TSTP Solution File: GRP701-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP701-1 : 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 01:19:46 EDT 2023
% Result : Unsatisfiable 5.12s 1.68s
% Output : Proof 7.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.18 % Problem : GRP701-1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.18 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.39 % Computer : n019.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8042.1875MB
% 0.10/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Aug 28 22:42:28 EDT 2023
% 0.14/0.40 % CPUTime :
% 5.12/1.68 Command-line arguments: --no-flatten-goal
% 5.12/1.68
% 5.12/1.68 % SZS status Unsatisfiable
% 5.12/1.68
% 7.28/2.12 % SZS output start Proof
% 7.28/2.12 Axiom 1 (c05): mult(X, unit) = X.
% 7.28/2.12 Axiom 2 (c06): mult(unit, X) = X.
% 7.28/2.12 Axiom 3 (c09): mult(X, i(X)) = unit.
% 7.28/2.12 Axiom 4 (c10): mult(i(X), X) = unit.
% 7.28/2.12 Axiom 5 (c02): ld(X, mult(X, Y)) = Y.
% 7.28/2.12 Axiom 6 (c04): rd(mult(X, Y), Y) = X.
% 7.28/2.12 Axiom 7 (c01): mult(X, ld(X, Y)) = Y.
% 7.28/2.12 Axiom 8 (c03): mult(rd(X, Y), Y) = X.
% 7.28/2.12 Axiom 9 (c07): mult(mult(mult(X, Y), X), mult(X, Z)) = mult(X, mult(mult(mult(Y, X), X), Z)).
% 7.28/2.12 Axiom 10 (c08): mult(mult(X, Y), mult(Y, mult(Z, Y))) = mult(mult(X, mult(Y, mult(Y, Z))), Y).
% 7.28/2.12
% 7.28/2.12 Lemma 11: ld(X, unit) = i(X).
% 7.28/2.12 Proof:
% 7.28/2.12 ld(X, unit)
% 7.28/2.12 = { by axiom 3 (c09) R->L }
% 7.28/2.12 ld(X, mult(X, i(X)))
% 7.28/2.12 = { by axiom 5 (c02) }
% 7.28/2.12 i(X)
% 7.28/2.12
% 7.28/2.12 Lemma 12: i(i(X)) = X.
% 7.28/2.12 Proof:
% 7.28/2.12 i(i(X))
% 7.28/2.12 = { by lemma 11 R->L }
% 7.28/2.12 ld(i(X), unit)
% 7.28/2.13 = { by axiom 4 (c10) R->L }
% 7.28/2.13 ld(i(X), mult(i(X), X))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 X
% 7.28/2.13
% 7.28/2.13 Lemma 13: mult(mult(mult(X, Y), X), X) = mult(X, mult(mult(Y, X), X)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(mult(X, Y), X), X)
% 7.28/2.13 = { by axiom 1 (c05) R->L }
% 7.28/2.13 mult(mult(mult(X, Y), X), mult(X, unit))
% 7.28/2.13 = { by axiom 9 (c07) }
% 7.28/2.13 mult(X, mult(mult(mult(Y, X), X), unit))
% 7.28/2.13 = { by axiom 1 (c05) }
% 7.28/2.13 mult(X, mult(mult(Y, X), X))
% 7.28/2.13
% 7.28/2.13 Lemma 14: rd(mult(X, mult(mult(Y, X), X)), X) = mult(mult(X, Y), X).
% 7.28/2.13 Proof:
% 7.28/2.13 rd(mult(X, mult(mult(Y, X), X)), X)
% 7.28/2.13 = { by lemma 13 R->L }
% 7.28/2.13 rd(mult(mult(mult(X, Y), X), X), X)
% 7.28/2.13 = { by axiom 6 (c04) }
% 7.28/2.13 mult(mult(X, Y), X)
% 7.28/2.13
% 7.28/2.13 Lemma 15: mult(mult(X, X), mult(X, Y)) = mult(X, mult(mult(X, X), Y)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(X, X), mult(X, Y))
% 7.28/2.13 = { by axiom 1 (c05) R->L }
% 7.28/2.13 mult(mult(mult(X, unit), X), mult(X, Y))
% 7.28/2.13 = { by axiom 9 (c07) }
% 7.28/2.13 mult(X, mult(mult(mult(unit, X), X), Y))
% 7.28/2.13 = { by axiom 2 (c06) }
% 7.28/2.13 mult(X, mult(mult(X, X), Y))
% 7.28/2.13
% 7.28/2.13 Lemma 16: mult(mult(X, X), i(X)) = X.
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(X, X), i(X))
% 7.28/2.13 = { by axiom 5 (c02) R->L }
% 7.28/2.13 ld(X, mult(X, mult(mult(X, X), i(X))))
% 7.28/2.13 = { by lemma 15 R->L }
% 7.28/2.13 ld(X, mult(mult(X, X), mult(X, i(X))))
% 7.28/2.13 = { by axiom 3 (c09) }
% 7.28/2.13 ld(X, mult(mult(X, X), unit))
% 7.28/2.13 = { by axiom 1 (c05) }
% 7.28/2.13 ld(X, mult(X, X))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 X
% 7.28/2.13
% 7.28/2.13 Lemma 17: mult(i(X), mult(X, X)) = X.
% 7.28/2.13 Proof:
% 7.28/2.13 mult(i(X), mult(X, X))
% 7.28/2.13 = { by axiom 6 (c04) R->L }
% 7.28/2.13 rd(mult(mult(i(X), mult(X, X)), i(X)), i(X))
% 7.28/2.13 = { by lemma 14 R->L }
% 7.28/2.13 rd(rd(mult(i(X), mult(mult(mult(X, X), i(X)), i(X))), i(X)), i(X))
% 7.28/2.13 = { by lemma 16 }
% 7.28/2.13 rd(rd(mult(i(X), mult(X, i(X))), i(X)), i(X))
% 7.28/2.13 = { by axiom 3 (c09) }
% 7.28/2.13 rd(rd(mult(i(X), unit), i(X)), i(X))
% 7.28/2.13 = { by axiom 1 (c05) }
% 7.28/2.13 rd(rd(i(X), i(X)), i(X))
% 7.28/2.13 = { by axiom 2 (c06) R->L }
% 7.28/2.13 rd(rd(mult(unit, i(X)), i(X)), i(X))
% 7.28/2.13 = { by axiom 6 (c04) }
% 7.28/2.13 rd(unit, i(X))
% 7.28/2.13 = { by axiom 4 (c10) R->L }
% 7.28/2.13 rd(mult(i(i(X)), i(X)), i(X))
% 7.28/2.13 = { by axiom 6 (c04) }
% 7.28/2.13 i(i(X))
% 7.28/2.13 = { by lemma 12 }
% 7.28/2.13 X
% 7.28/2.13
% 7.28/2.13 Lemma 18: ld(i(X), X) = mult(X, X).
% 7.28/2.13 Proof:
% 7.28/2.13 ld(i(X), X)
% 7.28/2.13 = { by lemma 17 R->L }
% 7.28/2.13 ld(i(X), mult(i(X), mult(X, X)))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 mult(X, X)
% 7.28/2.13
% 7.28/2.13 Lemma 19: ld(mult(X, X), mult(X, mult(mult(X, X), Y))) = mult(X, Y).
% 7.28/2.13 Proof:
% 7.28/2.13 ld(mult(X, X), mult(X, mult(mult(X, X), Y)))
% 7.28/2.13 = { by lemma 15 R->L }
% 7.28/2.13 ld(mult(X, X), mult(mult(X, X), mult(X, Y)))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 mult(X, Y)
% 7.28/2.13
% 7.28/2.13 Lemma 20: mult(X, i(mult(X, X))) = i(X).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, i(mult(X, X)))
% 7.28/2.13 = { by lemma 19 R->L }
% 7.28/2.13 ld(mult(X, X), mult(X, mult(mult(X, X), i(mult(X, X)))))
% 7.28/2.13 = { by axiom 3 (c09) }
% 7.28/2.13 ld(mult(X, X), mult(X, unit))
% 7.28/2.13 = { by axiom 1 (c05) }
% 7.28/2.13 ld(mult(X, X), X)
% 7.28/2.13 = { by lemma 16 R->L }
% 7.28/2.13 ld(mult(X, X), mult(mult(X, X), i(X)))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 i(X)
% 7.28/2.13
% 7.28/2.13 Lemma 21: i(mult(X, X)) = ld(X, i(X)).
% 7.28/2.13 Proof:
% 7.28/2.13 i(mult(X, X))
% 7.28/2.13 = { by axiom 5 (c02) R->L }
% 7.28/2.13 ld(X, mult(X, i(mult(X, X))))
% 7.28/2.13 = { by lemma 20 }
% 7.28/2.13 ld(X, i(X))
% 7.28/2.13
% 7.28/2.13 Lemma 22: ld(rd(X, Y), X) = Y.
% 7.28/2.13 Proof:
% 7.28/2.13 ld(rd(X, Y), X)
% 7.28/2.13 = { by axiom 8 (c03) R->L }
% 7.28/2.13 ld(rd(X, Y), mult(rd(X, Y), Y))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 Y
% 7.28/2.13
% 7.28/2.13 Lemma 23: mult(i(X), i(X)) = ld(X, i(X)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(i(X), i(X))
% 7.28/2.13 = { by lemma 18 R->L }
% 7.28/2.13 ld(i(i(X)), i(X))
% 7.28/2.13 = { by lemma 12 }
% 7.28/2.13 ld(X, i(X))
% 7.28/2.13
% 7.28/2.13 Lemma 24: rd(X, ld(Y, X)) = Y.
