = { by lemma 21 }
% 42.24/5.83 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.24/5.83 = { by lemma 42 }
% 42.24/5.83 ld(op_d, mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.24/5.83 = { by lemma 42 }
% 42.24/5.83 ld(op_d, ld(op_d, X))
% 42.24/5.83
% 42.24/5.83 Lemma 44: ld(rd(X, Y), X) = Y.
% 42.24/5.83 Proof:
% 42.24/5.83 ld(rd(X, Y), X)
% 42.24/5.83 = { by axiom 7 (c03) R->L }
% 42.24/5.83 ld(rd(X, Y), mult(rd(X, Y), Y))
% 42.24/5.83 = { by axiom 3 (c02) }
% 42.24/5.83 Y
% 42.24/5.83
% 42.24/5.83 Lemma 45: i(ld(X, i(Y))) = mult(X, Y).
% 42.24/5.83 Proof:
% 42.24/5.83 i(ld(X, i(Y)))
% 42.24/5.83 = { by lemma 17 R->L }
% 42.24/5.83 i(i(mult(X, Y)))
% 42.24/5.83 = { by lemma 14 }
% 42.24/5.83 mult(X, Y)
% 42.24/5.83
% 42.24/5.83 Lemma 46: rd(mult(X, mult(Y, mult(X, Z))), Z) = mult(X, mult(Y, X)).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(mult(X, mult(Y, mult(X, Z))), Z)
% 42.24/5.83 = { by axiom 10 (c07) }
% 42.24/5.83 rd(mult(mult(X, mult(Y, X)), Z), Z)
% 42.24/5.83 = { by axiom 4 (c04) }
% 42.24/5.83 mult(X, mult(Y, X))
% 42.24/5.83
% 42.24/5.83 Lemma 47: ld(X, i(ld(Y, X))) = rd(ld(X, Y), X).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(X, i(ld(Y, X)))
% 42.24/5.83 = { by lemma 18 R->L }
% 42.24/5.83 ld(X, mult(Y, i(X)))
% 42.24/5.83 = { by lemma 16 R->L }
% 42.24/5.83 mult(i(X), mult(Y, i(X)))
% 42.24/5.83 = { by lemma 46 R->L }
% 42.24/5.83 rd(mult(i(X), mult(Y, mult(i(X), X))), X)
% 42.24/5.83 = { by lemma 13 R->L }
% 42.24/5.83 rd(mult(i(X), mult(Y, mult(op_c, mult(op_c, mult(op_c, op_c))))), X)
% 42.24/5.83 = { by lemma 16 }
% 42.24/5.83 rd(ld(X, mult(Y, mult(op_c, mult(op_c, mult(op_c, op_c))))), X)
% 42.24/5.83 = { by lemma 12 }
% 42.24/5.83 rd(ld(X, Y), X)
% 42.24/5.83
% 42.24/5.83 Lemma 48: mult(X, ld(Y, X)) = rd(X, ld(X, Y)).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(X, ld(Y, X))
% 42.24/5.83 = { by lemma 45 R->L }
% 42.24/5.83 i(ld(X, i(ld(Y, X))))
% 42.24/5.83 = { by lemma 47 }
% 42.24/5.83 i(rd(ld(X, Y), X))
% 42.24/5.83 = { by lemma 34 }
% 42.24/5.83 rd(X, ld(X, Y))
% 42.24/5.83
% 42.24/5.83 Lemma 49: ld(mult(op_c, mult(op_c, op_c)), X) = mult(op_c, X).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_c, mult(op_c, op_c)), X)
% 42.24/5.83 = { by lemma 16 R->L }
% 42.24/5.83 mult(i(mult(op_c, mult(op_c, op_c))), X)
% 42.24/5.83 = { by lemma 31 }
% 42.24/5.83 mult(op_c, X)
% 42.24/5.83
% 42.24/5.83 Lemma 50: mult(mult(op_c, op_c), X) = ld(mult(op_c, op_c), X).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(mult(op_c, op_c), X)
% 42.24/5.83 = { by lemma 15 R->L }
% 42.24/5.83 ld(i(mult(op_c, op_c)), X)
% 42.24/5.83 = { by lemma 33 }
% 42.24/5.83 ld(mult(op_c, op_c), X)
% 42.24/5.83
% 42.24/5.83 Lemma 51: ld(mult(op_c, mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), X)) = ld(mult(op_c, op_c), X).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_c, mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), X))
% 42.24/5.83 = { by lemma 49 }
% 42.24/5.83 ld(mult(op_c, mult(op_c, op_c)), mult(op_c, X))
% 42.24/5.83 = { by lemma 49 }
% 42.24/5.83 mult(op_c, mult(op_c, X))
% 42.24/5.83 = { by lemma 21 R->L }
% 42.24/5.83 mult(mult(op_c, op_c), X)
% 42.24/5.83 = { by lemma 50 }
% 42.24/5.83 ld(mult(op_c, op_c), X)
% 42.24/5.83
% 42.24/5.83 Lemma 52: mult(op_c, mult(op_c, X)) = ld(mult(op_c, op_c), X).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(op_c, mult(op_c, X))
% 42.24/5.83 = { by lemma 49 R->L }
% 42.24/5.83 ld(mult(op_c, mult(op_c, op_c)), mult(op_c, X))
% 42.24/5.83 = { by lemma 49 R->L }
% 42.24/5.83 ld(mult(op_c, mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), X))
% 42.24/5.83 = { by lemma 51 }
% 42.24/5.83 ld(mult(op_c, op_c), X)
% 42.24/5.83
% 42.24/5.83 Lemma 53: mult(rd(X, Y), Z) = ld(rd(Y, X), Z).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(rd(X, Y), Z)
% 42.24/5.83 = { by lemma 15 R->L }
% 42.24/5.83 ld(i(rd(X, Y)), Z)
% 42.24/5.83 = { by lemma 34 }
% 42.24/5.83 ld(rd(Y, X), Z)
% 42.24/5.83
% 42.24/5.83 Lemma 54: rd(ld(X, Y), Y) = i(X).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(ld(X, Y), Y)
% 42.24/5.83 = { by lemma 16 R->L }
% 42.24/5.83 rd(mult(i(X), Y), Y)
% 42.24/5.83 = { by axiom 4 (c04) }
% 42.24/5.83 i(X)
% 42.24/5.83
% 42.24/5.83 Lemma 55: ld(X, i(ld(X, Y))) = i(Y).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(X, i(ld(X, Y)))
% 42.24/5.83 = { by lemma 17 R->L }
% 42.24/5.83 i(mult(X, ld(X, Y)))
% 42.24/5.83 = { by axiom 5 (c01) }
% 42.24/5.83 i(Y)
% 42.24/5.83
% 42.24/5.83 Lemma 56: mult(X, rd(ld(X, Y), X)) = i(ld(Y, X)).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(X, rd(ld(X, Y), X))
% 42.24/5.83 = { by lemma 47 R->L }
% 42.24/5.83 mult(X, ld(X, i(ld(Y, X))))
% 42.24/5.83 = { by axiom 5 (c01) }
% 42.24/5.83 i(ld(Y, X))
% 42.24/5.83
% 42.24/5.83 Lemma 57: mult(X, rd(i(X), Y)) = ld(ld(X, Y), i(X)).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(X, rd(i(X), Y))
% 42.24/5.83 = { by lemma 14 R->L }
% 42.24/5.83 mult(X, rd(i(X), i(i(Y))))
% 42.24/5.83 = { by lemma 26 }
% 42.24/5.83 mult(X, rd(i(Y), X))
% 42.24/5.83 = { by lemma 55 R->L }
% 42.24/5.83 mult(X, rd(ld(X, i(ld(X, Y))), X))
% 42.24/5.83 = { by lemma 56 }
% 42.24/5.83 i(ld(i(ld(X, Y)), X))
% 42.24/5.83 = { by lemma 15 }
% 42.24/5.83 i(mult(ld(X, Y), X))
% 42.24/5.83 = { by lemma 17 }
% 42.24/5.83 ld(ld(X, Y), i(X))
% 42.24/5.83
% 42.24/5.83 Lemma 58: mult(ld(X, i(X)), Y) = ld(X, ld(X, Y)).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(ld(X, i(X)), Y)
% 42.24/5.83 = { by lemma 16 R->L }
% 42.24/5.83 mult(mult(i(X), i(X)), Y)
% 42.24/5.83 = { by lemma 21 }
% 42.24/5.83 mult(i(X), mult(i(X), Y))
% 42.24/5.83 = { by lemma 16 }
% 42.24/5.83 ld(X, mult(i(X), Y))
% 42.24/5.83 = { by lemma 16 }
% 42.24/5.83 ld(X, ld(X, Y))
% 42.24/5.83
% 42.24/5.83 Lemma 59: mult(ld(X, i(Y)), Z) = ld(mult(X, Y), Z).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(ld(X, i(Y)), Z)
% 42.24/5.83 = { by lemma 17 R->L }
% 42.24/5.83 mult(i(mult(X, Y)), Z)
% 42.24/5.83 = { by lemma 16 }
% 42.24/5.83 ld(mult(X, Y), Z)
% 42.24/5.83
% 42.24/5.83 Lemma 60: rd(X, ld(X, i(Y))) = mult(X, mult(Y, X)).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(X, ld(X, i(Y)))
% 42.24/5.83 = { by lemma 17 R->L }
% 42.24/5.83 rd(X, i(mult(X, Y)))
% 42.24/5.83 = { by lemma 27 R->L }
% 42.24/5.83 rd(mult(X, Y), i(X))
% 42.24/5.83 = { by lemma 12 R->L }
% 42.24/5.83 rd(mult(X, mult(Y, mult(op_c, mult(op_c, mult(op_c, op_c))))), i(X))
% 42.24/5.83 = { by lemma 20 }
% 42.24/5.83 rd(mult(X, mult(Y, mult(X, i(X)))), i(X))
% 42.24/5.83 = { by lemma 46 }
% 42.24/5.83 mult(X, mult(Y, X))
% 42.24/5.83
% 42.24/5.83 Lemma 61: rd(ld(X, i(Y)), Z) = rd(i(Z), mult(X, Y)).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(ld(X, i(Y)), Z)
% 42.24/5.83 = { by lemma 26 R->L }
% 42.24/5.83 rd(i(Z), i(ld(X, i(Y))))
% 42.24/5.83 = { by lemma 45 }
% 42.24/5.83 rd(i(Z), mult(X, Y))
% 42.24/5.83
% 42.24/5.83 Lemma 62: rd(i(X), mult(X, Y)) = ld(X, ld(Y, i(X))).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(i(X), mult(X, Y))
% 42.24/5.83 = { by lemma 61 R->L }
% 42.24/5.83 rd(ld(X, i(Y)), X)
% 42.24/5.83 = { by lemma 47 R->L }
% 42.24/5.83 ld(X, i(ld(i(Y), X)))
% 42.24/5.83 = { by lemma 15 }
% 42.24/5.83 ld(X, i(mult(Y, X)))
% 42.24/5.83 = { by lemma 17 }
% 42.24/5.83 ld(X, ld(Y, i(X)))
% 42.24/5.83
% 42.24/5.83 Lemma 63: ld(rd(X, mult(op_c, op_c)), mult(op_c, op_c)) = i(X).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(rd(X, mult(op_c, op_c)), mult(op_c, op_c))
% 42.24/5.83 = { by lemma 33 R->L }
% 42.24/5.83 ld(rd(X, mult(op_c, op_c)), i(mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 24 }
% 42.24/5.83 i(X)
% 42.24/5.83
% 42.24/5.83 Lemma 64: rd(mult(op_c, op_c), i(X)) = rd(X, mult(op_c, op_c)).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(mult(op_c, op_c), i(X))
% 42.24/5.83 = { by lemma 63 R->L }
% 42.24/5.83 rd(mult(op_c, op_c), ld(rd(X, mult(op_c, op_c)), mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 25 }
% 42.24/5.83 rd(X, mult(op_c, op_c))
% 42.24/5.83
% 42.24/5.83 Lemma 65: rd(rd(X, Y), i(Z)) = rd(Z, rd(Y, X)).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(rd(X, Y), i(Z))
% 42.24/5.83 = { by lemma 27 R->L }
% 42.24/5.83 rd(Z, i(rd(X, Y)))
% 42.24/5.83 = { by lemma 34 }
% 42.24/5.83 rd(Z, rd(Y, X))
% 42.24/5.83
% 42.24/5.83 Lemma 66: i(ld(X, mult(op_c, op_c))) = mult(X, mult(op_c, op_c)).