% 7.28/2.13 Proof:
% 7.28/2.13 rd(X, ld(Y, X))
% 7.28/2.13 = { by axiom 7 (c01) R->L }
% 7.28/2.13 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 7.28/2.13 = { by axiom 6 (c04) }
% 7.28/2.13 Y
% 7.28/2.13
% 7.28/2.13 Lemma 25: mult(mult(X, rd(Y, X)), X) = rd(mult(X, mult(Y, X)), X).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(X, rd(Y, X)), X)
% 7.28/2.13 = { by lemma 14 R->L }
% 7.28/2.13 rd(mult(X, mult(mult(rd(Y, X), X), X)), X)
% 7.28/2.13 = { by axiom 8 (c03) }
% 7.28/2.13 rd(mult(X, mult(Y, X)), X)
% 7.28/2.13
% 7.28/2.13 Lemma 26: mult(X, mult(mult(mult(Y, X), X), i(X))) = mult(mult(X, Y), X).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, mult(mult(mult(Y, X), X), i(X)))
% 7.28/2.13 = { by axiom 9 (c07) R->L }
% 7.28/2.13 mult(mult(mult(X, Y), X), mult(X, i(X)))
% 7.28/2.13 = { by axiom 3 (c09) }
% 7.28/2.13 mult(mult(mult(X, Y), X), unit)
% 7.28/2.13 = { by axiom 1 (c05) }
% 7.28/2.13 mult(mult(X, Y), X)
% 7.28/2.13
% 7.28/2.13 Lemma 27: mult(mult(mult(X, Y), Y), i(Y)) = ld(Y, mult(mult(Y, X), Y)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(mult(X, Y), Y), i(Y))
% 7.28/2.13 = { by axiom 5 (c02) R->L }
% 7.28/2.13 ld(Y, mult(Y, mult(mult(mult(X, Y), Y), i(Y))))
% 7.28/2.13 = { by lemma 26 }
% 7.28/2.13 ld(Y, mult(mult(Y, X), Y))
% 7.28/2.13
% 7.28/2.13 Lemma 28: mult(mult(X, mult(X, Y)), X) = mult(X, mult(X, mult(Y, X))).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(X, mult(X, Y)), X)
% 7.28/2.13 = { by axiom 2 (c06) R->L }
% 7.28/2.13 mult(mult(unit, mult(X, mult(X, Y))), X)
% 7.28/2.13 = { by axiom 10 (c08) R->L }
% 7.28/2.13 mult(mult(unit, X), mult(X, mult(Y, X)))
% 7.28/2.13 = { by axiom 2 (c06) }
% 7.28/2.13 mult(X, mult(X, mult(Y, X)))
% 7.28/2.13
% 7.28/2.13 Lemma 29: mult(mult(X, mult(Y, X)), i(X)) = mult(X, Y).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(X, mult(Y, X)), i(X))
% 7.28/2.13 = { by axiom 8 (c03) R->L }
% 7.28/2.13 mult(mult(rd(mult(X, mult(Y, X)), X), X), i(X))
% 7.28/2.13 = { by lemma 25 R->L }
% 7.28/2.13 mult(mult(mult(mult(X, rd(Y, X)), X), X), i(X))
% 7.28/2.13 = { by lemma 27 }
% 7.28/2.13 ld(X, mult(mult(X, mult(X, rd(Y, X))), X))
% 7.28/2.13 = { by lemma 28 }
% 7.28/2.13 ld(X, mult(X, mult(X, mult(rd(Y, X), X))))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 mult(X, mult(rd(Y, X), X))
% 7.28/2.13 = { by axiom 8 (c03) }
% 7.28/2.13 mult(X, Y)
% 7.28/2.13
% 7.28/2.13 Lemma 30: mult(mult(X, Y), i(X)) = mult(X, rd(Y, X)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(X, Y), i(X))
% 7.28/2.13 = { by axiom 8 (c03) R->L }
% 7.28/2.13 mult(mult(X, mult(rd(Y, X), X)), i(X))
% 7.28/2.13 = { by lemma 29 }
% 7.28/2.13 mult(X, rd(Y, X))
% 7.28/2.13
% 7.28/2.13 Lemma 31: mult(X, rd(ld(X, Y), X)) = mult(Y, i(X)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, rd(ld(X, Y), X))
% 7.28/2.13 = { by lemma 30 R->L }
% 7.28/2.13 mult(mult(X, ld(X, Y)), i(X))
% 7.28/2.13 = { by axiom 7 (c01) }
% 7.28/2.13 mult(Y, i(X))
% 7.28/2.13
% 7.28/2.13 Lemma 32: ld(X, mult(Y, i(X))) = rd(ld(X, Y), X).
% 7.28/2.13 Proof:
% 7.28/2.13 ld(X, mult(Y, i(X)))
% 7.28/2.13 = { by lemma 31 R->L }
% 7.28/2.13 ld(X, mult(X, rd(ld(X, Y), X)))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 rd(ld(X, Y), X)
% 7.28/2.13
% 7.28/2.13 Lemma 33: mult(X, mult(X, mult(ld(X, Y), X))) = mult(mult(X, Y), X).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, mult(X, mult(ld(X, Y), X)))
% 7.28/2.13 = { by lemma 28 R->L }
% 7.28/2.13 mult(mult(X, mult(X, ld(X, Y))), X)
% 7.28/2.13 = { by axiom 7 (c01) }
% 7.28/2.13 mult(mult(X, Y), X)
% 7.28/2.13
% 7.28/2.13 Lemma 34: mult(X, mult(ld(X, Y), X)) = ld(X, mult(mult(X, Y), X)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, mult(ld(X, Y), X))
% 7.28/2.13 = { by axiom 5 (c02) R->L }
% 7.28/2.13 ld(X, mult(X, mult(X, mult(ld(X, Y), X))))
% 7.28/2.13 = { by lemma 33 }
% 7.28/2.13 ld(X, mult(mult(X, Y), X))
% 7.28/2.13
% 7.28/2.13 Lemma 35: rd(mult(X, Y), i(X)) = mult(X, mult(Y, X)).
% 7.28/2.13 Proof:
% 7.28/2.13 rd(mult(X, Y), i(X))
% 7.28/2.13 = { by lemma 29 R->L }
% 7.28/2.13 rd(mult(mult(X, mult(Y, X)), i(X)), i(X))
% 7.28/2.13 = { by axiom 6 (c04) }
% 7.28/2.13 mult(X, mult(Y, X))
% 7.28/2.13
% 7.28/2.13 Lemma 36: ld(X, mult(mult(X, Y), X)) = rd(Y, i(X)).
% 7.28/2.13 Proof:
% 7.28/2.13 ld(X, mult(mult(X, Y), X))
% 7.28/2.13 = { by lemma 34 R->L }
% 7.28/2.13 mult(X, mult(ld(X, Y), X))
% 7.28/2.13 = { by lemma 35 R->L }
% 7.28/2.13 rd(mult(X, ld(X, Y)), i(X))
% 7.28/2.13 = { by axiom 7 (c01) }
% 7.28/2.13 rd(Y, i(X))
% 7.28/2.13
% 7.28/2.13 Lemma 37: ld(X, rd(Y, i(X))) = mult(ld(X, Y), X).
% 7.28/2.13 Proof:
% 7.28/2.13 ld(X, rd(Y, i(X)))
% 7.28/2.13 = { by lemma 36 R->L }
% 7.28/2.13 ld(X, ld(X, mult(mult(X, Y), X)))
% 7.28/2.13 = { by lemma 34 R->L }
% 7.28/2.13 ld(X, mult(X, mult(ld(X, Y), X)))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 mult(ld(X, Y), X)
% 7.28/2.13
% 7.28/2.13 Lemma 38: mult(X, mult(mult(X, X), mult(Y, X))) = mult(X, mult(X, mult(mult(X, Y), X))).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, mult(mult(X, X), mult(Y, X)))
% 7.28/2.13 = { by lemma 15 R->L }
% 7.28/2.13 mult(mult(X, X), mult(X, mult(Y, X)))
% 7.28/2.13 = { by axiom 10 (c08) }
% 7.28/2.13 mult(mult(X, mult(X, mult(X, Y))), X)
% 7.28/2.13 = { by lemma 28 }
% 7.28/2.13 mult(X, mult(X, mult(mult(X, Y), X)))
% 7.28/2.13
% 7.28/2.13 Lemma 39: mult(mult(X, X), mult(Y, X)) = mult(X, mult(mult(X, Y), X)).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(mult(X, X), mult(Y, X))
% 7.28/2.13 = { by axiom 5 (c02) R->L }
% 7.28/2.13 ld(X, mult(X, mult(mult(X, X), mult(Y, X))))
% 7.28/2.13 = { by lemma 38 }
% 7.28/2.13 ld(X, mult(X, mult(X, mult(mult(X, Y), X))))
% 7.28/2.13 = { by axiom 5 (c02) }
% 7.28/2.13 mult(X, mult(mult(X, Y), X))
% 7.28/2.13
% 7.28/2.13 Lemma 40: mult(X, rd(mult(X, mult(Y, X)), X)) = mult(mult(X, X), Y).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, rd(mult(X, mult(Y, X)), X))
% 7.28/2.13 = { by lemma 25 R->L }
% 7.28/2.13 mult(X, mult(mult(X, rd(Y, X)), X))
% 7.28/2.13 = { by lemma 39 R->L }
% 7.28/2.13 mult(mult(X, X), mult(rd(Y, X), X))
% 7.28/2.13 = { by axiom 8 (c03) }
% 7.28/2.13 mult(mult(X, X), Y)
% 7.28/2.13
% 7.28/2.13 Lemma 41: rd(mult(X, mult(Y, X)), X) = ld(X, mult(mult(X, X), Y)).
% 7.28/2.13 Proof:
% 7.28/2.13 rd(mult(X, mult(Y, X)), X)
% 7.28/2.13 = { by axiom 5 (c02) R->L }
% 7.28/2.13 ld(X, mult(X, rd(mult(X, mult(Y, X)), X)))
% 7.28/2.13 = { by lemma 40 }
% 7.28/2.13 ld(X, mult(mult(X, X), Y))
% 7.28/2.13
% 7.28/2.13 Lemma 42: mult(X, mult(Y, i(X))) = rd(mult(X, Y), X).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, mult(Y, i(X)))
% 7.28/2.13 = { by axiom 8 (c03) R->L }
% 7.28/2.13 mult(X, mult(mult(rd(Y, X), X), i(X)))
% 7.28/2.13 = { by axiom 8 (c03) R->L }
% 7.28/2.13 mult(X, mult(mult(mult(rd(rd(Y, X), X), X), X), i(X)))
% 7.28/2.13 = { by lemma 26 }
% 7.28/2.13 mult(mult(X, rd(rd(Y, X), X)), X)
% 7.28/2.13 = { by lemma 25 }
% 7.28/2.13 rd(mult(X, mult(rd(Y, X), X)), X)
% 7.28/2.13 = { by axiom 8 (c03) }
% 7.28/2.13 rd(mult(X, Y), X)
% 7.28/2.13
% 7.28/2.13 Lemma 43: rd(mult(X, rd(Y, i(X))), X) = mult(X, Y).
% 7.28/2.13 Proof:
% 7.28/2.13 rd(mult(X, rd(Y, i(X))), X)
% 7.28/2.13 = { by lemma 42 R->L }
% 7.28/2.13 mult(X, mult(rd(Y, i(X)), i(X)))
% 7.28/2.13 = { by axiom 8 (c03) }
% 7.28/2.13 mult(X, Y)
% 7.28/2.13
% 7.28/2.13 Lemma 44: mult(X, rd(Y, i(X))) = mult(mult(X, Y), X).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(X, rd(Y, i(X)))
% 7.28/2.13 = { by axiom 8 (c03) R->L }
% 7.28/2.13 mult(rd(mult(X, rd(Y, i(X))), X), X)
% 7.28/2.13 = { by lemma 43 }
% 7.28/2.13 mult(mult(X, Y), X)
% 7.28/2.13
% 7.28/2.13 Lemma 45: rd(mult(i(X), Y), i(X)) = mult(i(X), mult(Y, X)).
% 7.28/2.13 Proof:
% 7.28/2.13 rd(mult(i(X), Y), i(X))
% 7.28/2.13 = { by lemma 42 R->L }
% 7.28/2.13 mult(i(X), mult(Y, i(i(X))))
% 7.28/2.13 = { by lemma 12 }
% 7.28/2.13 mult(i(X), mult(Y, X))
% 7.28/2.13
% 7.28/2.13 Lemma 46: mult(i(X), mult(X, mult(X, X))) = mult(X, X).
% 7.28/2.13 Proof:
% 7.28/2.13 mult(i(X), mult(X, mult(X, X)))
% 7.28/2.13 = { by axiom 1 (c05) R->L }
% 7.28/2.13 mult(i(X), mult(X, mult(mult(X, X), unit)))
% 7.28/2.13 = { by lemma 15 R->L }
% 7.28/2.13 mult(i(X), mult(mult(X, X), mult(X, unit)))
% 7.28/2.13 = { by axiom 1 (c05) }
% 7.28/2.13 mult(i(X), mult(mult(X, X), X))
% 7.28/2.13 = { by lemma 18 R->L }
% 7.28/2.13 mult(i(X), mult(ld(i(X), X), X))
% 7.28/2.13 = { by lemma 12 R->L }
% 7.28/2.13 mult(i(X), mult(ld(i(X), i(i(X))), X))
% 7.28/2.13 = { by lemma 21 R->L }
% 7.28/2.13 mult(i(X), mult(i(mult(i(X), i(X))), X))
% 7.28/2.13 = { by lemma 45 R->L }
% 7.28/2.13 rd(mult(i(X), i(mult(i(X), i(X)))), i(X))
% 7.28/2.13 = { by lemma 20 }
% 7.28/2.13 rd(i(i(X)), i(X))
% 7.28/2.13 = { by lemma 12 R->L }
% 7.28/2.13 rd(i(i(X)), i(i(i(X))))
% 7.28/2.13 = { by lemma 16 R->L }
% 7.28/2.13 rd(mult(mult(i(i(X)), i(i(X))), i(i(i(X)))), i(i(i(X))))
% 7.28/2.13 = { by axiom 6 (c04) }
% 7.28/2.14 mult(i(i(X)), i(i(X)))
% 7.28/2.14 = { by lemma 12 R->L }
% 7.28/2.14 i(i(mult(i(i(X)), i(i(X)))))
% 7.28/2.14 = { by lemma 21 }
% 7.28/2.14 i(ld(i(i(X)), i(i(i(X)))))
% 7.28/2.14 = { by lemma 12 }
% 7.28/2.14 i(ld(i(i(X)), i(X)))
% 7.28/2.14 = { by lemma 18 }
% 7.28/2.14 i(mult(i(X), i(X)))
% 7.28/2.14 = { by lemma 21 }
% 7.28/2.14 ld(i(X), i(i(X)))
% 7.28/2.14 = { by lemma 12 }
% 7.28/2.14 ld(i(X), X)
% 7.28/2.14 = { by lemma 18 }
% 7.28/2.14 mult(X, X)
% 7.28/2.14
% 7.28/2.14 Lemma 47: mult(i(X), mult(Y, i(X))) = rd(mult(i(X), Y), X).
% 7.28/2.14 Proof:
% 7.28/2.14 mult(i(X), mult(Y, i(X)))
% 7.28/2.14 = { by lemma 35 R->L }
% 7.28/2.14 rd(mult(i(X), Y), i(i(X)))
% 7.28/2.14 = { by lemma 12 }
% 7.28/2.14 rd(mult(i(X), Y), X)
% 7.28/2.14
% 7.28/2.14 Lemma 48: mult(mult(X, i(Y)), Y) = mult(mult(X, Y), i(Y)).
% 7.28/2.14 Proof:
% 7.28/2.14 mult(mult(X, i(Y)), Y)
% 7.28/2.14 = { by axiom 6 (c04) R->L }
% 7.28/2.14 mult(mult(X, i(Y)), rd(mult(Y, Y), Y))
% 7.28/2.14 = { by lemma 46 R->L }
% 7.28/2.14 mult(mult(X, i(Y)), rd(mult(i(Y), mult(Y, mult(Y, Y))), Y))
% 7.28/2.14 = { by lemma 47 R->L }
% 7.28/2.14 mult(mult(X, i(Y)), mult(i(Y), mult(mult(Y, mult(Y, Y)), i(Y))))
% 7.28/2.14 = { by axiom 10 (c08) }
% 7.28/2.14 mult(mult(X, mult(i(Y), mult(i(Y), mult(Y, mult(Y, Y))))), i(Y))
% 7.28/2.14 = { by lemma 46 }
% 7.28/2.14 mult(mult(X, mult(i(Y), mult(Y, Y))), i(Y))
% 7.28/2.14 = { by lemma 17 }
% 7.28/2.14 mult(mult(X, Y), i(Y))
% 7.28/2.14
% 7.28/2.14 Lemma 49: ld(X, rd(mult(X, Y), X)) = mult(Y, i(X)).
% 7.28/2.14 Proof:
% 7.28/2.14 ld(X, rd(mult(X, Y), X))
% 7.28/2.14 = { by lemma 42 R->L }
% 7.28/2.14 ld(X, mult(X, mult(Y, i(X))))
% 7.28/2.14 = { by axiom 5 (c02) }
% 7.28/2.14 mult(Y, i(X))
% 7.28/2.14
% 7.28/2.14 Lemma 50: mult(mult(X, Y), i(Y)) = rd(rd(X, Y), i(Y)).
% 7.28/2.14 Proof:
% 7.28/2.14 mult(mult(X, Y), i(Y))
% 7.28/2.14 = { by lemma 49 R->L }
% 7.28/2.14 ld(Y, rd(mult(Y, mult(X, Y)), Y))
% 7.28/2.14 = { by lemma 25 R->L }
% 7.28/2.14 ld(Y, mult(mult(Y, rd(X, Y)), Y))
% 7.28/2.14 = { by lemma 36 }
% 7.28/2.14 rd(rd(X, Y), i(Y))
% 7.28/2.14
% 7.28/2.14 Lemma 51: rd(rd(X, i(Y)), Y) = rd(rd(X, Y), i(Y)).
% 7.28/2.14 Proof:
% 7.28/2.14 rd(rd(X, i(Y)), Y)
% 7.28/2.14 = { by lemma 36 R->L }
% 7.28/2.14 rd(ld(Y, mult(mult(Y, X), Y)), Y)
% 7.28/2.14 = { by lemma 34 R->L }
% 7.28/2.14 rd(mult(Y, mult(ld(Y, X), Y)), Y)
% 7.28/2.14 = { by lemma 25 R->L }
% 7.28/2.14 mult(mult(Y, rd(ld(Y, X), Y)), Y)
% 7.28/2.14 = { by lemma 31 }
% 7.28/2.14 mult(mult(X, i(Y)), Y)
% 7.28/2.14 = { by lemma 48 }
% 7.28/2.14 mult(mult(X, Y), i(Y))
% 7.28/2.14 = { by lemma 50 }
% 7.28/2.14 rd(rd(X, Y), i(Y))
% 7.28/2.14
% 7.28/2.14 Lemma 52: mult(i(X), mult(ld(i(X), Y), X)) = rd(Y, i(X)).
% 7.28/2.14 Proof:
% 7.28/2.14 mult(i(X), mult(ld(i(X), Y), X))
% 7.28/2.14 = { by lemma 45 R->L }
% 7.28/2.14 rd(mult(i(X), ld(i(X), Y)), i(X))
% 7.28/2.14 = { by axiom 7 (c01) }
% 7.28/2.14 rd(Y, i(X))
% 7.28/2.14
% 7.28/2.14 Lemma 53: mult(X, mult(mult(ld(X, Y), X), X)) = mult(mult(Y, X), X).
% 7.28/2.14 Proof:
% 7.28/2.14 mult(X, mult(mult(ld(X, Y), X), X))
% 7.28/2.14 = { by lemma 13 R->L }
% 7.28/2.14 mult(mult(mult(X, ld(X, Y)), X), X)
% 7.28/2.14 = { by axiom 7 (c01) }
% 7.28/2.14 mult(mult(Y, X), X)
% 7.28/2.14
% 7.28/2.15 Lemma 54: mult(mult(X, Y), rd(Z, i(Y))) = mult(mult(X, mult(Y, Z)), Y).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(mult(X, Y), rd(Z, i(Y)))
% 7.28/2.15 = { by lemma 36 R->L }
% 7.28/2.15 mult(mult(X, Y), ld(Y, mult(mult(Y, Z), Y)))
% 7.28/2.15 = { by lemma 27 R->L }
% 7.28/2.15 mult(mult(X, Y), mult(mult(mult(Z, Y), Y), i(Y)))
% 7.28/2.15 = { by lemma 48 R->L }
% 7.28/2.15 mult(mult(X, Y), mult(mult(mult(Z, Y), i(Y)), Y))
% 7.28/2.15 = { by lemma 48 R->L }
% 7.28/2.15 mult(mult(X, Y), mult(mult(mult(Z, i(Y)), Y), Y))
% 7.28/2.15 = { by lemma 53 R->L }
% 7.28/2.15 mult(mult(X, Y), mult(Y, mult(mult(ld(Y, mult(Z, i(Y))), Y), Y)))
% 7.28/2.15 = { by axiom 10 (c08) }
% 7.28/2.15 mult(mult(X, mult(Y, mult(Y, mult(ld(Y, mult(Z, i(Y))), Y)))), Y)
% 7.28/2.15 = { by lemma 33 }
% 7.28/2.15 mult(mult(X, mult(mult(Y, mult(Z, i(Y))), Y)), Y)
% 7.28/2.15 = { by lemma 42 }
% 7.28/2.15 mult(mult(X, mult(rd(mult(Y, Z), Y), Y)), Y)
% 7.28/2.15 = { by axiom 8 (c03) }
% 7.28/2.15 mult(mult(X, mult(Y, Z)), Y)
% 7.28/2.15
% 7.28/2.15 Lemma 55: mult(X, rd(mult(i(X), Y), X)) = rd(Y, X).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(X, rd(mult(i(X), Y), X))
% 7.28/2.15 = { by lemma 30 R->L }
% 7.28/2.15 mult(mult(X, mult(i(X), Y)), i(X))
% 7.28/2.15 = { by lemma 54 R->L }
% 7.28/2.15 mult(mult(X, i(X)), rd(Y, i(i(X))))
% 7.28/2.15 = { by axiom 3 (c09) }
% 7.28/2.15 mult(unit, rd(Y, i(i(X))))
% 7.28/2.15 = { by axiom 2 (c06) }
% 7.28/2.15 rd(Y, i(i(X)))
% 7.28/2.15 = { by lemma 12 }
% 7.28/2.15 rd(Y, X)
% 7.28/2.15
% 7.28/2.15 Lemma 56: ld(X, mult(mult(X, X), Y)) = ld(i(X), Y).