% 42.24/5.83 Proof:
% 42.24/5.83 i(ld(X, mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 18 R->L }
% 42.24/5.83 mult(X, i(mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 33 }
% 42.24/5.83 mult(X, mult(op_c, op_c))
% 42.24/5.83
% 42.24/5.83 Lemma 67: i(ld(X, rd(Y, Z))) = mult(X, rd(Z, Y)).
% 42.24/5.83 Proof:
% 42.24/5.83 i(ld(X, rd(Y, Z)))
% 42.24/5.83 = { by lemma 18 R->L }
% 42.24/5.83 mult(X, i(rd(Y, Z)))
% 42.24/5.83 = { by lemma 34 }
% 42.24/5.83 mult(X, rd(Z, Y))
% 42.24/5.83
% 42.24/5.83 Lemma 68: i(ld(mult(op_c, op_c), X)) = ld(mult(op_c, op_c), i(X)).
% 42.24/5.83 Proof:
% 42.24/5.83 i(ld(mult(op_c, op_c), X))
% 42.24/5.83 = { by lemma 50 R->L }
% 42.24/5.83 i(mult(mult(op_c, op_c), X))
% 42.24/5.83 = { by lemma 17 }
% 42.24/5.83 ld(mult(op_c, op_c), i(X))
% 42.24/5.83
% 42.24/5.83 Lemma 69: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X) = mult(op_d, X).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)
% 42.24/5.83 = { by lemma 16 R->L }
% 42.24/5.83 mult(i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), X)
% 42.24/5.83 = { by lemma 37 }
% 42.24/5.83 mult(op_d, X)
% 42.24/5.83
% 42.24/5.83 Lemma 70: i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)) = ld(op_d, i(X)).
% 42.24/5.83 Proof:
% 42.24/5.83 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.24/5.83 = { by lemma 69 }
% 42.24/5.83 i(mult(op_d, X))
% 42.24/5.83 = { by lemma 17 }
% 42.24/5.83 ld(op_d, i(X))
% 42.24/5.83
% 42.24/5.83 Lemma 71: ld(op_d, ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))) = ld(mult(op_d, op_c), i(mult(op_d, op_c))).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(op_d, ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.24/5.83 = { by lemma 50 R->L }
% 42.24/5.83 ld(op_d, mult(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.24/5.83 = { by lemma 42 R->L }
% 42.24/5.83 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.24/5.83 = { by lemma 46 R->L }
% 42.24/5.83 rd(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, op_c)))), mult(op_d, op_c))
% 42.24/5.83 = { by lemma 41 }
% 42.24/5.83 rd(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), op_c)), mult(op_d, op_c))
% 42.24/5.83 = { by lemma 42 }
% 42.24/5.83 rd(ld(op_d, mult(mult(op_c, op_c), op_c)), mult(op_d, op_c))
% 42.24/5.83 = { by lemma 50 }
% 42.24/5.83 rd(ld(op_d, ld(mult(op_c, op_c), op_c)), mult(op_d, op_c))
% 42.24/5.83 = { by lemma 52 R->L }
% 42.24/5.83 rd(ld(op_d, mult(op_c, mult(op_c, op_c))), mult(op_d, op_c))
% 42.24/5.83 = { by lemma 32 }
% 42.24/5.83 rd(ld(op_d, i(op_c)), mult(op_d, op_c))
% 42.24/5.83 = { by lemma 17 R->L }
% 42.24/5.83 rd(i(mult(op_d, op_c)), mult(op_d, op_c))
% 42.24/5.83 = { by lemma 29 }
% 42.24/5.83 ld(mult(op_d, op_c), i(mult(op_d, op_c)))
% 42.24/5.83
% 42.24/5.83 Lemma 72: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X) = mult(mult(op_d, op_d), X).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)
% 42.24/5.83 = { by lemma 39 }
% 42.24/5.83 ld(i(mult(op_d, op_d)), X)
% 42.24/5.83 = { by lemma 15 }
% 42.24/5.83 mult(mult(op_d, op_d), X)
% 42.24/5.83
% 42.24/5.83 Lemma 73: mult(ld(X, mult(op_c, op_c)), Y) = ld(mult(X, mult(op_c, op_c)), Y).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(ld(X, mult(op_c, op_c)), Y)
% 42.24/5.83 = { by lemma 33 R->L }
% 42.24/5.83 mult(ld(X, i(mult(op_c, op_c))), Y)
% 42.24/5.83 = { by lemma 59 }
% 42.24/5.83 ld(mult(X, mult(op_c, op_c)), Y)
% 42.24/5.83
% 42.24/5.83 Lemma 74: ld(mult(X, mult(op_c, op_c)), ld(X, mult(op_c, op_c))) = ld(X, i(X)).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(X, mult(op_c, op_c)), ld(X, mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 73 R->L }
% 42.24/5.83 mult(ld(X, mult(op_c, op_c)), ld(X, mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 23 R->L }
% 42.24/5.83 rd(ld(X, mult(op_c, op_c)), i(ld(X, mult(op_c, op_c))))
% 42.24/5.83 = { by lemma 66 }
% 42.24/5.83 rd(ld(X, mult(op_c, op_c)), mult(X, mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 16 R->L }
% 42.24/5.83 rd(mult(i(X), mult(op_c, op_c)), mult(X, mult(op_c, op_c)))
% 42.24/5.83 = { by axiom 8 (c08) R->L }
% 42.24/5.83 rd(mult(i(X), mult(i(X), mult(X, mult(op_c, op_c)))), mult(X, mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 22 }
% 42.24/5.83 mult(i(X), i(X))
% 42.24/5.83 = { by axiom 6 (c09) R->L }
% 42.24/5.83 i(mult(X, X))
% 42.24/5.83 = { by lemma 17 }
% 42.24/5.83 ld(X, i(X))
% 42.24/5.83
% 42.24/5.83 Lemma 75: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.24/5.83 = { by lemma 69 }
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, X))
% 42.24/5.83 = { by lemma 69 }
% 42.24/5.83 mult(op_d, mult(op_d, X))
% 42.24/5.83 = { by lemma 21 R->L }
% 42.24/5.83 mult(mult(op_d, op_d), X)
% 42.24/5.83 = { by lemma 72 R->L }
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)
% 42.24/5.83
% 42.24/5.83 Lemma 76: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X) = mult(op_d, mult(op_d, X)).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)
% 42.24/5.83 = { by lemma 75 R->L }
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.24/5.83 = { by lemma 69 }
% 42.24/5.83 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, X))
% 42.24/5.83 = { by lemma 69 }
% 42.24/5.83 mult(op_d, mult(op_d, X))
% 42.24/5.83
% 42.24/5.83 Lemma 77: ld(mult(op_d, op_d), mult(op_d, mult(op_d, X))) = X.
% 42.24/5.83 Proof:
% 42.24/5.83 ld(mult(op_d, op_d), mult(op_d, mult(op_d, X)))
% 42.24/5.83 = { by lemma 40 R->L }
% 42.24/5.83 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, X)))
% 42.24/5.83 = { by lemma 76 R->L }
% 42.24/5.83 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.24/5.83 = { by axiom 5 (c01) }
% 42.24/5.83 X
% 42.24/5.83
% 42.24/5.83 Lemma 78: ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), ld(mult(op_d, op_d), mult(op_c, op_c))) = mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))).
% 42.24/5.83 Proof:
% 42.24/5.83 ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), ld(mult(op_d, op_d), mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 72 }
% 42.24/5.83 ld(mult(mult(op_d, op_d), mult(op_c, op_c)), ld(mult(op_d, op_d), mult(op_c, op_c)))
% 42.24/5.83 = { by lemma 74 }
% 42.24/5.83 ld(mult(op_d, op_d), i(mult(op_d, op_d)))
% 42.24/5.83 = { by lemma 39 R->L }
% 42.24/5.83 ld(mult(op_d, op_d), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.83 = { by lemma 77 }
% 42.24/5.83 mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))
% 42.24/5.83
% 42.24/5.83 Lemma 79: mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))) = i(mult(op_d, mult(op_d, op_d))).
% 42.24/5.83 Proof:
% 42.24/5.83 mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.24/5.83 = { by axiom 3 (c02) R->L }
% 42.24/5.83 ld(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.83 = { by lemma 39 }
% 42.24/5.83 ld(op_d, i(mult(op_d, op_d)))
% 42.24/5.83 = { by lemma 17 R->L }
% 42.24/5.83 i(mult(op_d, mult(op_d, op_d)))
% 42.24/5.83
% 42.24/5.83 Lemma 80: i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))) = mult(op_d, mult(op_d, op_d)).
% 42.24/5.83 Proof:
% 42.24/5.83 i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.83 = { by lemma 79 }
% 42.24/5.83 i(i(mult(op_d, mult(op_d, op_d))))
% 42.24/5.83 = { by lemma 14 }
% 42.24/5.83 mult(op_d, mult(op_d, op_d))
% 42.24/5.83
% 42.24/5.83 Lemma 81: rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)) = rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))).