% 7.28/2.15 Proof:
% 7.28/2.15 ld(X, mult(mult(X, X), Y))
% 7.28/2.15 = { by lemma 41 R->L }
% 7.28/2.15 rd(mult(X, mult(Y, X)), X)
% 7.28/2.15 = { by lemma 25 R->L }
% 7.28/2.15 mult(mult(X, rd(Y, X)), X)
% 7.28/2.15 = { by lemma 44 R->L }
% 7.28/2.15 mult(X, rd(rd(Y, X), i(X)))
% 7.28/2.15 = { by lemma 51 R->L }
% 7.28/2.15 mult(X, rd(rd(Y, i(X)), X))
% 7.28/2.15 = { by lemma 52 R->L }
% 7.28/2.15 mult(X, rd(mult(i(X), mult(ld(i(X), Y), X)), X))
% 7.28/2.15 = { by lemma 55 }
% 7.28/2.15 rd(mult(ld(i(X), Y), X), X)
% 7.28/2.15 = { by axiom 6 (c04) }
% 7.28/2.15 ld(i(X), Y)
% 7.28/2.15
% 7.28/2.15 Lemma 57: mult(X, mult(mult(X, X), ld(X, Y))) = mult(mult(X, X), Y).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(X, mult(mult(X, X), ld(X, Y)))
% 7.28/2.15 = { by lemma 15 R->L }
% 7.28/2.15 mult(mult(X, X), mult(X, ld(X, Y)))
% 7.28/2.15 = { by axiom 7 (c01) }
% 7.28/2.15 mult(mult(X, X), Y)
% 7.28/2.15
% 7.28/2.15 Lemma 58: mult(mult(X, X), ld(X, Y)) = ld(X, mult(mult(X, X), Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(mult(X, X), ld(X, Y))
% 7.28/2.15 = { by axiom 5 (c02) R->L }
% 7.28/2.15 ld(X, mult(X, mult(mult(X, X), ld(X, Y))))
% 7.28/2.15 = { by lemma 57 }
% 7.28/2.15 ld(X, mult(mult(X, X), Y))
% 7.28/2.15
% 7.28/2.15 Lemma 59: ld(i(X), ld(X, Y)) = ld(X, ld(i(X), Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 ld(i(X), ld(X, Y))
% 7.28/2.15 = { by lemma 56 R->L }
% 7.28/2.15 ld(X, mult(mult(X, X), ld(X, Y)))
% 7.28/2.15 = { by lemma 58 }
% 7.28/2.15 ld(X, ld(X, mult(mult(X, X), Y)))
% 7.28/2.15 = { by lemma 56 }
% 7.28/2.15 ld(X, ld(i(X), Y))
% 7.28/2.15
% 7.28/2.15 Lemma 60: ld(i(X), mult(X, Y)) = mult(mult(X, X), Y).
% 7.28/2.15 Proof:
% 7.28/2.15 ld(i(X), mult(X, Y))
% 7.28/2.15 = { by lemma 56 R->L }
% 7.28/2.15 ld(X, mult(mult(X, X), mult(X, Y)))
% 7.28/2.15 = { by lemma 15 }
% 7.28/2.15 ld(X, mult(X, mult(mult(X, X), Y)))
% 7.28/2.15 = { by axiom 5 (c02) }
% 7.28/2.15 mult(mult(X, X), Y)
% 7.28/2.15
% 7.28/2.15 Lemma 61: mult(ld(X, i(X)), Y) = mult(i(X), ld(X, Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(ld(X, i(X)), Y)
% 7.28/2.15 = { by lemma 23 R->L }
% 7.28/2.15 mult(mult(i(X), i(X)), Y)
% 7.28/2.15 = { by axiom 7 (c01) R->L }
% 7.28/2.15 mult(i(X), ld(i(X), mult(mult(i(X), i(X)), Y)))
% 7.28/2.15 = { by lemma 56 }
% 7.28/2.15 mult(i(X), ld(i(i(X)), Y))
% 7.28/2.15 = { by lemma 12 }
% 7.28/2.15 mult(i(X), ld(X, Y))
% 7.28/2.15
% 7.28/2.15 Lemma 62: ld(ld(X, i(X)), Y) = mult(mult(X, X), Y).
% 7.28/2.15 Proof:
% 7.28/2.15 ld(ld(X, i(X)), Y)
% 7.28/2.15 = { by lemma 23 R->L }
% 7.28/2.15 ld(mult(i(X), i(X)), Y)
% 7.28/2.15 = { by axiom 7 (c01) R->L }
% 7.28/2.15 mult(i(i(X)), ld(i(i(X)), ld(mult(i(X), i(X)), Y)))
% 7.28/2.15 = { by lemma 56 R->L }
% 7.28/2.15 mult(i(i(X)), ld(i(X), mult(mult(i(X), i(X)), ld(mult(i(X), i(X)), Y))))
% 7.28/2.15 = { by axiom 7 (c01) }
% 7.28/2.15 mult(i(i(X)), ld(i(X), Y))
% 7.28/2.15 = { by lemma 61 R->L }
% 7.28/2.15 mult(ld(i(X), i(i(X))), Y)
% 7.28/2.15 = { by lemma 23 R->L }
% 7.28/2.15 mult(mult(i(i(X)), i(i(X))), Y)
% 7.28/2.15 = { by lemma 60 R->L }
% 7.28/2.15 ld(i(i(i(X))), mult(i(i(X)), Y))
% 7.28/2.15 = { by lemma 12 }
% 7.28/2.15 ld(i(X), mult(i(i(X)), Y))
% 7.28/2.15 = { by lemma 12 }
% 7.28/2.15 ld(i(X), mult(X, Y))
% 7.28/2.15 = { by lemma 60 }
% 7.28/2.15 mult(mult(X, X), Y)
% 7.28/2.15
% 7.28/2.15 Lemma 63: mult(X, mult(i(X), Y)) = rd(rd(Y, X), i(X)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(X, mult(i(X), Y))
% 7.28/2.15 = { by axiom 8 (c03) R->L }
% 7.28/2.15 mult(X, mult(rd(mult(i(X), Y), X), X))
% 7.28/2.15 = { by lemma 35 R->L }
% 7.28/2.15 rd(mult(X, rd(mult(i(X), Y), X)), i(X))
% 7.28/2.15 = { by lemma 55 }
% 7.28/2.15 rd(rd(Y, X), i(X))
% 7.28/2.15
% 7.28/2.15 Lemma 64: mult(mult(ld(X, Y), X), X) = ld(X, mult(mult(Y, X), X)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(mult(ld(X, Y), X), X)
% 7.28/2.15 = { by axiom 5 (c02) R->L }
% 7.28/2.15 ld(X, mult(X, mult(mult(ld(X, Y), X), X)))
% 7.28/2.15 = { by lemma 53 }
% 7.28/2.15 ld(X, mult(mult(Y, X), X))
% 7.28/2.15
% 7.28/2.15 Lemma 65: mult(X, mult(ld(X, mult(mult(Y, X), X)), Z)) = mult(mult(Y, X), mult(X, Z)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(X, mult(ld(X, mult(mult(Y, X), X)), Z))
% 7.28/2.15 = { by lemma 64 R->L }
% 7.28/2.15 mult(X, mult(mult(mult(ld(X, Y), X), X), Z))
% 7.28/2.15 = { by axiom 9 (c07) R->L }
% 7.28/2.15 mult(mult(mult(X, ld(X, Y)), X), mult(X, Z))
% 7.28/2.15 = { by axiom 7 (c01) }
% 7.28/2.15 mult(mult(Y, X), mult(X, Z))
% 7.28/2.15
% 7.28/2.15 Lemma 66: mult(X, mult(ld(X, mult(Y, X)), Z)) = mult(Y, mult(X, Z)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(X, mult(ld(X, mult(Y, X)), Z))
% 7.28/2.15 = { by axiom 8 (c03) R->L }
% 7.28/2.15 mult(X, mult(ld(X, mult(mult(rd(Y, X), X), X)), Z))
% 7.28/2.15 = { by lemma 65 }
% 7.28/2.15 mult(mult(rd(Y, X), X), mult(X, Z))
% 7.28/2.15 = { by axiom 8 (c03) }
% 7.28/2.15 mult(Y, mult(X, Z))
% 7.28/2.15
% 7.28/2.15 Lemma 67: mult(X, i(ld(X, mult(Y, X)))) = ld(Y, X).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(X, i(ld(X, mult(Y, X))))
% 7.28/2.15 = { by axiom 5 (c02) R->L }
% 7.28/2.15 ld(Y, mult(Y, mult(X, i(ld(X, mult(Y, X))))))
% 7.28/2.15 = { by lemma 66 R->L }
% 7.28/2.15 ld(Y, mult(X, mult(ld(X, mult(Y, X)), i(ld(X, mult(Y, X))))))
% 7.28/2.15 = { by axiom 3 (c09) }
% 7.28/2.15 ld(Y, mult(X, unit))
% 7.28/2.15 = { by axiom 1 (c05) }
% 7.28/2.15 ld(Y, X)
% 7.28/2.15
% 7.28/2.15 Lemma 68: mult(X, i(ld(X, Y))) = ld(rd(Y, X), X).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(X, i(ld(X, Y)))
% 7.28/2.15 = { by axiom 8 (c03) R->L }
% 7.28/2.15 mult(X, i(ld(X, mult(rd(Y, X), X))))
% 7.28/2.15 = { by lemma 67 }
% 7.28/2.15 ld(rd(Y, X), X)
% 7.28/2.15
% 7.28/2.15 Lemma 69: rd(rd(mult(X, i(Y)), Y), i(Y)) = rd(X, Y).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(rd(mult(X, i(Y)), Y), i(Y))
% 7.28/2.15 = { by lemma 50 R->L }
% 7.28/2.15 mult(mult(mult(X, i(Y)), Y), i(Y))
% 7.28/2.15 = { by lemma 48 R->L }
% 7.28/2.15 mult(mult(mult(X, i(Y)), i(Y)), Y)
% 7.28/2.15 = { by lemma 12 R->L }
% 7.28/2.15 mult(mult(mult(X, i(Y)), i(Y)), i(i(Y)))
% 7.28/2.15 = { by lemma 27 }
% 7.28/2.15 ld(i(Y), mult(mult(i(Y), X), i(Y)))
% 7.28/2.15 = { by lemma 36 }
% 7.28/2.15 rd(X, i(i(Y)))
% 7.28/2.15 = { by lemma 12 }
% 7.28/2.15 rd(X, Y)
% 7.28/2.15
% 7.28/2.15 Lemma 70: mult(rd(X, Y), i(Y)) = rd(mult(X, i(Y)), Y).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(rd(X, Y), i(Y))
% 7.28/2.15 = { by lemma 69 R->L }
% 7.28/2.15 mult(rd(rd(mult(X, i(Y)), Y), i(Y)), i(Y))
% 7.28/2.15 = { by axiom 8 (c03) }
% 7.28/2.15 rd(mult(X, i(Y)), Y)
% 7.28/2.15
% 7.28/2.15 Lemma 71: mult(rd(X, i(Y)), Y) = rd(mult(X, Y), i(Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(rd(X, i(Y)), Y)
% 7.28/2.15 = { by lemma 36 R->L }
% 7.28/2.15 mult(ld(Y, mult(mult(Y, X), Y)), Y)
% 7.28/2.15 = { by lemma 27 R->L }
% 7.28/2.15 mult(mult(mult(mult(X, Y), Y), i(Y)), Y)
% 7.28/2.15 = { by lemma 48 }
% 7.28/2.15 mult(mult(mult(mult(X, Y), Y), Y), i(Y))
% 7.28/2.15 = { by lemma 27 }
% 7.28/2.15 ld(Y, mult(mult(Y, mult(X, Y)), Y))
% 7.28/2.15 = { by lemma 36 }
% 7.28/2.15 rd(mult(X, Y), i(Y))
% 7.28/2.15
% 7.28/2.15 Lemma 72: mult(mult(X, mult(Y, Y)), Y) = mult(mult(X, Y), mult(Y, Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(mult(X, mult(Y, Y)), Y)
% 7.28/2.15 = { by axiom 1 (c05) R->L }
% 7.28/2.15 mult(mult(X, mult(Y, mult(Y, unit))), Y)
% 7.28/2.15 = { by axiom 10 (c08) R->L }
% 7.28/2.15 mult(mult(X, Y), mult(Y, mult(unit, Y)))
% 7.28/2.15 = { by axiom 2 (c06) }
% 7.28/2.15 mult(mult(X, Y), mult(Y, Y))
% 7.28/2.15
% 7.28/2.15 Lemma 73: rd(mult(mult(X, Y), mult(Y, Y)), Y) = mult(X, mult(Y, Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(mult(mult(X, Y), mult(Y, Y)), Y)
% 7.28/2.15 = { by lemma 72 R->L }
% 7.28/2.15 rd(mult(mult(X, mult(Y, Y)), Y), Y)
% 7.28/2.15 = { by axiom 6 (c04) }
% 7.28/2.15 mult(X, mult(Y, Y))
% 7.28/2.15
% 7.28/2.15 Lemma 74: mult(mult(X, mult(Y, X)), X) = mult(mult(X, Y), mult(X, X)).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(mult(X, mult(Y, X)), X)
% 7.28/2.15 = { by lemma 14 R->L }
% 7.28/2.15 rd(mult(X, mult(mult(mult(Y, X), X), X)), X)
% 7.28/2.15 = { by axiom 9 (c07) R->L }
% 7.28/2.15 rd(mult(mult(mult(X, Y), X), mult(X, X)), X)
% 7.28/2.15 = { by lemma 73 }
% 7.28/2.15 mult(mult(X, Y), mult(X, X))
% 7.28/2.15
% 7.28/2.15 Lemma 75: mult(mult(X, Y), mult(X, X)) = mult(X, mult(Y, mult(X, X))).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(mult(X, Y), mult(X, X))
% 7.28/2.15 = { by lemma 74 R->L }
% 7.28/2.15 mult(mult(X, mult(Y, X)), X)
% 7.28/2.15 = { by axiom 5 (c02) R->L }
% 7.28/2.15 ld(X, mult(X, mult(mult(X, mult(Y, X)), X)))
% 7.28/2.15 = { by lemma 39 R->L }
% 7.28/2.15 ld(X, mult(mult(X, X), mult(mult(Y, X), X)))
% 7.28/2.15 = { by lemma 58 R->L }
% 7.28/2.15 mult(mult(X, X), ld(X, mult(mult(Y, X), X)))
% 7.28/2.15 = { by lemma 64 R->L }
% 7.28/2.15 mult(mult(X, X), mult(mult(ld(X, Y), X), X))
% 7.28/2.15 = { by lemma 39 }
% 7.28/2.15 mult(X, mult(mult(X, mult(ld(X, Y), X)), X))
% 7.28/2.15 = { by lemma 74 }
% 7.28/2.15 mult(X, mult(mult(X, ld(X, Y)), mult(X, X)))
% 7.28/2.15 = { by axiom 7 (c01) }
% 7.28/2.15 mult(X, mult(Y, mult(X, X)))
% 7.28/2.15
% 7.28/2.15 Lemma 76: mult(mult(X, mult(Y, Y)), i(Y)) = mult(X, Y).