% 42.24/5.83 Proof:
% 42.24/5.83 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))
% 42.24/5.83 = { by lemma 64 R->L }
% 42.24/5.83 rd(mult(op_c, op_c), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.83 = { by lemma 80 }
% 42.24/5.83 rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d)))
% 42.24/5.83
% 42.24/5.84 Lemma 82: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.24/5.84 = { by lemma 75 R->L }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)))
% 42.24/5.84 = { by lemma 75 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.24/5.84
% 42.24/5.84 Lemma 83: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X) = mult(mult(op_d, mult(op_d, op_d)), X).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)
% 42.24/5.84 = { by lemma 79 }
% 42.24/5.84 ld(i(mult(op_d, mult(op_d, op_d))), X)
% 42.24/5.84 = { by lemma 15 }
% 42.24/5.84 mult(mult(op_d, mult(op_d, op_d)), X)
% 42.24/5.84
% 42.24/5.84 Lemma 84: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.24/5.84 = { by lemma 82 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.24/5.84 = { by lemma 69 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, X))
% 42.24/5.84 = { by lemma 75 R->L }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, X)))
% 42.24/5.84 = { by lemma 69 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, mult(op_d, X)))
% 42.24/5.84 = { by lemma 69 }
% 42.24/5.84 mult(op_d, mult(op_d, mult(op_d, X)))
% 42.24/5.84 = { by axiom 10 (c07) }
% 42.24/5.84 mult(mult(op_d, mult(op_d, op_d)), X)
% 42.24/5.84 = { by lemma 83 R->L }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)
% 42.24/5.84
% 42.24/5.84 Lemma 85: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X) = mult(op_d, mult(op_d, mult(op_d, X))).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)
% 42.24/5.84 = { by lemma 84 R->L }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.24/5.84 = { by lemma 76 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, mult(op_d, X)))
% 42.24/5.84 = { by lemma 69 }
% 42.24/5.84 mult(op_d, mult(op_d, mult(op_d, X)))
% 42.24/5.84
% 42.24/5.84 Lemma 86: rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))) = rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)).
% 42.24/5.84 Proof:
% 42.24/5.84 rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84 = { by lemma 79 }
% 42.24/5.84 rd(mult(op_c, op_c), i(mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 64 }
% 42.24/5.84 rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))
% 42.24/5.84
% 42.24/5.84 Lemma 87: rd(mult(X, Y), ld(X, Y)) = mult(X, X).
% 42.24/5.84 Proof:
% 42.24/5.84 rd(mult(X, Y), ld(X, Y))
% 42.24/5.84 = { by axiom 5 (c01) R->L }
% 42.24/5.84 rd(mult(X, mult(X, ld(X, Y))), ld(X, Y))
% 42.24/5.84 = { by lemma 22 }
% 42.24/5.84 mult(X, X)
% 42.24/5.84
% 42.24/5.84 Lemma 88: ld(rd(X, mult(op_c, op_c)), mult(X, X)) = rd(X, mult(op_c, op_c)).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(rd(X, mult(op_c, op_c)), mult(X, X))
% 42.24/5.84 = { by lemma 53 R->L }
% 42.24/5.84 mult(rd(mult(op_c, op_c), X), mult(X, X))
% 42.24/5.84 = { by lemma 23 R->L }
% 42.24/5.84 mult(rd(mult(op_c, op_c), X), rd(X, i(X)))
% 42.24/5.84 = { by axiom 7 (c03) R->L }
% 42.24/5.84 mult(rd(mult(op_c, op_c), X), rd(mult(rd(X, mult(op_c, op_c)), mult(op_c, op_c)), i(X)))
% 42.24/5.84 = { by lemma 63 R->L }
% 42.24/5.84 mult(rd(mult(op_c, op_c), X), rd(mult(rd(X, mult(op_c, op_c)), mult(op_c, op_c)), ld(rd(X, mult(op_c, op_c)), mult(op_c, op_c))))
% 42.24/5.84 = { by lemma 87 }
% 42.24/5.84 mult(rd(mult(op_c, op_c), X), mult(rd(X, mult(op_c, op_c)), rd(X, mult(op_c, op_c))))
% 42.24/5.84 = { by lemma 53 }
% 42.24/5.84 mult(rd(mult(op_c, op_c), X), ld(rd(mult(op_c, op_c), X), rd(X, mult(op_c, op_c))))
% 42.24/5.84 = { by axiom 5 (c01) }
% 42.24/5.84 rd(X, mult(op_c, op_c))
% 42.24/5.84
% 42.24/5.84 Lemma 89: ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))) = rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84 = { by lemma 85 R->L }
% 42.24/5.84 ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 86 }
% 42.24/5.84 ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 83 }
% 42.24/5.84 ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(mult(op_d, mult(op_d, op_d)), mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 88 }
% 42.24/5.84 rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 86 R->L }
% 42.24/5.84 rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84
% 42.24/5.84 Lemma 90: ld(rd(X, mult(op_c, op_c)), rd(mult(op_c, op_c), X)) = ld(X, i(X)).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(rd(X, mult(op_c, op_c)), rd(mult(op_c, op_c), X))
% 42.24/5.84 = { by lemma 53 R->L }
% 42.24/5.84 mult(rd(mult(op_c, op_c), X), rd(mult(op_c, op_c), X))
% 42.24/5.84 = { by lemma 22 R->L }
% 42.24/5.84 rd(mult(rd(mult(op_c, op_c), X), mult(rd(mult(op_c, op_c), X), X)), X)
% 42.24/5.84 = { by axiom 7 (c03) }
% 42.24/5.84 rd(mult(rd(mult(op_c, op_c), X), mult(op_c, op_c)), X)
% 42.24/5.84 = { by lemma 53 }
% 42.24/5.84 rd(ld(rd(X, mult(op_c, op_c)), mult(op_c, op_c)), X)
% 42.24/5.84 = { by lemma 63 }
% 42.24/5.84 rd(i(X), X)
% 42.24/5.84 = { by lemma 29 }
% 42.24/5.84 ld(X, i(X))
% 42.24/5.84
% 42.24/5.84 Lemma 91: rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)).
% 42.24/5.84 Proof:
% 42.24/5.84 rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84 = { by lemma 44 R->L }
% 42.24/5.84 ld(rd(mult(op_c, op_c), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))
% 42.24/5.84 = { by axiom 7 (c03) R->L }
% 42.24/5.84 ld(rd(mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 89 R->L }
% 42.24/5.84 ld(rd(mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 87 }
% 42.24/5.84 ld(mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 53 }
% 42.24/5.84 ld(ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 90 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 80 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, op_d))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 85 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))
% 42.24/5.84
% 42.24/5.84 Lemma 92: i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)) = ld(mult(op_d, mult(op_d, op_d)), i(X)).
% 42.24/5.84 Proof:
% 42.24/5.84 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X))
% 42.24/5.84 = { by lemma 83 }
% 42.24/5.84 i(mult(mult(op_d, mult(op_d, op_d)), X))
% 42.24/5.84 = { by lemma 17 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, op_d)), i(X))
% 42.24/5.84
% 42.24/5.84 Lemma 93: rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))) = ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)).
% 42.24/5.84 Proof:
% 42.24/5.84 rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d)))
% 42.24/5.84 = { by lemma 81 R->L }
% 42.24/5.84 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 34 R->L }
% 42.24/5.84 i(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.84 = { by lemma 91 }
% 42.24/5.84 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 92 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, op_d)), i(mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 33 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))
% 42.24/5.84
% 42.24/5.84 Lemma 94: mult(X, mult(ld(X, Y), X)) = rd(X, i(Y)).
% 42.24/5.84 Proof:
% 42.24/5.84 mult(X, mult(ld(X, Y), X))
% 42.24/5.84 = { by lemma 60 R->L }
% 42.24/5.84 rd(X, ld(X, i(ld(X, Y))))
% 42.24/5.84 = { by lemma 55 }
% 42.24/5.84 rd(X, i(Y))
% 42.24/5.84
% 42.24/5.84 Lemma 95: rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))) = mult(op_c, op_c).
% 42.24/5.84 Proof:
% 42.24/5.84 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 93 R->L }
% 42.24/5.84 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 81 R->L }
% 42.24/5.84 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 65 R->L }
% 42.24/5.84 rd(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.84 = { by lemma 94 R->L }
% 42.24/5.84 mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.84 = { by lemma 89 }
% 42.24/5.84 mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.84 = { by lemma 53 }
% 42.24/5.84 ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.84 = { by lemma 81 }
% 42.24/5.84 ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.84 = { by lemma 93 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.84 = { by lemma 53 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.84 = { by lemma 90 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.84 = { by lemma 80 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 85 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84 = { by lemma 79 }
% 42.24/5.84 ld(ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), i(mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 57 R->L }
% 42.24/5.84 mult(mult(op_d, mult(op_d, op_d)), rd(i(mult(op_d, mult(op_d, op_d))), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 79 R->L }
% 42.24/5.84 mult(mult(op_d, mult(op_d, op_d)), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 83 R->L }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 81 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))
% 42.24/5.84 = { by lemma 93 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 83 }
% 42.24/5.84 mult(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))
% 42.24/5.84 = { by axiom 5 (c01) }
% 42.24/5.84 mult(op_c, op_c)
% 42.24/5.84
% 42.24/5.84 Lemma 96: ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))) = ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84 = { by lemma 95 R->L }
% 42.24/5.84 ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84 = { by lemma 44 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))
% 42.24/5.84
% 42.24/5.84 Lemma 97: ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))) = rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.24/5.84 = { by lemma 96 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 33 R->L }
% 42.24/5.84 ld(mult(op_d, mult(op_d, op_d)), i(mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 92 R->L }
% 42.24/5.84 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)))
% 42.24/5.84 = { by lemma 91 R->L }
% 42.24/5.84 i(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.84 = { by lemma 34 }
% 42.24/5.84 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 81 }
% 42.24/5.84 rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d)))
% 42.24/5.84
% 42.24/5.84 Lemma 98: ld(rd(X, Y), rd(rd(X, Y), Y)) = ld(X, rd(X, Y)).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(rd(X, Y), rd(rd(X, Y), Y))
% 42.24/5.84 = { by lemma 26 R->L }
% 42.24/5.84 ld(rd(X, Y), rd(i(Y), i(rd(X, Y))))
% 42.24/5.84 = { by lemma 34 }
% 42.24/5.84 ld(rd(X, Y), rd(i(Y), rd(Y, X)))
% 42.24/5.84 = { by lemma 53 R->L }
% 42.24/5.84 mult(rd(Y, X), rd(i(Y), rd(Y, X)))
% 42.24/5.84 = { by lemma 24 R->L }
% 42.24/5.84 mult(rd(Y, X), rd(ld(rd(Y, X), i(X)), rd(Y, X)))
% 42.24/5.84 = { by lemma 56 }
% 42.24/5.84 i(ld(i(X), rd(Y, X)))
% 42.24/5.84 = { by lemma 67 }
% 42.24/5.84 mult(i(X), rd(X, Y))
% 42.24/5.84 = { by lemma 16 }
% 42.24/5.84 ld(X, rd(X, Y))
% 42.24/5.84
% 42.24/5.84 Lemma 99: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X) = ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)
% 42.24/5.84 = { by axiom 5 (c01) R->L }
% 42.24/5.84 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)))
% 42.24/5.84 = { by lemma 75 }
% 42.24/5.84 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.24/5.84 = { by lemma 42 }
% 42.24/5.84 ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.24/5.84
% 42.24/5.84 Lemma 100: mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X) = ld(mult(op_d, mult(op_d, op_d)), X).
% 42.24/5.84 Proof:
% 42.24/5.84 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)
% 42.24/5.84 = { by lemma 79 }
% 42.24/5.84 mult(i(mult(op_d, mult(op_d, op_d))), X)
% 42.24/5.84 = { by lemma 16 }
% 42.24/5.84 ld(mult(op_d, mult(op_d, op_d)), X)
% 42.24/5.84
% 42.24/5.84 Lemma 101: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), X)) = ld(mult(op_d, op_d), X).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), X))
% 42.24/5.84 = { by lemma 99 }
% 42.24/5.84 ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, op_d)), X)))
% 42.24/5.84 = { by lemma 100 R->L }
% 42.24/5.84 ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)))
% 42.24/5.84 = { by axiom 5 (c01) R->L }
% 42.24/5.84 ld(op_d, mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)))))
% 42.24/5.84 = { by lemma 84 }
% 42.24/5.84 ld(op_d, mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X))))
% 42.24/5.84 = { by lemma 42 }
% 42.24/5.84 ld(op_d, ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X))))
% 42.24/5.84 = { by axiom 3 (c02) }
% 42.24/5.84 ld(op_d, ld(op_d, X))
% 42.24/5.84 = { by lemma 43 R->L }
% 42.24/5.84 ld(mult(op_d, op_d), X)
% 42.24/5.84
% 42.24/5.84 Lemma 102: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)) = ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))).
% 42.24/5.84 Proof:
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))
% 42.24/5.84 = { by lemma 95 R->L }
% 42.24/5.84 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.84 = { by lemma 98 R->L }
% 42.24/5.84 ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), rd(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.84 = { by lemma 95 }
% 42.24/5.84 ld(mult(op_c, op_c), rd(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.84 = { by lemma 95 }
% 42.24/5.84 ld(mult(op_c, op_c), rd(mult(op_c, op_c), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.84 = { by lemma 25 }
% 42.24/5.85 ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d)))
% 42.24/5.85
% 42.24/5.85 Lemma 103: ld(mult(op_c, op_c), ld(mult(op_c, op_c), X)) = X.
% 42.24/5.85 Proof:
% 42.24/5.85 ld(mult(op_c, op_c), ld(mult(op_c, op_c), X))
% 42.24/5.85 = { by lemma 58 R->L }
% 42.24/5.85 mult(ld(mult(op_c, op_c), i(mult(op_c, op_c))), X)
% 42.24/5.85 = { by lemma 33 }
% 42.24/5.85 mult(ld(mult(op_c, op_c), mult(op_c, op_c)), X)
% 42.24/5.85 = { by lemma 19 R->L }
% 42.24/5.85 mult(mult(op_c, mult(op_c, mult(op_c, op_c))), X)
% 42.24/5.85 = { by axiom 9 (c10) }
% 42.24/5.85 mult(unit, X)
% 42.24/5.85 = { by axiom 2 (c06) }
% 42.24/5.85 X
% 42.24/5.85
% 42.24/5.85 Lemma 104: ld(mult(op_d, mult(op_d, op_d)), mult(op_d, mult(op_d, mult(op_d, X)))) = X.
% 42.24/5.85 Proof:
% 42.24/5.85 ld(mult(op_d, mult(op_d, op_d)), mult(op_d, mult(op_d, mult(op_d, X))))
% 42.24/5.85 = { by lemma 100 R->L }
% 42.24/5.85 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, mult(op_d, X))))
% 42.24/5.85 = { by lemma 85 R->L }
% 42.24/5.85 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X))
% 42.24/5.85 = { by axiom 5 (c01) }
% 42.24/5.85 X
% 42.24/5.85
% 42.24/5.85 Lemma 105: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))) = ld(mult(op_d, op_d), mult(op_c, op_c)).
% 42.24/5.85 Proof:
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.24/5.85 = { by lemma 97 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))
% 42.24/5.85 = { by lemma 34 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 28 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, mult(op_c, mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 19 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), ld(mult(op_c, op_c), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 50 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(mult(op_c, op_c), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 23 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), rd(mult(op_c, op_c), i(mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 55 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), rd(mult(op_c, op_c), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by lemma 16 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), rd(mult(op_c, op_c), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by lemma 16 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), rd(mult(op_c, op_c), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by lemma 67 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(ld(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), rd(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 44 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(ld(rd(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), ld(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), rd(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), mult(op_c, op_c)))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))))
% 42.24/5.85 = { by lemma 48 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(ld(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), ld(rd(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), mult(op_c, op_c)), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))))
% 42.24/5.85 = { by lemma 53 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(ld(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), mult(rd(mult(op_c, op_c), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))))
% 42.24/5.85 = { by lemma 46 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(ld(rd(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), mult(rd(mult(op_c, op_c), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))))), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))))), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))))
% 42.24/5.85 = { by axiom 7 (c03) }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(ld(rd(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), mult(op_c, op_c)), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))))
% 42.24/5.85 = { by lemma 45 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(rd(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), mult(op_c, op_c)), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 53 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), mult(op_c, op_c))), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 16 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 29 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(ld(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), i(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 17 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(i(mult(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 15 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 21 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), mult(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 63 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(i(mult(op_d, mult(op_d, op_d))), mult(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 16 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), mult(ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 73 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), ld(mult(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 16 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), mult(i(mult(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 45 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), i(ld(i(mult(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by axiom 6 (c09) }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), i(ld(mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(mult(op_c, op_c))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by lemma 56 R->L }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), rd(ld(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), i(mult(op_c, op_c)))), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by axiom 3 (c02) }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), mult(i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), rd(i(mult(op_c, op_c)), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by lemma 16 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), rd(i(mult(op_c, op_c)), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))))
% 42.24/5.85 = { by lemma 26 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), rd(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 98 }
% 42.24/5.85 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, op_d)), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 101 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(mult(op_d, mult(op_d, op_d)), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 98 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), rd(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 64 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(rd(mult(op_c, op_c), i(mult(op_d, mult(op_d, op_d)))), rd(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 79 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), rd(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 91 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), rd(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 102 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(op_c, op_c))))
% 42.24/5.85 = { by lemma 64 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), i(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))))
% 42.24/5.85 = { by lemma 34 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.85 = { by lemma 97 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.24/5.85 = { by lemma 50 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), mult(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.24/5.85 = { by lemma 33 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(i(mult(op_c, op_c)), mult(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.24/5.85 = { by lemma 62 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), i(mult(op_c, op_c))))))
% 42.24/5.85 = { by lemma 33 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)))))
% 42.24/5.85 = { by lemma 102 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), ld(mult(op_c, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.85 = { by lemma 103 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(op_d, mult(op_d, op_d))))
% 42.24/5.85 = { by lemma 104 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, op_d)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.85 = { by lemma 79 }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, op_d)), i(mult(op_d, mult(op_d, op_d))))))
% 42.24/5.85 = { by lemma 90 R->L }
% 42.24/5.85 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.85 = { by lemma 53 R->L }
% 42.24/5.86 ld(mult(op_d, op_d), ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 102 R->L }
% 42.24/5.86 ld(mult(op_d, op_d), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 91 R->L }
% 42.24/5.86 ld(mult(op_d, op_d), ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 86 }
% 42.24/5.86 ld(mult(op_d, op_d), ld(rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c)), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 53 R->L }
% 42.24/5.86 ld(mult(op_d, op_d), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 81 R->L }
% 42.24/5.86 ld(mult(op_d, op_d), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 88 R->L }
% 42.24/5.86 ld(mult(op_d, op_d), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 100 }
% 42.24/5.86 ld(mult(op_d, op_d), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c)), ld(mult(op_d, mult(op_d, op_d)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 81 }
% 42.24/5.86 ld(mult(op_d, op_d), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, op_d)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 104 }
% 42.24/5.86 ld(mult(op_d, op_d), mult(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(ld(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), mult(op_d, mult(op_d, op_d))), rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))))))
% 42.24/5.86 = { by lemma 94 }
% 42.24/5.86 ld(mult(op_d, op_d), rd(rd(mult(op_c, op_c), mult(op_d, mult(op_d, op_d))), i(mult(op_d, mult(op_d, op_d)))))
% 42.24/5.86 = { by lemma 65 }
% 42.24/5.86 ld(mult(op_d, op_d), rd(mult(op_d, mult(op_d, op_d)), rd(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))))
% 42.24/5.86 = { by lemma 86 R->L }
% 42.24/5.86 ld(mult(op_d, op_d), rd(mult(op_d, mult(op_d, op_d)), rd(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.86 = { by lemma 91 }
% 42.24/5.86 ld(mult(op_d, op_d), rd(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))))
% 42.24/5.86 = { by lemma 102 }
% 42.24/5.86 ld(mult(op_d, op_d), rd(mult(op_d, mult(op_d, op_d)), ld(mult(op_c, op_c), mult(op_d, mult(op_d, op_d)))))
% 42.24/5.86 = { by lemma 25 }
% 42.24/5.86 ld(mult(op_d, op_d), mult(op_c, op_c))
% 42.24/5.86
% 42.24/5.86 Lemma 106: rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, mult(op_d, Y))), Y) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, op_d)).
% 42.24/5.86 Proof:
% 42.24/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, mult(op_d, Y))), Y)
% 42.24/5.86 = { by lemma 69 }
% 42.24/5.86 rd(mult(op_d, mult(X, mult(op_d, Y))), Y)
% 42.24/5.86 = { by lemma 46 }
% 42.24/5.86 mult(op_d, mult(X, op_d))
% 42.24/5.86 = { by lemma 69 R->L }
% 42.24/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, op_d))
% 42.24/5.86
% 42.24/5.86 Lemma 107: rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(X, mult(op_d, Y))), Y) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(X, op_d)).