% 7.28/2.15 Proof:
% 7.28/2.15 mult(mult(X, mult(Y, Y)), i(Y))
% 7.28/2.15 = { by lemma 49 R->L }
% 7.28/2.15 ld(Y, rd(mult(Y, mult(X, mult(Y, Y))), Y))
% 7.28/2.15 = { by lemma 75 R->L }
% 7.28/2.15 ld(Y, rd(mult(mult(Y, X), mult(Y, Y)), Y))
% 7.28/2.15 = { by lemma 74 R->L }
% 7.28/2.15 ld(Y, rd(mult(mult(Y, mult(X, Y)), Y), Y))
% 7.28/2.15 = { by axiom 6 (c04) }
% 7.28/2.15 ld(Y, mult(Y, mult(X, Y)))
% 7.28/2.15 = { by axiom 5 (c02) }
% 7.28/2.15 mult(X, Y)
% 7.28/2.15
% 7.28/2.15 Lemma 77: rd(mult(X, Y), mult(Y, Y)) = mult(X, i(Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(mult(X, Y), mult(Y, Y))
% 7.28/2.15 = { by axiom 8 (c03) R->L }
% 7.28/2.15 rd(mult(mult(rd(X, mult(Y, Y)), mult(Y, Y)), Y), mult(Y, Y))
% 7.28/2.15 = { by lemma 72 }
% 7.28/2.15 rd(mult(mult(rd(X, mult(Y, Y)), Y), mult(Y, Y)), mult(Y, Y))
% 7.28/2.15 = { by axiom 6 (c04) }
% 7.28/2.15 mult(rd(X, mult(Y, Y)), Y)
% 7.28/2.15 = { by lemma 76 R->L }
% 7.28/2.15 mult(mult(rd(X, mult(Y, Y)), mult(Y, Y)), i(Y))
% 7.28/2.15 = { by axiom 8 (c03) }
% 7.28/2.15 mult(X, i(Y))
% 7.28/2.15
% 7.28/2.15 Lemma 78: rd(mult(X, i(Y)), Y) = rd(X, mult(Y, Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(mult(X, i(Y)), Y)
% 7.28/2.15 = { by lemma 70 R->L }
% 7.28/2.15 mult(rd(X, Y), i(Y))
% 7.28/2.15 = { by lemma 77 R->L }
% 7.28/2.15 rd(mult(rd(X, Y), Y), mult(Y, Y))
% 7.28/2.15 = { by axiom 8 (c03) }
% 7.28/2.15 rd(X, mult(Y, Y))
% 7.28/2.15
% 7.28/2.15 Lemma 79: rd(mult(X, Y), i(Y)) = mult(X, mult(Y, Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(mult(X, Y), i(Y))
% 7.28/2.15 = { by lemma 76 R->L }
% 7.28/2.15 rd(mult(mult(X, mult(Y, Y)), i(Y)), i(Y))
% 7.28/2.15 = { by axiom 6 (c04) }
% 7.28/2.15 mult(X, mult(Y, Y))
% 7.28/2.15
% 7.28/2.15 Lemma 80: rd(X, ld(Y, i(Y))) = mult(X, mult(Y, Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(X, ld(Y, i(Y)))
% 7.28/2.15 = { by lemma 23 R->L }
% 7.28/2.15 rd(X, mult(i(Y), i(Y)))
% 7.28/2.15 = { by lemma 78 R->L }
% 7.28/2.15 rd(mult(X, i(i(Y))), i(Y))
% 7.28/2.15 = { by lemma 12 }
% 7.28/2.15 rd(mult(X, Y), i(Y))
% 7.28/2.15 = { by lemma 79 }
% 7.28/2.15 mult(X, mult(Y, Y))
% 7.28/2.15
% 7.28/2.15 Lemma 81: rd(mult(X, mult(Y, Y)), Y) = rd(X, i(Y)).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(mult(X, mult(Y, Y)), Y)
% 7.28/2.15 = { by lemma 69 R->L }
% 7.28/2.15 rd(rd(mult(mult(X, mult(Y, Y)), i(Y)), Y), i(Y))
% 7.28/2.15 = { by lemma 76 }
% 7.28/2.15 rd(rd(mult(X, Y), Y), i(Y))
% 7.28/2.15 = { by axiom 6 (c04) }
% 7.28/2.15 rd(X, i(Y))
% 7.28/2.15
% 7.28/2.15 Lemma 82: rd(X, i(ld(Y, X))) = mult(rd(X, Y), X).
% 7.28/2.15 Proof:
% 7.28/2.15 rd(X, i(ld(Y, X)))
% 7.28/2.15 = { by axiom 8 (c03) R->L }
% 7.28/2.15 rd(X, i(ld(Y, mult(rd(X, Y), Y))))
% 7.28/2.15 = { by axiom 8 (c03) R->L }
% 7.28/2.16 rd(mult(rd(X, Y), Y), i(ld(Y, mult(rd(X, Y), Y))))
% 7.28/2.16 = { by lemma 81 R->L }
% 7.28/2.16 rd(mult(mult(rd(X, Y), Y), mult(ld(Y, mult(rd(X, Y), Y)), ld(Y, mult(rd(X, Y), Y)))), ld(Y, mult(rd(X, Y), Y)))
% 7.28/2.16 = { by axiom 7 (c01) R->L }
% 7.28/2.16 rd(mult(mult(Y, ld(Y, mult(rd(X, Y), Y))), mult(ld(Y, mult(rd(X, Y), Y)), ld(Y, mult(rd(X, Y), Y)))), ld(Y, mult(rd(X, Y), Y)))
% 7.28/2.16 = { by lemma 73 }
% 7.28/2.16 mult(Y, mult(ld(Y, mult(rd(X, Y), Y)), ld(Y, mult(rd(X, Y), Y))))
% 7.28/2.16 = { by lemma 66 }
% 7.28/2.16 mult(rd(X, Y), mult(Y, ld(Y, mult(rd(X, Y), Y))))
% 7.28/2.16 = { by axiom 7 (c01) }
% 7.28/2.16 mult(rd(X, Y), mult(rd(X, Y), Y))
% 7.28/2.16 = { by axiom 8 (c03) }
% 7.28/2.16 mult(rd(X, Y), X)
% 7.28/2.16
% 7.28/2.16 Lemma 83: rd(mult(i(X), Y), X) = ld(X, rd(Y, X)).
% 7.28/2.16 Proof:
% 7.28/2.16 rd(mult(i(X), Y), X)
% 7.28/2.16 = { by axiom 5 (c02) R->L }
% 7.28/2.16 ld(X, mult(X, rd(mult(i(X), Y), X)))
% 7.28/2.16 = { by lemma 55 }
% 7.28/2.16 ld(X, rd(Y, X))
% 7.28/2.16
% 7.28/2.16 Lemma 84: rd(rd(X, Y), i(Y)) = ld(Y, ld(i(Y), X)).
% 7.28/2.16 Proof:
% 7.28/2.16 rd(rd(X, Y), i(Y))
% 7.28/2.16 = { by lemma 51 R->L }
% 7.28/2.16 rd(rd(X, i(Y)), Y)
% 7.28/2.16 = { by lemma 52 R->L }
% 7.28/2.16 rd(mult(i(Y), mult(ld(i(Y), X), Y)), Y)
% 7.28/2.16 = { by lemma 83 }
% 7.28/2.16 ld(Y, rd(mult(ld(i(Y), X), Y), Y))
% 7.28/2.16 = { by axiom 6 (c04) }
% 7.28/2.16 ld(Y, ld(i(Y), X))
% 7.28/2.16
% 7.28/2.16 Lemma 85: i(ld(X, mult(Y, X))) = ld(X, ld(Y, X)).
% 7.28/2.16 Proof:
% 7.28/2.16 i(ld(X, mult(Y, X)))
% 7.28/2.16 = { by axiom 5 (c02) R->L }
% 7.28/2.16 ld(X, mult(X, i(ld(X, mult(Y, X)))))
% 7.28/2.16 = { by lemma 67 }
% 7.28/2.16 ld(X, ld(Y, X))
% 7.28/2.16
% 7.28/2.16 Lemma 86: mult(ld(mult(X, X), Y), mult(X, X)) = ld(mult(X, X), mult(Y, mult(X, X))).