% 42.24/5.86 Proof:
% 42.24/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(X, mult(op_d, Y))), Y)
% 42.24/5.86 = { by lemma 16 R->L }
% 42.24/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(i(X), mult(op_d, Y))), Y)
% 42.24/5.86 = { by lemma 106 }
% 42.24/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(i(X), op_d))
% 42.24/5.86 = { by lemma 16 }
% 42.24/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(X, op_d))
% 42.24/5.86
% 42.24/5.86 Lemma 108: ld(mult(op_c, mult(op_c, op_c)), mult(op_c, X)) = ld(mult(op_c, op_c), X).
% 42.24/5.86 Proof:
% 42.24/5.86 ld(mult(op_c, mult(op_c, op_c)), mult(op_c, X))
% 42.24/5.86 = { by lemma 49 R->L }
% 42.24/5.86 ld(mult(op_c, mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), X))
% 42.24/5.86 = { by lemma 51 }
% 42.24/5.86 ld(mult(op_c, op_c), X)
% 42.24/5.86
% 42.24/5.86 Lemma 109: rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, op_d)).
% 42.24/5.86 Proof:
% 42.24/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.86 = { by lemma 12 R->L }
% 42.24/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, mult(op_c, mult(op_c, mult(op_c, op_c))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.86 = { by lemma 36 R->L }
% 42.24/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.86 = { by lemma 69 }
% 42.24/5.86 rd(mult(op_d, mult(X, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.24/5.86 = { by lemma 46 }
% 42.24/5.86 mult(op_d, mult(X, op_d))
% 42.24/5.86 = { by lemma 69 R->L }
% 42.24/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(X, op_d))
% 42.24/5.86
% 42.24/5.86 Lemma 110: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d))) = mult(mult(op_d, op_c), mult(op_d, op_c)).
% 42.24/5.86 Proof:
% 42.73/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.86 = { by lemma 108 }
% 42.73/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), op_d))
% 42.73/5.86 = { by lemma 50 R->L }
% 42.73/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), op_d))
% 42.73/5.86 = { by lemma 109 R->L }
% 42.73/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.73/5.86 = { by lemma 47 R->L }
% 42.73/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))
% 42.73/5.86 = { by lemma 17 R->L }
% 42.73/5.86 i(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))
% 42.73/5.86 = { by lemma 42 }
% 42.73/5.86 i(ld(op_d, ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))
% 42.73/5.86 = { by lemma 71 }
% 42.73/5.86 i(ld(mult(op_d, op_c), i(mult(op_d, op_c))))
% 42.73/5.86 = { by lemma 45 }
% 42.73/5.86 mult(mult(op_d, op_c), mult(op_d, op_c))
% 42.73/5.86
% 42.73/5.86 Lemma 111: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)) = mult(mult(op_d, op_c), mult(op_d, op_c)).
% 42.73/5.86 Proof:
% 42.73/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c))
% 42.73/5.86 = { by lemma 25 R->L }
% 42.73/5.86 rd(ld(mult(op_d, op_d), mult(op_c, op_c)), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), ld(mult(op_d, op_d), mult(op_c, op_c))))
% 42.73/5.86 = { by lemma 78 }
% 42.73/5.86 rd(ld(mult(op_d, op_d), mult(op_c, op_c)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.73/5.86 = { by lemma 105 R->L }
% 42.73/5.86 rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.73/5.86 = { by lemma 107 }
% 42.73/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), op_d))
% 42.73/5.86 = { by lemma 108 R->L }
% 42.73/5.86 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.86 = { by lemma 110 }
% 42.73/5.86 mult(mult(op_d, op_c), mult(op_d, op_c))
% 42.73/5.86
% 42.73/5.86 Lemma 112: ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), X))) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X).
% 42.73/5.86 Proof:
% 42.73/5.86 ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), X)))
% 42.73/5.86 = { by lemma 69 }
% 42.73/5.86 ld(mult(op_c, op_c), mult(op_d, ld(mult(op_c, op_c), X)))
% 42.73/5.86 = { by lemma 16 R->L }
% 42.73/5.86 ld(mult(op_c, op_c), mult(op_d, mult(i(mult(op_c, op_c)), X)))
% 42.73/5.86 = { by lemma 16 R->L }
% 42.73/5.86 mult(i(mult(op_c, op_c)), mult(op_d, mult(i(mult(op_c, op_c)), X)))
% 42.73/5.86 = { by axiom 10 (c07) }
% 42.73/5.86 mult(mult(i(mult(op_c, op_c)), mult(op_d, i(mult(op_c, op_c)))), X)
% 42.73/5.86 = { by lemma 16 }
% 42.73/5.86 mult(ld(mult(op_c, op_c), mult(op_d, i(mult(op_c, op_c)))), X)
% 42.73/5.86 = { by lemma 18 }
% 42.73/5.86 mult(ld(mult(op_c, op_c), i(ld(op_d, mult(op_c, op_c)))), X)
% 42.73/5.87 = { by lemma 59 }
% 42.73/5.87 ld(mult(mult(op_c, op_c), ld(op_d, mult(op_c, op_c))), X)
% 42.73/5.87 = { by lemma 48 }
% 42.73/5.87 ld(rd(mult(op_c, op_c), ld(mult(op_c, op_c), op_d)), X)
% 42.73/5.87 = { by lemma 37 R->L }
% 42.73/5.87 ld(rd(mult(op_c, op_c), ld(mult(op_c, op_c), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), X)
% 42.73/5.87 = { by lemma 68 R->L }
% 42.73/5.87 ld(rd(mult(op_c, op_c), i(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), X)
% 42.73/5.87 = { by lemma 55 R->L }
% 42.73/5.87 ld(rd(mult(op_c, op_c), ld(op_d, i(ld(op_d, ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))))), X)
% 42.73/5.87 = { by lemma 71 }
% 42.73/5.87 ld(rd(mult(op_c, op_c), ld(op_d, i(ld(mult(op_d, op_c), i(mult(op_d, op_c)))))), X)
% 42.73/5.87 = { by lemma 45 }
% 42.73/5.87 ld(rd(mult(op_c, op_c), ld(op_d, mult(mult(op_d, op_c), mult(op_d, op_c)))), X)
% 42.73/5.87 = { by lemma 111 R->L }
% 42.73/5.87 ld(rd(mult(op_c, op_c), ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)))), X)
% 42.73/5.87 = { by lemma 99 R->L }
% 42.73/5.87 ld(rd(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))), X)
% 42.73/5.87 = { by lemma 25 }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)
% 42.73/5.87
% 42.73/5.87 Lemma 113: ld(mult(op_c, op_c), ld(op_d, X)) = ld(op_d, ld(mult(op_c, op_c), X)).
% 42.73/5.87 Proof:
% 42.73/5.87 ld(mult(op_c, op_c), ld(op_d, X))
% 42.73/5.87 = { by lemma 14 R->L }
% 42.73/5.87 ld(mult(op_c, op_c), ld(op_d, i(i(X))))
% 42.73/5.87 = { by lemma 70 R->L }
% 42.73/5.87 ld(mult(op_c, op_c), i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(X))))
% 42.73/5.87 = { by lemma 68 R->L }
% 42.73/5.87 i(ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(X))))
% 42.73/5.87 = { by axiom 3 (c02) R->L }
% 42.73/5.87 i(ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), mult(mult(op_c, op_c), i(X))))))
% 42.73/5.87 = { by lemma 112 }
% 42.73/5.87 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), i(X))))
% 42.73/5.87 = { by lemma 50 }
% 42.73/5.87 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), i(X))))
% 42.73/5.87 = { by lemma 17 R->L }
% 42.73/5.87 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(mult(mult(op_c, op_c), X))))
% 42.73/5.87 = { by lemma 45 }
% 42.73/5.87 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), X))
% 42.73/5.87 = { by lemma 42 }
% 42.73/5.87 ld(op_d, mult(mult(op_c, op_c), X))
% 42.73/5.87 = { by lemma 50 }
% 42.73/5.87 ld(op_d, ld(mult(op_c, op_c), X))
% 42.73/5.87
% 42.73/5.87 Lemma 114: i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))) = mult(op_d, op_d).
% 42.73/5.87 Proof:
% 42.73/5.87 i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.73/5.87 = { by lemma 41 R->L }
% 42.73/5.87 i(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.73/5.87 = { by lemma 17 }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.73/5.87 = { by lemma 37 }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), op_d)
% 42.73/5.87 = { by lemma 69 }
% 42.73/5.87 mult(op_d, op_d)
% 42.73/5.87
% 42.73/5.87 Lemma 115: mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))) = i(mult(op_d, mult(op_d, mult(op_d, op_d)))).
% 42.73/5.87 Proof:
% 42.73/5.87 mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))
% 42.73/5.87 = { by axiom 3 (c02) R->L }
% 42.73/5.87 ld(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.73/5.87 = { by lemma 79 }
% 42.73/5.87 ld(op_d, i(mult(op_d, mult(op_d, op_d))))
% 42.73/5.87 = { by lemma 17 R->L }
% 42.73/5.87 i(mult(op_d, mult(op_d, mult(op_d, op_d))))
% 42.73/5.87
% 42.73/5.87 Lemma 116: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X) = mult(mult(op_d, mult(op_d, mult(op_d, op_d))), X).
% 42.73/5.87 Proof:
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.73/5.87 = { by lemma 115 }
% 42.73/5.87 ld(i(mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.73/5.87 = { by lemma 15 }
% 42.73/5.87 mult(mult(op_d, mult(op_d, mult(op_d, op_d))), X)
% 42.73/5.87
% 42.73/5.87 Lemma 117: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X).
% 42.73/5.87 Proof:
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.73/5.87 = { by lemma 58 R->L }
% 42.73/5.87 mult(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), X)
% 42.73/5.87 = { by lemma 114 }
% 42.73/5.87 mult(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, op_d)), X)
% 42.73/5.87 = { by lemma 76 }
% 42.73/5.87 mult(mult(op_d, mult(op_d, mult(op_d, op_d))), X)
% 42.73/5.87 = { by lemma 116 R->L }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.73/5.87
% 42.73/5.87 Lemma 118: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X).
% 42.73/5.87 Proof:
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X))
% 42.73/5.87 = { by lemma 84 R->L }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)))
% 42.73/5.87 = { by lemma 75 }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.73/5.87 = { by lemma 117 }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.73/5.87
% 42.73/5.87 Lemma 119: mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X) = ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X).
% 42.73/5.87 Proof:
% 42.73/5.87 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.73/5.87 = { by lemma 115 }
% 42.73/5.87 mult(i(mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.73/5.87 = { by lemma 16 }
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X)
% 42.73/5.87
% 42.73/5.87 Lemma 120: ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X) = ld(mult(op_d, op_d), ld(mult(op_d, op_d), X)).