% 7.28/2.16 Proof:
% 7.28/2.16 mult(ld(mult(X, X), Y), mult(X, X))
% 7.28/2.16 = { by lemma 37 R->L }
% 7.28/2.16 ld(mult(X, X), rd(Y, i(mult(X, X))))
% 7.28/2.16 = { by lemma 21 }
% 7.28/2.16 ld(mult(X, X), rd(Y, ld(X, i(X))))
% 7.28/2.16 = { by lemma 80 }
% 7.28/2.16 ld(mult(X, X), mult(Y, mult(X, X)))
% 7.28/2.16
% 7.28/2.16 Lemma 87: ld(X, rd(X, mult(Y, Y))) = ld(Y, i(Y)).
% 7.28/2.16 Proof:
% 7.28/2.16 ld(X, rd(X, mult(Y, Y)))
% 7.28/2.16 = { by axiom 8 (c03) R->L }
% 7.28/2.16 ld(mult(rd(X, mult(Y, Y)), mult(Y, Y)), rd(X, mult(Y, Y)))
% 7.28/2.16 = { by axiom 7 (c01) R->L }
% 7.28/2.16 ld(mult(rd(X, mult(Y, Y)), mult(Y, Y)), mult(mult(Y, Y), ld(mult(Y, Y), rd(X, mult(Y, Y)))))
% 7.28/2.16 = { by axiom 7 (c01) R->L }
% 7.28/2.16 ld(mult(mult(Y, Y), ld(mult(Y, Y), mult(rd(X, mult(Y, Y)), mult(Y, Y)))), mult(mult(Y, Y), ld(mult(Y, Y), rd(X, mult(Y, Y)))))
% 7.28/2.16 = { by lemma 86 R->L }
% 7.28/2.16 ld(mult(mult(Y, Y), mult(ld(mult(Y, Y), rd(X, mult(Y, Y))), mult(Y, Y))), mult(mult(Y, Y), ld(mult(Y, Y), rd(X, mult(Y, Y)))))
% 7.28/2.16 = { by lemma 29 R->L }
% 7.28/2.16 ld(mult(mult(Y, Y), mult(ld(mult(Y, Y), rd(X, mult(Y, Y))), mult(Y, Y))), mult(mult(mult(Y, Y), mult(ld(mult(Y, Y), rd(X, mult(Y, Y))), mult(Y, Y))), i(mult(Y, Y))))
% 7.28/2.16 = { by axiom 5 (c02) }
% 7.28/2.16 i(mult(Y, Y))
% 7.28/2.16 = { by lemma 21 }
% 7.28/2.16 ld(Y, i(Y))
% 7.28/2.16
% 7.28/2.16 Lemma 88: ld(rd(mult(X, Y), X), X) = mult(X, i(Y)).
% 7.28/2.16 Proof:
% 7.28/2.16 ld(rd(mult(X, Y), X), X)
% 7.28/2.16 = { by lemma 68 R->L }
% 7.28/2.16 mult(X, i(ld(X, mult(X, Y))))
% 7.28/2.16 = { by axiom 5 (c02) }
% 7.28/2.16 mult(X, i(Y))
% 7.28/2.16
% 7.28/2.16 Lemma 89: mult(X, ld(mult(X, X), Y)) = ld(mult(X, X), mult(X, Y)).
% 7.28/2.16 Proof:
% 7.28/2.16 mult(X, ld(mult(X, X), Y))
% 7.28/2.16 = { by lemma 19 R->L }
% 7.28/2.16 ld(mult(X, X), mult(X, mult(mult(X, X), ld(mult(X, X), Y))))
% 7.28/2.16 = { by axiom 7 (c01) }
% 7.28/2.16 ld(mult(X, X), mult(X, Y))
% 7.28/2.16
% 7.28/2.16 Lemma 90: rd(rd(rd(X, Y), Y), i(Y)) = mult(X, i(Y)).
% 7.28/2.16 Proof:
% 7.28/2.16 rd(rd(rd(X, Y), Y), i(Y))
% 7.28/2.16 = { by lemma 51 R->L }
% 7.28/2.16 rd(rd(rd(X, Y), i(Y)), Y)
% 7.28/2.16 = { by lemma 50 R->L }
% 7.28/2.16 rd(mult(mult(X, Y), i(Y)), Y)
% 7.28/2.16 = { by lemma 70 R->L }
% 7.28/2.16 mult(rd(mult(X, Y), Y), i(Y))
% 7.28/2.16 = { by axiom 6 (c04) }
% 7.28/2.16 mult(X, i(Y))
% 7.28/2.16
% 7.28/2.16 Lemma 91: mult(X, rd(rd(Y, X), X)) = rd(rd(mult(X, Y), X), X).
% 7.28/2.16 Proof:
% 7.28/2.16 mult(X, rd(rd(Y, X), X))
% 7.28/2.16 = { by lemma 43 R->L }
% 7.28/2.16 rd(mult(X, rd(rd(rd(Y, X), X), i(X))), X)
% 7.28/2.16 = { by lemma 90 }
% 7.28/2.16 rd(mult(X, mult(Y, i(X))), X)
% 7.28/2.16 = { by lemma 42 }
% 7.28/2.16 rd(rd(mult(X, Y), X), X)
% 7.28/2.16
% 7.28/2.16 Lemma 92: mult(rd(X, Y), mult(Y, Y)) = rd(mult(X, mult(Y, Y)), Y).
% 7.28/2.16 Proof:
% 7.28/2.16 mult(rd(X, Y), mult(Y, Y))
% 7.28/2.16 = { by lemma 73 R->L }
% 7.28/2.16 rd(mult(mult(rd(X, Y), Y), mult(Y, Y)), Y)
% 7.28/2.16 = { by axiom 8 (c03) }
% 7.28/2.16 rd(mult(X, mult(Y, Y)), Y)
% 7.28/2.16
% 7.28/2.16 Lemma 93: mult(mult(i(X), Y), i(X)) = mult(i(X), rd(Y, X)).
% 7.28/2.16 Proof:
% 7.28/2.16 mult(mult(i(X), Y), i(X))
% 7.28/2.16 = { by lemma 44 R->L }
% 7.28/2.16 mult(i(X), rd(Y, i(i(X))))
% 7.28/2.16 = { by lemma 12 }
% 7.28/2.16 mult(i(X), rd(Y, X))
% 7.28/2.16
% 7.28/2.16 Lemma 94: rd(ld(X, mult(mult(Y, X), X)), X) = mult(ld(X, Y), X).
% 7.28/2.16 Proof:
% 7.28/2.16 rd(ld(X, mult(mult(Y, X), X)), X)
% 7.28/2.16 = { by lemma 64 R->L }
% 7.28/2.16 rd(mult(mult(ld(X, Y), X), X), X)
% 7.28/2.16 = { by axiom 6 (c04) }
% 7.28/2.16 mult(ld(X, Y), X)
% 7.28/2.16
% 7.28/2.16 Lemma 95: mult(ld(X, rd(Y, X)), X) = rd(ld(X, mult(Y, X)), X).
% 7.28/2.16 Proof:
% 7.28/2.16 mult(ld(X, rd(Y, X)), X)
% 7.28/2.16 = { by lemma 94 R->L }
% 7.28/2.16 rd(ld(X, mult(mult(rd(Y, X), X), X)), X)
% 7.28/2.16 = { by axiom 8 (c03) }
% 7.28/2.16 rd(ld(X, mult(Y, X)), X)
% 7.28/2.16
% 7.28/2.16 Lemma 96: rd(rd(mult(i(X), mult(Y, X)), X), X) = mult(i(X), rd(Y, X)).
% 7.28/2.16 Proof:
% 7.28/2.16 rd(rd(mult(i(X), mult(Y, X)), X), X)
% 7.28/2.16 = { by lemma 47 R->L }
% 7.28/2.16 rd(mult(i(X), mult(mult(Y, X), i(X))), X)
% 7.28/2.16 = { by lemma 48 R->L }
% 7.28/2.16 rd(mult(i(X), mult(mult(Y, i(X)), X)), X)
% 7.28/2.16 = { by lemma 47 R->L }
% 7.28/2.16 mult(i(X), mult(mult(mult(Y, i(X)), X), i(X)))
% 7.28/2.16 = { by lemma 48 R->L }
% 7.28/2.16 mult(i(X), mult(mult(mult(Y, i(X)), i(X)), X))
% 7.28/2.16 = { by axiom 9 (c07) R->L }
% 7.28/2.16 mult(mult(mult(i(X), Y), i(X)), mult(i(X), X))
% 7.28/2.16 = { by axiom 4 (c10) }
% 7.28/2.16 mult(mult(mult(i(X), Y), i(X)), unit)
% 7.28/2.16 = { by axiom 1 (c05) }
% 7.28/2.16 mult(mult(i(X), Y), i(X))
% 7.28/2.16 = { by lemma 93 }
% 7.28/2.16 mult(i(X), rd(Y, X))
% 7.28/2.16
% 7.28/2.16 Lemma 97: rd(ld(X, ld(i(X), Y)), X) = mult(Y, i(X)).
% 7.28/2.16 Proof:
% 7.28/2.16 rd(ld(X, ld(i(X), Y)), X)
% 7.28/2.16 = { by lemma 32 R->L }
% 7.28/2.16 ld(X, mult(ld(i(X), Y), i(X)))
% 7.28/2.16 = { by lemma 37 R->L }
% 7.28/2.16 ld(X, ld(i(X), rd(Y, i(i(X)))))
% 7.28/2.16 = { by lemma 84 R->L }
% 7.28/2.16 rd(rd(rd(Y, i(i(X))), X), i(X))
% 7.28/2.16 = { by lemma 63 R->L }
% 7.28/2.16 mult(X, mult(i(X), rd(Y, i(i(X)))))
% 7.28/2.16 = { by lemma 43 R->L }
% 7.28/2.16 rd(mult(X, rd(mult(i(X), rd(Y, i(i(X)))), i(X))), X)
% 7.28/2.16 = { by lemma 43 }
% 7.28/2.16 rd(mult(X, mult(i(X), Y)), X)
% 7.28/2.16 = { by lemma 63 }
% 7.28/2.16 rd(rd(rd(Y, X), i(X)), X)
% 7.28/2.16 = { by lemma 51 }
% 7.28/2.16 rd(rd(rd(Y, X), X), i(X))
% 7.28/2.16 = { by lemma 90 }
% 7.28/2.16 mult(Y, i(X))
% 7.28/2.16
% 7.28/2.16 Lemma 98: ld(X, ld(X, ld(i(X), Y))) = mult(i(X), Y).