% 42.73/5.87 Proof:
% 42.73/5.87 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X)
% 42.73/5.87 = { by lemma 119 R->L }
% 42.73/5.87 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.73/5.88 = { by lemma 77 R->L }
% 42.73/5.88 mult(ld(mult(op_d, op_d), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)
% 42.73/5.88 = { by lemma 39 }
% 42.73/5.88 mult(ld(mult(op_d, op_d), i(mult(op_d, op_d))), X)
% 42.73/5.88 = { by lemma 58 }
% 42.73/5.88 ld(mult(op_d, op_d), ld(mult(op_d, op_d), X))
% 42.73/5.88
% 42.73/5.88 Lemma 121: ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))) = ld(mult(op_d, op_d), mult(op_c, op_c)).
% 42.73/5.88 Proof:
% 42.73/5.88 ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.73/5.88 = { by axiom 7 (c03) R->L }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 108 }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), op_d)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 50 R->L }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), op_d)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 34 R->L }
% 42.73/5.88 mult(i(rd(mult(mult(op_c, op_c), op_d), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by axiom 7 (c03) R->L }
% 42.73/5.88 mult(i(rd(mult(mult(op_c, op_c), mult(rd(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by axiom 5 (c01) R->L }
% 42.73/5.88 mult(i(rd(mult(mult(op_c, op_c), mult(rd(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 46 }
% 42.73/5.88 mult(i(mult(mult(op_c, op_c), mult(rd(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c)))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 53 }
% 42.73/5.88 mult(i(mult(mult(op_c, op_c), ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d), mult(op_c, op_c)))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 48 }
% 42.73/5.88 mult(i(rd(mult(op_c, op_c), ld(mult(op_c, op_c), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 34 }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 37 R->L }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 28 R->L }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, mult(op_c, mult(op_c, op_c)))))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 19 }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 84 }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 25 }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 12 R->L }
% 42.73/5.88 mult(rd(ld(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, mult(op_c, op_c))))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 50 R->L }
% 42.73/5.88 mult(rd(mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, mult(op_c, op_c))))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 21 R->L }
% 42.73/5.88 mult(rd(mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(mult(op_c, op_c), mult(op_c, op_c)))), mult(op_c, op_c)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 46 }
% 42.73/5.88 mult(mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 50 }
% 42.73/5.88 mult(ld(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, op_c))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 100 }
% 42.73/5.88 mult(ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, op_d)), mult(op_c, op_c))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 96 R->L }
% 42.73/5.88 mult(ld(mult(op_c, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 103 }
% 42.73/5.88 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.88 = { by lemma 100 }
% 42.73/5.88 ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))
% 42.73/5.89 = { by axiom 5 (c01) R->L }
% 42.73/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))))
% 42.73/5.89 = { by lemma 100 R->L }
% 42.73/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d)))))
% 42.73/5.89 = { by lemma 118 R->L }
% 42.73/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d))))))
% 42.73/5.89 = { by axiom 3 (c02) }
% 42.73/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d))))
% 42.73/5.89 = { by lemma 119 }
% 42.73/5.89 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, mult(op_c, op_c)), mult(op_c, op_d))))
% 42.73/5.89 = { by lemma 110 }
% 42.73/5.89 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(mult(op_d, op_c), mult(op_d, op_c)))
% 42.73/5.89 = { by lemma 111 R->L }
% 42.73/5.89 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)))
% 42.73/5.89 = { by lemma 72 }
% 42.73/5.89 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(mult(op_d, op_d), mult(op_c, op_c)))
% 42.73/5.89 = { by lemma 120 }
% 42.73/5.89 ld(mult(op_d, op_d), ld(mult(op_d, op_d), mult(mult(op_d, op_d), mult(op_c, op_c))))
% 42.73/5.89 = { by axiom 3 (c02) }
% 42.73/5.89 ld(mult(op_d, op_d), mult(op_c, op_c))
% 42.73/5.89
% 42.73/5.89 Lemma 122: ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))) = ld(mult(op_d, op_c), i(mult(op_d, op_c))).
% 42.73/5.89 Proof:
% 42.73/5.89 ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.73/5.89 = { by lemma 121 }
% 42.73/5.89 ld(mult(op_d, op_d), mult(op_c, op_c))
% 42.73/5.89 = { by lemma 33 R->L }
% 42.73/5.89 ld(mult(op_d, op_d), i(mult(op_c, op_c)))
% 42.73/5.89 = { by lemma 17 R->L }
% 42.73/5.89 i(mult(mult(op_d, op_d), mult(op_c, op_c)))
% 42.73/5.89 = { by lemma 72 R->L }
% 42.73/5.89 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)))
% 42.73/5.89 = { by lemma 54 R->L }
% 42.73/5.89 rd(ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), ld(mult(op_d, op_d), mult(op_c, op_c))), ld(mult(op_d, op_d), mult(op_c, op_c)))
% 42.94/5.89 = { by lemma 78 }
% 42.94/5.89 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_d), mult(op_c, op_c)))
% 42.94/5.89 = { by lemma 105 R->L }
% 42.94/5.89 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.94/5.89 = { by lemma 34 R->L }
% 42.94/5.89 i(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.94/5.89 = { by lemma 107 }
% 42.94/5.89 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), op_d)))
% 42.94/5.89 = { by lemma 70 }
% 42.94/5.89 ld(op_d, i(ld(mult(op_c, op_c), op_d)))
% 42.94/5.89 = { by lemma 47 }
% 42.94/5.89 rd(ld(op_d, mult(op_c, op_c)), op_d)
% 42.94/5.89 = { by lemma 12 R->L }
% 42.94/5.89 rd(ld(op_d, mult(mult(op_c, op_c), mult(op_c, mult(op_c, mult(op_c, op_c))))), op_d)
% 42.94/5.89 = { by lemma 42 R->L }
% 42.94/5.89 rd(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), mult(op_c, mult(op_c, mult(op_c, op_c))))), op_d)
% 42.94/5.89 = { by lemma 20 }
% 42.94/5.89 rd(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))), op_d)
% 42.94/5.89 = { by lemma 37 }
% 42.94/5.89 rd(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), op_d))), op_d)
% 42.94/5.89 = { by lemma 46 }
% 42.94/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.94/5.89 = { by lemma 42 }
% 42.94/5.89 ld(op_d, mult(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.94/5.89 = { by lemma 50 }
% 42.94/5.89 ld(op_d, ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))
% 42.94/5.89 = { by lemma 71 }
% 42.94/5.89 ld(mult(op_d, op_c), i(mult(op_d, op_c)))
% 42.94/5.89
% 42.94/5.89 Lemma 123: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)) = ld(mult(op_c, op_c), mult(op_d, op_d)).
% 42.94/5.89 Proof:
% 42.94/5.89 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c))
% 42.94/5.89 = { by lemma 111 }
% 42.94/5.89 mult(mult(op_d, op_c), mult(op_d, op_c))
% 42.94/5.89 = { by lemma 45 R->L }
% 42.94/5.89 i(ld(mult(op_d, op_c), i(mult(op_d, op_c))))
% 42.94/5.89 = { by lemma 122 R->L }
% 42.94/5.89 i(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.94/5.89 = { by lemma 68 }
% 42.94/5.89 ld(mult(op_c, op_c), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.94/5.89 = { by lemma 114 }
% 42.94/5.89 ld(mult(op_c, op_c), mult(op_d, op_d))
% 42.94/5.89
% 42.94/5.89 Lemma 124: ld(ld(mult(op_c, op_c), mult(op_d, op_d)), X) = ld(mult(op_d, op_c), ld(mult(op_d, op_c), X)).
% 42.94/5.89 Proof:
% 42.94/5.89 ld(ld(mult(op_c, op_c), mult(op_d, op_d)), X)
% 42.94/5.89 = { by lemma 123 R->L }
% 42.94/5.89 ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), X)
% 42.94/5.89 = { by lemma 111 }
% 42.94/5.89 ld(mult(mult(op_d, op_c), mult(op_d, op_c)), X)
% 42.94/5.89 = { by lemma 35 }
% 42.94/5.89 ld(mult(op_d, op_c), ld(mult(op_d, op_c), X))
% 42.94/5.89
% 42.94/5.89 Lemma 125: ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)) = ld(mult(op_d, op_d), X).
% 42.94/5.89 Proof:
% 42.94/5.89 ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.94/5.89 = { by lemma 100 R->L }
% 42.94/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.94/5.89 = { by axiom 3 (c02) R->L }
% 42.94/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))))
% 42.94/5.89 = { by lemma 84 }
% 42.94/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)))
% 42.94/5.89 = { by lemma 40 }
% 42.94/5.89 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, op_d), X)))
% 42.94/5.89 = { by axiom 5 (c01) }
% 42.94/5.89 ld(mult(op_d, op_d), X)
% 42.94/5.89
% 42.94/5.90 Lemma 126: ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X) = ld(mult(op_d, mult(op_d, op_d)), ld(op_d, X)).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X)
% 42.94/5.90 = { by lemma 120 }
% 42.94/5.90 ld(mult(op_d, op_d), ld(mult(op_d, op_d), X))
% 42.94/5.90 = { by lemma 125 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, op_d), X)))
% 42.94/5.90 = { by lemma 69 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), mult(op_d, ld(mult(op_d, op_d), X)))
% 42.94/5.90 = { by lemma 43 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), mult(op_d, ld(op_d, ld(op_d, X))))
% 42.94/5.90 = { by axiom 5 (c01) }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), ld(op_d, X))
% 42.94/5.90
% 42.94/5.90 Lemma 127: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), i(mult(op_d, op_c))).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c)))
% 42.94/5.90 = { by lemma 32 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), i(op_c))
% 42.94/5.90 = { by lemma 41 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), i(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, op_c))))
% 42.94/5.90 = { by lemma 17 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(mult(op_d, op_c))))
% 42.94/5.90 = { by lemma 84 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(mult(op_d, op_c)))))
% 42.94/5.90 = { by lemma 82 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), i(mult(op_d, op_c)))))
% 42.94/5.90 = { by lemma 75 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), i(mult(op_d, op_c))))
% 42.94/5.90 = { by lemma 117 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), i(mult(op_d, op_c)))
% 42.94/5.90
% 42.94/5.90 Lemma 128: ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)) = ld(mult(op_d, mult(op_d, op_d)), op_c).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c))
% 42.94/5.90 = { by lemma 119 R->L }
% 42.94/5.90 mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_d, op_c))
% 42.94/5.90 = { by lemma 45 R->L }
% 42.94/5.90 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), i(mult(op_d, op_c))))
% 42.94/5.90 = { by lemma 127 R->L }
% 42.94/5.90 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))))
% 42.94/5.90 = { by lemma 92 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), i(mult(op_c, mult(op_c, op_c))))
% 42.94/5.90 = { by lemma 31 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), op_c)
% 42.94/5.90
% 42.94/5.90 Lemma 129: mult(X, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))) = i(ld(X, mult(op_d, mult(op_d, mult(op_d, op_d))))).
% 42.94/5.90 Proof:
% 42.94/5.90 mult(X, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.94/5.90 = { by lemma 115 }
% 42.94/5.90 mult(X, i(mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.94/5.90 = { by lemma 18 }
% 42.94/5.90 i(ld(X, mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.94/5.90
% 42.94/5.90 Lemma 130: ld(mult(op_d, op_c), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d))))) = ld(mult(op_c, op_c), mult(op_d, op_d)).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.94/5.90 = { by lemma 76 R->L }
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, op_d))))
% 42.94/5.90 = { by lemma 72 }
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_d, op_c), mult(mult(op_d, op_d), mult(op_d, op_d))))
% 42.94/5.90 = { by lemma 124 R->L }
% 42.94/5.90 ld(ld(mult(op_c, op_c), mult(op_d, op_d)), mult(mult(op_d, op_d), mult(op_d, op_d)))
% 42.94/5.90 = { by lemma 123 R->L }
% 42.94/5.90 ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), mult(mult(op_d, op_d), mult(op_d, op_d)))
% 42.94/5.90 = { by lemma 72 }
% 42.94/5.90 ld(mult(mult(op_d, op_d), mult(op_c, op_c)), mult(mult(op_d, op_d), mult(op_d, op_d)))
% 42.94/5.90 = { by lemma 45 R->L }
% 42.94/5.90 ld(mult(mult(op_d, op_d), mult(op_c, op_c)), i(ld(mult(op_d, op_d), i(mult(op_d, op_d)))))
% 42.94/5.90 = { by lemma 74 R->L }
% 42.94/5.90 ld(mult(mult(op_d, op_d), mult(op_c, op_c)), i(ld(mult(mult(op_d, op_d), mult(op_c, op_c)), ld(mult(op_d, op_d), mult(op_c, op_c)))))
% 42.94/5.90 = { by lemma 55 }
% 42.94/5.90 i(ld(mult(op_d, op_d), mult(op_c, op_c)))
% 42.94/5.90 = { by lemma 66 }
% 42.94/5.90 mult(mult(op_d, op_d), mult(op_c, op_c))
% 42.94/5.90 = { by lemma 72 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c))
% 42.94/5.90 = { by lemma 123 }
% 42.94/5.90 ld(mult(op_c, op_c), mult(op_d, op_d))
% 42.94/5.90
% 42.94/5.90 Lemma 131: ld(mult(op_d, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))) = mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.94/5.90 = { by lemma 39 }
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_c, op_c), i(mult(op_d, op_d))))
% 42.94/5.90 = { by lemma 68 R->L }
% 42.94/5.90 ld(mult(op_d, op_c), i(ld(mult(op_c, op_c), mult(op_d, op_d))))
% 42.94/5.90 = { by lemma 130 R->L }
% 42.94/5.90 ld(mult(op_d, op_c), i(ld(mult(op_d, op_c), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.94/5.90 = { by lemma 55 }
% 42.94/5.90 i(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.94/5.90 = { by lemma 129 R->L }
% 42.94/5.90 mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.94/5.90
% 42.94/5.90 Lemma 132: ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c)))) = ld(mult(op_c, op_c), mult(op_d, op_d)).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))))
% 42.94/5.90 = { by lemma 127 }
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), i(mult(op_d, op_c))))
% 42.94/5.90 = { by lemma 62 R->L }
% 42.94/5.90 rd(i(mult(op_d, op_c)), mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.94/5.90 = { by lemma 129 }
% 42.94/5.90 rd(i(mult(op_d, op_c)), i(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.94/5.90 = { by lemma 26 }
% 42.94/5.90 rd(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_d, op_c))
% 42.94/5.90 = { by axiom 3 (c02) R->L }
% 42.94/5.90 rd(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), mult(mult(op_d, op_c), mult(op_d, op_c))))
% 42.94/5.90 = { by lemma 111 R->L }
% 42.94/5.90 rd(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c))))
% 42.94/5.90 = { by lemma 123 }
% 42.94/5.90 rd(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_c, op_c), mult(op_d, op_d))))
% 42.94/5.90 = { by lemma 130 R->L }
% 42.94/5.90 rd(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))))))
% 42.94/5.90 = { by lemma 35 R->L }
% 42.94/5.90 rd(ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(mult(op_d, op_c), mult(op_d, op_c)), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.94/5.90 = { by lemma 25 }
% 42.94/5.90 mult(mult(op_d, op_c), mult(op_d, op_c))
% 42.94/5.90 = { by lemma 111 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c))
% 42.94/5.90 = { by lemma 123 }
% 42.94/5.90 ld(mult(op_c, op_c), mult(op_d, op_d))
% 42.94/5.90
% 42.94/5.90 Lemma 133: mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))) = ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)).
% 42.94/5.90 Proof:
% 42.94/5.90 mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))
% 42.94/5.90 = { by lemma 131 R->L }
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))
% 42.94/5.90 = { by lemma 39 }
% 42.94/5.90 ld(mult(op_d, op_c), ld(mult(op_c, op_c), i(mult(op_d, op_d))))
% 42.94/5.90 = { by lemma 68 R->L }
% 42.94/5.90 ld(mult(op_d, op_c), i(ld(mult(op_c, op_c), mult(op_d, op_d))))
% 42.94/5.90 = { by lemma 132 R->L }
% 42.94/5.90 ld(mult(op_d, op_c), i(ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))))))
% 42.94/5.90 = { by lemma 55 }
% 42.94/5.90 i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))))
% 42.94/5.90 = { by lemma 92 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), i(mult(op_c, mult(op_c, op_c))))
% 42.94/5.90 = { by lemma 31 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, op_d)), op_c)
% 42.94/5.90 = { by lemma 128 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c))
% 42.94/5.90
% 42.94/5.90 Lemma 134: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, X)) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, X))
% 42.94/5.90 = { by lemma 84 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, X)))
% 42.94/5.90 = { by lemma 75 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, X))))
% 42.94/5.90 = { by lemma 69 R->L }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))))
% 42.94/5.90 = { by lemma 75 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)))
% 42.94/5.90 = { by lemma 84 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X))
% 42.94/5.90 = { by lemma 118 }
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X)
% 42.94/5.90
% 42.94/5.90 Lemma 135: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X) = ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X)).
% 42.94/5.90 Proof:
% 42.94/5.90 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)
% 42.94/5.90 = { by lemma 69 }
% 42.94/5.90 mult(op_d, X)
% 42.94/5.91 = { by lemma 77 R->L }
% 42.94/5.91 mult(ld(mult(op_d, op_d), mult(op_d, mult(op_d, op_d))), X)
% 42.94/5.91 = { by lemma 77 R->L }
% 42.94/5.91 mult(ld(mult(op_d, op_d), ld(mult(op_d, op_d), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)
% 42.94/5.91 = { by lemma 120 R->L }
% 42.94/5.91 mult(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), X)
% 42.94/5.91 = { by lemma 115 }
% 42.94/5.91 mult(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), i(mult(op_d, mult(op_d, mult(op_d, op_d))))), X)
% 42.94/5.91 = { by lemma 58 }
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), X))
% 42.94/5.91
% 42.94/5.91 Lemma 136: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X) = ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(op_d, X)).
% 42.94/5.91 Proof:
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)
% 42.94/5.91 = { by axiom 3 (c02) R->L }
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)))
% 42.94/5.91 = { by lemma 75 }
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.94/5.91 = { by lemma 42 }
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(op_d, X))
% 42.94/5.91
% 42.94/5.91 Lemma 137: ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_c, op_c), X)) = ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X)).
% 42.94/5.91 Proof:
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_c, op_c), X))
% 42.94/5.91 = { by lemma 75 R->L }
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), X)))
% 42.94/5.91 = { by lemma 112 R->L }
% 42.94/5.91 ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), X)))))
% 42.94/5.91 = { by lemma 112 }
% 42.94/5.91 ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)))
% 42.94/5.91 = { by lemma 75 }
% 42.94/5.91 ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), X))
% 42.94/5.91
% 42.94/5.91 Lemma 138: ld(mult(op_d, op_d), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X)) = ld(op_d, X).
% 42.94/5.91 Proof:
% 42.94/5.91 ld(mult(op_d, op_d), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), X))
% 42.94/5.91 = { by lemma 69 }
% 42.94/5.91 ld(mult(op_d, op_d), mult(op_d, X))
% 42.94/5.91 = { by lemma 43 }
% 42.94/5.91 ld(op_d, ld(op_d, mult(op_d, X)))
% 42.94/5.91 = { by axiom 3 (c02) }
% 42.94/5.91 ld(op_d, X)
% 42.94/5.91
% 42.94/5.91 Lemma 139: rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X)) = ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(X, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))).
% 42.94/5.91 Proof:
% 42.94/5.91 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), X))
% 42.94/5.91 = { by lemma 116 }
% 42.94/5.91 rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, op_d))), X))
% 42.94/5.91 = { by lemma 115 }
% 42.94/5.91 rd(i(mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, op_d))), X))
% 42.94/5.91 = { by lemma 62 }
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(X, i(mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.94/5.91 = { by lemma 115 R->L }
% 42.94/5.91 ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(X, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))
% 42.94/5.91
% 42.94/5.91 Goal 1 (goals): mult(op_c, op_d) = mult(op_d, op_c).