% 7.28/2.16 Proof:
% 7.28/2.16 ld(X, ld(X, ld(i(X), Y)))
% 7.28/2.16 = { by axiom 6 (c04) R->L }
% 7.28/2.16 ld(X, rd(mult(ld(X, ld(i(X), Y)), X), X))
% 7.28/2.16 = { by lemma 83 R->L }
% 7.28/2.16 rd(mult(i(X), mult(ld(X, ld(i(X), Y)), X)), X)
% 7.28/2.16 = { by axiom 8 (c03) R->L }
% 7.28/2.16 mult(rd(rd(mult(i(X), mult(ld(X, ld(i(X), Y)), X)), X), X), X)
% 7.28/2.16 = { by lemma 96 }
% 7.28/2.16 mult(mult(i(X), rd(ld(X, ld(i(X), Y)), X)), X)
% 7.28/2.16 = { by lemma 97 }
% 7.28/2.16 mult(mult(i(X), mult(Y, i(X))), X)
% 7.28/2.16 = { by axiom 8 (c03) R->L }
% 7.28/2.16 mult(mult(rd(mult(i(X), mult(Y, i(X))), X), X), X)
% 7.28/2.16 = { by axiom 5 (c02) R->L }
% 7.28/2.16 ld(X, mult(X, mult(mult(rd(mult(i(X), mult(Y, i(X))), X), X), X)))
% 7.28/2.16 = { by lemma 13 R->L }
% 7.28/2.16 ld(X, mult(mult(mult(X, rd(mult(i(X), mult(Y, i(X))), X)), X), X))
% 7.28/2.16 = { by lemma 44 R->L }
% 7.28/2.16 ld(X, mult(mult(X, rd(rd(mult(i(X), mult(Y, i(X))), X), i(X))), X))
% 7.28/2.16 = { by lemma 36 }
% 7.28/2.16 rd(rd(rd(mult(i(X), mult(Y, i(X))), X), i(X)), i(X))
% 7.28/2.16 = { by lemma 51 R->L }
% 7.28/2.16 rd(rd(rd(mult(i(X), mult(Y, i(X))), i(X)), X), i(X))
% 7.28/2.16 = { by lemma 51 R->L }
% 7.28/2.16 rd(rd(rd(mult(i(X), mult(Y, i(X))), i(X)), i(X)), X)
% 7.28/2.16 = { by lemma 91 R->L }
% 7.28/2.16 rd(mult(i(X), rd(rd(mult(Y, i(X)), i(X)), i(X))), X)
% 7.28/2.16 = { by lemma 83 }
% 7.28/2.16 ld(X, rd(rd(rd(mult(Y, i(X)), i(X)), i(X)), X))
% 7.28/2.16 = { by lemma 51 }
% 7.28/2.16 ld(X, rd(rd(rd(mult(Y, i(X)), i(X)), X), i(X)))
% 7.28/2.16 = { by lemma 37 }
% 7.28/2.16 mult(ld(X, rd(rd(mult(Y, i(X)), i(X)), X)), X)
% 7.28/2.16 = { by lemma 95 }
% 7.28/2.16 rd(ld(X, mult(rd(mult(Y, i(X)), i(X)), X)), X)
% 7.28/2.16 = { by lemma 71 }
% 7.28/2.16 rd(ld(X, rd(mult(mult(Y, i(X)), X), i(X))), X)
% 7.28/2.16 = { by lemma 37 }
% 7.28/2.16 rd(mult(ld(X, mult(mult(Y, i(X)), X)), X), X)
% 7.28/2.16 = { by axiom 6 (c04) }
% 7.28/2.16 ld(X, mult(mult(Y, i(X)), X))
% 7.28/2.16 = { by lemma 48 }
% 7.28/2.16 ld(X, mult(mult(Y, X), i(X)))
% 7.28/2.16 = { by lemma 32 }
% 7.28/2.16 rd(ld(X, mult(Y, X)), X)
% 7.28/2.16 = { by lemma 95 R->L }
% 7.28/2.16 mult(ld(X, rd(Y, X)), X)
% 7.28/2.16 = { by lemma 83 R->L }
% 7.28/2.16 mult(rd(mult(i(X), Y), X), X)
% 7.28/2.16 = { by axiom 8 (c03) }
% 7.28/2.16 mult(i(X), Y)
% 7.28/2.16
% 7.28/2.16 Lemma 99: ld(X, mult(i(mult(X, Y)), X)) = rd(i(X), Y).
% 7.28/2.16 Proof:
% 7.28/2.16 ld(X, mult(i(mult(X, Y)), X))
% 7.28/2.16 = { by axiom 6 (c04) R->L }
% 7.28/2.16 rd(mult(ld(X, mult(i(mult(X, Y)), X)), Y), Y)
% 7.28/2.16 = { by axiom 5 (c02) R->L }
% 7.28/2.16 rd(ld(X, mult(X, mult(ld(X, mult(i(mult(X, Y)), X)), Y))), Y)
% 7.28/2.16 = { by lemma 66 }
% 7.28/2.16 rd(ld(X, mult(i(mult(X, Y)), mult(X, Y))), Y)
% 7.28/2.16 = { by axiom 4 (c10) }
% 7.28/2.16 rd(ld(X, unit), Y)
% 7.28/2.16 = { by lemma 11 }
% 7.28/2.17 rd(i(X), Y)
% 7.28/2.17
% 7.28/2.17 Goal 1 (goals): mult(a, i(mult(b, a))) = i(b).
% 7.28/2.17 Proof:
% 7.28/2.17 mult(a, i(mult(b, a)))
% 7.28/2.17 = { by lemma 88 R->L }
% 7.28/2.17 ld(rd(mult(a, mult(b, a)), a), a)
% 7.28/2.17 = { by lemma 41 }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), b)), a)
% 7.28/2.17 = { by axiom 1 (c05) R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, unit))), a)
% 7.28/2.17 = { by axiom 4 (c10) R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, mult(i(a), a)))), a)
% 7.28/2.17 = { by lemma 98 R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, ld(a, ld(a, ld(i(a), a)))))), a)
% 7.28/2.17 = { by lemma 59 R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, ld(a, ld(i(a), ld(a, a)))))), a)
% 7.28/2.17 = { by lemma 84 R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, rd(rd(ld(a, a), a), i(a))))), a)
% 7.28/2.17 = { by lemma 63 R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, mult(a, mult(i(a), ld(a, a)))))), a)
% 7.28/2.17 = { by lemma 61 R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, mult(a, mult(ld(a, i(a)), a))))), a)
% 7.28/2.17 = { by lemma 21 R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, mult(a, mult(i(mult(a, a)), a))))), a)
% 7.28/2.17 = { by lemma 98 R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, mult(a, ld(mult(a, a), ld(mult(a, a), ld(i(mult(a, a)), a))))))), a)
% 7.28/2.17 = { by lemma 89 }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, ld(mult(a, a), mult(a, ld(mult(a, a), ld(i(mult(a, a)), a))))))), a)
% 7.28/2.17 = { by lemma 89 }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, ld(mult(a, a), ld(mult(a, a), mult(a, ld(i(mult(a, a)), a))))))), a)
% 7.28/2.17 = { by lemma 21 }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, ld(mult(a, a), ld(mult(a, a), mult(a, ld(ld(a, i(a)), a))))))), a)
% 7.28/2.17 = { by lemma 62 }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, ld(mult(a, a), ld(mult(a, a), mult(a, mult(mult(a, a), a))))))), a)
% 7.28/2.17 = { by lemma 19 }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(b, ld(mult(a, a), mult(a, a))))), a)
% 7.28/2.17 = { by axiom 5 (c02) R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(ld(mult(a, a), mult(mult(a, a), b)), ld(mult(a, a), mult(a, a))))), a)
% 7.28/2.17 = { by axiom 8 (c03) R->L }
% 7.28/2.17 ld(ld(a, mult(mult(a, a), mult(ld(mult(a, a), mult(rd(mult(mult(a, a), b), mult(a, a)), mult(a, a))), ld(mult(a, a), mult(a, a))))), a)
% 7.28/2.17 = { by lemma 66 }
% 7.28/2.17 ld(ld(a, mult(rd(mult(mult(a, a), b), mult(a, a)), mult(mult(a, a), ld(mult(a, a), mult(a, a))))), a)
% 7.28/2.17 = { by axiom 7 (c01) }
% 7.28/2.17 ld(ld(a, mult(rd(mult(mult(a, a), b), mult(a, a)), mult(a, a))), a)
% 7.28/2.17 = { by lemma 80 R->L }
% 7.28/2.17 ld(ld(a, rd(rd(mult(mult(a, a), b), mult(a, a)), ld(a, i(a)))), a)
% 7.28/2.17 = { by lemma 87 R->L }
% 7.28/2.17 ld(ld(a, rd(rd(mult(mult(a, a), b), mult(a, a)), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by axiom 8 (c03) R->L }
% 7.28/2.17 ld(ld(a, rd(mult(rd(rd(mult(mult(a, a), b), mult(a, a)), mult(a, a)), mult(a, a)), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by lemma 91 R->L }
% 7.28/2.17 ld(ld(a, rd(mult(mult(mult(a, a), rd(rd(b, mult(a, a)), mult(a, a))), mult(a, a)), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by lemma 33 R->L }
% 7.28/2.17 ld(ld(a, rd(mult(mult(a, a), mult(mult(a, a), mult(ld(mult(a, a), rd(rd(b, mult(a, a)), mult(a, a))), mult(a, a)))), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by lemma 86 }
% 7.28/2.17 ld(ld(a, rd(mult(mult(a, a), mult(mult(a, a), ld(mult(a, a), mult(rd(rd(b, mult(a, a)), mult(a, a)), mult(a, a))))), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by axiom 7 (c01) }
% 7.28/2.17 ld(ld(a, rd(mult(mult(a, a), mult(rd(rd(b, mult(a, a)), mult(a, a)), mult(a, a))), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by axiom 8 (c03) }
% 7.28/2.17 ld(ld(a, rd(mult(mult(a, a), rd(b, mult(a, a))), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by lemma 62 R->L }
% 7.28/2.17 ld(ld(a, rd(ld(ld(a, i(a)), rd(b, mult(a, a))), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by lemma 87 R->L }
% 7.28/2.17 ld(ld(a, rd(ld(ld(b, rd(b, mult(a, a))), rd(b, mult(a, a))), ld(b, rd(b, mult(a, a))))), a)
% 7.28/2.17 = { by lemma 32 R->L }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), mult(rd(b, mult(a, a)), i(ld(b, rd(b, mult(a, a))))))), a)
% 7.28/2.17 = { by lemma 31 R->L }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), mult(ld(b, rd(b, mult(a, a))), rd(ld(ld(b, rd(b, mult(a, a))), rd(b, mult(a, a))), ld(b, rd(b, mult(a, a))))))), a)
% 7.28/2.17 = { by axiom 6 (c04) R->L }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), rd(mult(mult(ld(b, rd(b, mult(a, a))), rd(ld(ld(b, rd(b, mult(a, a))), rd(b, mult(a, a))), ld(b, rd(b, mult(a, a))))), ld(b, rd(b, mult(a, a)))), ld(b, rd(b, mult(a, a)))))), a)
% 7.28/2.17 = { by lemma 25 }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), rd(rd(mult(ld(b, rd(b, mult(a, a))), mult(ld(ld(b, rd(b, mult(a, a))), rd(b, mult(a, a))), ld(b, rd(b, mult(a, a))))), ld(b, rd(b, mult(a, a)))), ld(b, rd(b, mult(a, a)))))), a)
% 7.28/2.17 = { by axiom 7 (c01) R->L }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), rd(rd(mult(ld(b, rd(b, mult(a, a))), mult(ld(ld(b, rd(b, mult(a, a))), mult(b, ld(b, rd(b, mult(a, a))))), ld(b, rd(b, mult(a, a))))), ld(b, rd(b, mult(a, a)))), ld(b, rd(b, mult(a, a)))))), a)
% 7.28/2.17 = { by lemma 66 }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), rd(rd(mult(b, mult(ld(b, rd(b, mult(a, a))), ld(b, rd(b, mult(a, a))))), ld(b, rd(b, mult(a, a)))), ld(b, rd(b, mult(a, a)))))), a)
% 7.28/2.17 = { by lemma 81 }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), rd(rd(b, i(ld(b, rd(b, mult(a, a))))), ld(b, rd(b, mult(a, a)))))), a)