% 42.94/5.91 Proof:
% 42.94/5.91 mult(op_c, op_d)
% 42.94/5.91 = { by lemma 49 R->L }
% 42.94/5.91 ld(mult(op_c, mult(op_c, op_c)), op_d)
% 42.94/5.91 = { by axiom 3 (c02) R->L }
% 42.94/5.91 ld(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_c, mult(op_c, op_c)))), op_d)
% 42.94/5.91 = { by lemma 116 R->L }
% 42.94/5.91 ld(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_c, mult(op_c, op_c)))), op_d)
% 42.94/5.91 = { by lemma 119 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_c, mult(op_c, op_c)))), op_d)
% 42.94/5.91 = { by lemma 52 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), op_c))), op_d)
% 42.94/5.91 = { by lemma 117 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_c, op_c), op_c)))), op_d)
% 42.94/5.91 = { by lemma 137 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c)))), op_d)
% 42.94/5.91 = { by lemma 137 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c)))), op_d)
% 42.94/5.91 = { by lemma 117 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), op_c))), op_d)
% 42.94/5.91 = { by lemma 134 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, op_c)))), op_d)
% 42.94/5.91 = { by lemma 84 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, op_c))))), op_d)
% 42.94/5.91 = { by lemma 136 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 99 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, op_c))))), op_d)
% 42.94/5.91 = { by lemma 135 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 72 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), mult(mult(op_d, op_d), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 120 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), mult(mult(op_d, op_d), ld(mult(op_d, op_d), ld(mult(op_d, op_d), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c))))))), op_d)
% 42.94/5.91 = { by axiom 5 (c01) }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(mult(op_d, op_d), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c))))), op_d)
% 42.94/5.91 = { by lemma 43 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_c, op_c), ld(op_d, ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 113 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(op_d, ld(mult(op_c, op_c), ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 50 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(op_d, mult(mult(op_c, op_c), ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 42 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(op_d, mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 42 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 15 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(i(mult(op_c, op_c)), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by lemma 16 R->L }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(i(i(mult(op_c, op_c))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))))), op_d)
% 42.94/5.91 = { by axiom 10 (c07) }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(i(i(mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.91 = { by lemma 16 }
% 42.94/5.91 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(i(mult(op_c, op_c)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.91 = { by lemma 48 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(mult(op_c, op_c)))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 53 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), i(mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 61 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(rd(i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 62 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 37 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_c, op_c), op_d)), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 50 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), op_d)), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 109 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 53 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 34 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(i(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_c, op_c)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 109 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_c, op_c), op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 70 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(op_d, i(mult(mult(op_c, op_c), op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 17 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(op_d, ld(mult(op_c, op_c), i(op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 38 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(op_d, ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 113 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(mult(op_c, op_c), ld(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by axiom 3 (c02) }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 39 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(mult(op_c, op_c), i(mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 59 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(mult(op_c, op_c), mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 50 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(ld(mult(op_c, op_c), mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 124 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c))))), op_d)
% 42.94/5.92 = { by lemma 128 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, op_d)), op_c)))), op_d)
% 42.94/5.92 = { by lemma 31 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, op_d)), i(mult(op_c, mult(op_c, op_c))))))), op_d)
% 42.94/5.92 = { by lemma 92 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))))))), op_d)
% 42.94/5.92 = { by axiom 5 (c01) R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(mult(op_d, op_c), ld(mult(op_d, op_c), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))))))))), op_d)
% 42.94/5.92 = { by lemma 132 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(mult(op_d, op_c), ld(mult(op_c, op_c), mult(op_d, op_d))))))), op_d)
% 42.94/5.92 = { by lemma 50 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(mult(op_d, op_c), mult(mult(op_c, op_c), mult(op_d, op_d))))))), op_d)
% 42.94/5.92 = { by lemma 114 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(mult(op_d, op_c), mult(mult(op_c, op_c), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))))), op_d)
% 42.94/5.92 = { by lemma 18 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(mult(op_d, op_c), i(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))))), op_d)
% 42.94/5.92 = { by lemma 15 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(ld(i(mult(op_d, op_c)), i(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))))), op_d)
% 42.94/5.92 = { by lemma 122 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(ld(i(mult(op_d, op_c)), i(ld(mult(op_d, op_c), i(mult(op_d, op_c))))))))), op_d)
% 42.94/5.92 = { by lemma 47 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(ld(i(mult(op_d, op_c)), mult(op_d, op_c)), i(mult(op_d, op_c))))))), op_d)
% 42.94/5.92 = { by lemma 15 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(mult(mult(op_d, op_c), mult(op_d, op_c)), i(mult(op_d, op_c))))))), op_d)
% 42.94/5.92 = { by lemma 111 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), i(mult(op_d, op_c))))))), op_d)
% 42.94/5.92 = { by lemma 27 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(mult(op_d, op_c), i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)))))))), op_d)
% 42.94/5.92 = { by lemma 66 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(mult(op_d, op_c), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c))))))), op_d)
% 42.94/5.92 = { by lemma 40 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(mult(op_d, op_c), ld(mult(op_d, op_d), mult(op_c, op_c))))))), op_d)
% 42.94/5.92 = { by lemma 121 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(mult(op_d, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))))))), op_d)
% 42.94/5.92 = { by lemma 122 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(rd(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(op_d, op_c)))))))), op_d)
% 42.94/5.92 = { by lemma 60 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(mult(op_d, op_c), mult(mult(op_d, op_c), mult(op_d, op_c))))))), op_d)
% 42.94/5.92 = { by lemma 21 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(mult(mult(op_d, op_c), mult(op_d, op_c)), mult(op_d, op_c)))))), op_d)
% 42.94/5.92 = { by lemma 111 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(mult(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), mult(op_d, op_c)))))), op_d)
% 42.94/5.92 = { by lemma 73 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_c, op_c)), mult(op_d, op_c)))))), op_d)
% 42.94/5.92 = { by lemma 40 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(ld(ld(mult(op_d, op_d), mult(op_c, op_c)), mult(op_d, op_c)))))), op_d)
% 42.94/5.92 = { by lemma 121 R->L }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), ld(mult(op_d, op_c), i(ld(ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, op_c)))))), op_d)
% 42.94/5.92 = { by lemma 47 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), rd(ld(mult(op_d, op_c), ld(mult(op_c, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 131 }
% 42.94/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), rd(mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, op_c)))), op_d)
% 42.94/5.92 = { by lemma 133 }
% 43.22/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), rd(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c)), mult(op_d, op_c)))), op_d)
% 43.22/5.92 = { by lemma 54 }
% 43.22/5.92 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), i(mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)
% 43.22/5.93 = { by lemma 115 R->L }
% 43.22/5.93 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)
% 43.22/5.93 = { by lemma 48 }
% 43.22/5.93 ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_d, op_c))), op_d)
% 43.22/5.93 = { by lemma 139 }
% 43.22/5.93 ld(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)
% 43.22/5.93 = { by lemma 120 }
% 43.22/5.93 ld(ld(mult(op_d, op_d), ld(mult(op_d, op_d), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), op_d)
% 43.22/5.93 = { by lemma 101 R->L }
% 43.22/5.93 ld(ld(mult(op_d, op_d), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), op_d)
% 43.22/5.93 = { by lemma 138 }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), op_d)
% 43.22/5.93 = { by axiom 3 (c02) R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), op_d)
% 43.22/5.93 = { by lemma 125 }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, op_d), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), op_d)
% 43.22/5.93 = { by lemma 42 }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, op_d), ld(op_d, ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), op_d)
% 43.22/5.93 = { by lemma 101 R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, op_d)), ld(op_d, ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))), op_d)
% 43.22/5.93 = { by lemma 126 R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), op_d)
% 43.22/5.93 = { by lemma 139 R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_d, op_c))))), op_d)
% 43.22/5.93 = { by lemma 118 R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, op_c)))))), op_d)
% 43.22/5.93 = { by lemma 134 }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), op_c))))), op_d)
% 43.22/5.93 = { by lemma 118 R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), op_c)))))), op_d)
% 43.22/5.93 = { by lemma 75 }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), op_c))))), op_d)
% 43.22/5.93 = { by lemma 84 R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c)))))), op_d)
% 43.22/5.93 = { by lemma 82 R->L }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c)))))), op_d)
% 43.22/5.93 = { by lemma 84 }
% 43.22/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c))))), op_d)
% 43.22/5.93 = { by lemma 83 }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c))))), op_d)
% 43.29/5.93 = { by lemma 104 R->L }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(mult(op_d, mult(op_d, op_d)), mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c))))), op_d)
% 43.29/5.93 = { by lemma 79 }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(ld(mult(op_d, mult(op_d, op_d)), i(mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c))))), op_d)
% 43.29/5.93 = { by lemma 58 }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_c)))))), op_d)
% 43.29/5.93 = { by lemma 75 R->L }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), op_c))))))), op_d)
% 43.29/5.93 = { by lemma 125 }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, op_d)), ld(mult(op_d, op_d), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), op_c)))))), op_d)
% 43.29/5.93 = { by lemma 138 }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, op_d)), ld(op_d, op_c))))), op_d)
% 43.29/5.93 = { by lemma 126 R->L }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), op_c)))), op_d)
% 43.29/5.93 = { by lemma 119 R->L }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), op_c)))), op_d)
% 43.29/5.93 = { by lemma 31 R->L }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), i(mult(op_c, mult(op_c, op_c))))))), op_d)
% 43.29/5.93 = { by lemma 18 }
% 43.29/5.93 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), i(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_c, mult(op_c, op_c))))))), op_d)
% 43.29/5.94 = { by lemma 24 R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_c, mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, op_d)))), i(mult(op_d, mult(op_d, mult(op_d, op_d)))))))), op_d)
% 43.29/5.94 = { by lemma 115 R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_c, mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), op_d)
% 43.29/5.94 = { by lemma 25 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(op_c, mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)
% 43.29/5.94 = { by lemma 118 R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c)))), mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)
% 43.29/5.94 = { by axiom 7 (c03) R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d)
% 43.29/5.94 = { by lemma 106 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(rd(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c))), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), op_d)))), op_d)
% 43.29/5.94 = { by lemma 53 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c)))), op_d)))), op_d)
% 43.29/5.94 = { by lemma 75 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))), mult(op_c, mult(op_c, op_c)))), op_d))), op_d)
% 43.29/5.94 = { by lemma 127 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(rd(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), i(mult(op_d, op_c)))), op_d))), op_d)
% 43.29/5.94 = { by lemma 60 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))), mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d))), op_d)
% 43.29/5.94 = { by lemma 119 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(mult(op_d, op_c), mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), op_d))), op_d)
% 43.29/5.94 = { by lemma 133 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(ld(mult(op_d, mult(op_d, mult(op_d, op_d))), ld(mult(op_d, mult(op_d, mult(op_d, op_d))), mult(op_d, op_c))), op_d))), op_d)
% 43.29/5.94 = { by lemma 135 R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, op_c)), op_d))), op_d)
% 43.29/5.94 = { by lemma 37 R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), mult(op_d, op_c)), i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))))))), op_d)
% 43.29/5.94 = { by lemma 57 R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(i(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))))), mult(op_d, op_c))))), op_d)
% 43.29/5.94 = { by lemma 37 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(op_d, mult(op_d, op_c))))), op_d)
% 43.29/5.94 = { by lemma 42 }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d)))))), ld(op_d, rd(op_d, mult(op_d, op_c))))), op_d)
% 43.29/5.94 = { by lemma 136 R->L }
% 43.29/5.94 ld(ld(op_d, ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(op_d, mult(op_d, op_c)))), op_d)
% 43.29/5.94 = { by lemma 42 R->L }
% 43.29/5.94 ld(mult(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), ld(mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, mult(op_d, op_d))))))), rd(op_d, mult(op_d, op_c)))), op_d)
% 43.29/5.94 = { by axiom 5 (c01) }
% 43.29/5.94 ld(rd(op_d, mult(op_d, op_c)), op_d)
% 43.29/5.94 = { by lemma 44 }
% 43.29/5.94 mult(op_d, op_c)
% 43.29/5.94 % SZS output end Proof
% 43.29/5.94
% 43.29/5.94 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------