% 7.28/2.17 = { by lemma 51 }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), rd(rd(b, ld(b, rd(b, mult(a, a)))), i(ld(b, rd(b, mult(a, a))))))), a)
% 7.28/2.17 = { by lemma 84 }
% 7.28/2.17 ld(ld(a, ld(ld(b, rd(b, mult(a, a))), ld(ld(b, rd(b, mult(a, a))), ld(i(ld(b, rd(b, mult(a, a)))), b)))), a)
% 7.28/2.17 = { by lemma 98 }
% 7.28/2.17 ld(ld(a, mult(i(ld(b, rd(b, mult(a, a)))), b)), a)
% 7.28/2.17 = { by lemma 22 R->L }
% 7.28/2.17 ld(ld(a, mult(i(ld(b, ld(rd(b, rd(b, mult(a, a))), b))), b)), a)
% 7.28/2.17 = { by lemma 85 R->L }
% 7.28/2.17 ld(ld(a, mult(i(i(ld(b, mult(rd(b, rd(b, mult(a, a))), b)))), b)), a)
% 7.28/2.17 = { by lemma 82 R->L }
% 7.28/2.17 ld(ld(a, mult(i(i(ld(b, rd(b, i(ld(rd(b, mult(a, a)), b)))))), b)), a)
% 7.28/2.17 = { by lemma 22 }
% 7.28/2.17 ld(ld(a, mult(i(i(ld(b, rd(b, i(mult(a, a)))))), b)), a)
% 7.28/2.17 = { by lemma 12 }
% 7.28/2.17 ld(ld(a, mult(ld(b, rd(b, i(mult(a, a)))), b)), a)
% 7.28/2.17 = { by lemma 12 R->L }
% 7.28/2.17 ld(ld(a, mult(ld(b, rd(i(i(b)), i(mult(a, a)))), b)), a)
% 7.28/2.17 = { by lemma 37 R->L }
% 7.28/2.17 ld(ld(a, ld(b, rd(rd(i(i(b)), i(mult(a, a))), i(b)))), a)
% 7.28/2.17 = { by lemma 81 R->L }
% 7.28/2.17 ld(ld(a, ld(b, rd(mult(rd(i(i(b)), i(mult(a, a))), mult(b, b)), b))), a)
% 7.28/2.17 = { by lemma 92 R->L }
% 7.28/2.17 ld(ld(a, ld(b, mult(rd(rd(i(i(b)), i(mult(a, a))), b), mult(b, b)))), a)
% 7.28/2.17 = { by lemma 79 R->L }
% 7.28/2.17 ld(ld(a, ld(b, rd(mult(rd(rd(i(i(b)), i(mult(a, a))), b), b), i(b)))), a)
% 7.28/2.17 = { by lemma 71 R->L }
% 7.28/2.17 ld(ld(a, ld(b, mult(rd(rd(rd(i(i(b)), i(mult(a, a))), b), i(b)), b))), a)
% 7.28/2.17 = { by lemma 36 R->L }
% 7.28/2.17 ld(ld(a, ld(b, mult(ld(b, mult(mult(b, rd(rd(i(i(b)), i(mult(a, a))), b)), b)), b))), a)
% 7.28/2.17 = { by lemma 34 R->L }
% 7.28/2.17 ld(ld(a, ld(b, mult(mult(b, mult(ld(b, rd(rd(i(i(b)), i(mult(a, a))), b)), b)), b))), a)
% 7.28/2.18 = { by lemma 74 }
% 7.28/2.18 ld(ld(a, ld(b, mult(mult(b, ld(b, rd(rd(i(i(b)), i(mult(a, a))), b))), mult(b, b)))), a)
% 7.28/2.18 = { by lemma 75 }
% 7.28/2.18 ld(ld(a, ld(b, mult(b, mult(ld(b, rd(rd(i(i(b)), i(mult(a, a))), b)), mult(b, b))))), a)
% 7.28/2.18 = { by axiom 5 (c02) }
% 7.28/2.18 ld(ld(a, mult(ld(b, rd(rd(i(i(b)), i(mult(a, a))), b)), mult(b, b))), a)
% 7.28/2.18 = { by lemma 83 R->L }
% 7.28/2.18 ld(ld(a, mult(rd(mult(i(b), rd(i(i(b)), i(mult(a, a)))), b), mult(b, b))), a)
% 7.28/2.18 = { by lemma 92 }
% 7.28/2.18 ld(ld(a, rd(mult(mult(i(b), rd(i(i(b)), i(mult(a, a)))), mult(b, b)), b)), a)
% 7.28/2.18 = { by lemma 81 }
% 7.28/2.18 ld(ld(a, rd(mult(i(b), rd(i(i(b)), i(mult(a, a)))), i(b))), a)
% 7.28/2.18 = { by lemma 45 }
% 7.28/2.18 ld(ld(a, mult(i(b), mult(rd(i(i(b)), i(mult(a, a))), b))), a)
% 7.28/2.18 = { by lemma 99 R->L }
% 7.28/2.18 ld(ld(a, mult(i(b), mult(ld(i(b), mult(i(mult(i(b), i(mult(a, a)))), i(b))), b))), a)
% 7.28/2.18 = { by lemma 52 }
% 7.28/2.18 ld(ld(a, rd(mult(i(mult(i(b), i(mult(a, a)))), i(b)), i(b))), a)
% 7.28/2.18 = { by axiom 6 (c04) }
% 7.28/2.18 ld(ld(a, i(mult(i(b), i(mult(a, a))))), a)
% 7.28/2.18 = { by lemma 21 }
% 7.28/2.18 ld(ld(a, i(mult(i(b), ld(a, i(a))))), a)
% 7.28/2.18 = { by lemma 23 R->L }
% 7.28/2.18 ld(ld(a, i(mult(i(b), mult(i(a), i(a))))), a)
% 7.28/2.18 = { by lemma 79 R->L }
% 7.28/2.18 ld(ld(a, i(rd(mult(i(b), i(a)), i(i(a))))), a)
% 7.28/2.18 = { by lemma 12 }
% 7.28/2.18 ld(ld(a, i(rd(mult(i(b), i(a)), a))), a)
% 7.28/2.18 = { by lemma 24 R->L }
% 7.28/2.18 ld(ld(a, i(rd(a, ld(rd(mult(i(b), i(a)), a), a)))), a)
% 7.28/2.18 = { by lemma 22 R->L }
% 7.28/2.18 ld(ld(a, i(rd(a, ld(rd(ld(rd(a, mult(i(b), i(a))), a), a), a)))), a)
% 7.28/2.18 = { by lemma 68 R->L }
% 7.28/2.18 ld(ld(a, i(rd(a, mult(a, i(ld(a, ld(rd(a, mult(i(b), i(a))), a))))))), a)
% 7.28/2.18 = { by lemma 85 R->L }
% 7.28/2.18 ld(ld(a, i(rd(a, mult(a, i(i(ld(a, mult(rd(a, mult(i(b), i(a))), a)))))))), a)
% 7.28/2.18 = { by lemma 12 }
% 7.28/2.18 ld(ld(a, i(rd(a, mult(a, ld(a, mult(rd(a, mult(i(b), i(a))), a)))))), a)
% 7.28/2.18 = { by axiom 7 (c01) }
% 7.28/2.18 ld(ld(a, i(rd(a, mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by axiom 6 (c04) R->L }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by axiom 6 (c04) R->L }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by lemma 40 R->L }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by lemma 25 R->L }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by lemma 41 }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by lemma 15 }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by axiom 5 (c02) }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by lemma 40 R->L }
% 7.28/2.18 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.18 = { by axiom 8 (c03) }
% 7.28/2.19 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.19 = { by axiom 7 (c01) R->L }
% 7.28/2.19 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.19 = { by lemma 55 }
% 7.28/2.19 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.19 = { by lemma 12 R->L }
% 7.28/2.19 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), i(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.19 = { by lemma 36 R->L }
% 7.28/2.19 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))))), i(rd(a, mult(rd(a, mult(i(b), i(a))), a))))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.19 = { by axiom 7 (c01) }
% 7.28/2.19 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), i(rd(a, mult(rd(a, mult(i(b), i(a))), a))))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.19 = { by lemma 29 R->L }
% 7.28/2.19 ld(ld(a, rd(mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), i(rd(a, mult(rd(a, mult(i(b), i(a))), a)))), i(rd(a, mult(rd(a, mult(i(b), i(a))), a))))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.19 = { by lemma 65 }
% 7.28/2.19 ld(ld(a, rd(mult(mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), i(rd(a, mult(rd(a, mult(i(b), i(a))), a)))), mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 29 }
% 7.28/2.20 ld(ld(a, rd(mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 98 R->L }
% 7.28/2.20 ld(ld(a, rd(mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 58 }
% 7.28/2.20 ld(ld(a, rd(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), ld(i(rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a))))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 84 R->L }
% 7.28/2.20 ld(ld(a, rd(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(rd(mult(rd(a, mult(i(b), i(a))), a), rd(a, mult(rd(a, mult(i(b), i(a))), a))), i(rd(a, mult(rd(a, mult(i(b), i(a))), a)))))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 57 R->L }
% 7.28/2.20 ld(ld(a, rd(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(rd(mult(rd(a, mult(i(b), i(a))), a), rd(a, mult(rd(a, mult(i(b), i(a))), a))), i(rd(a, mult(rd(a, mult(i(b), i(a))), a)))))))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 37 }
% 7.28/2.20 ld(ld(a, rd(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(mult(rd(a, mult(i(b), i(a))), a), rd(a, mult(rd(a, mult(i(b), i(a))), a)))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 38 }
% 7.28/2.20 ld(ld(a, rd(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(mult(rd(a, mult(i(b), i(a))), a), rd(a, mult(rd(a, mult(i(b), i(a))), a))))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by axiom 7 (c01) }
% 7.28/2.20 ld(ld(a, rd(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(mult(rd(a, mult(i(b), i(a))), a), rd(a, mult(rd(a, mult(i(b), i(a))), a))), rd(a, mult(rd(a, mult(i(b), i(a))), a)))))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by axiom 8 (c03) }
% 7.28/2.20 ld(ld(a, rd(ld(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)))), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by axiom 5 (c02) }
% 7.28/2.20 ld(ld(a, rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(a, mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by axiom 7 (c01) R->L }
% 7.28/2.20 ld(ld(a, rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), rd(mult(mult(rd(a, mult(i(b), i(a))), a), ld(mult(rd(a, mult(i(b), i(a))), a), a)), mult(rd(a, mult(i(b), i(a))), a))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.20 = { by lemma 42 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(i(b), i(a))), a), mult(ld(mult(rd(a, mult(i(b), i(a))), a), a), i(mult(rd(a, mult(i(b), i(a))), a))))), mult(rd(a, mult(i(b), i(a))), a)))), a)
% 7.28/2.21 = { by lemma 54 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), rd(mult(ld(mult(rd(a, mult(i(b), i(a))), a), a), i(mult(rd(a, mult(i(b), i(a))), a))), i(mult(rd(a, mult(i(b), i(a))), a)))))), a)
% 7.28/2.21 = { by axiom 6 (c04) }
% 7.28/2.21 ld(ld(a, rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), mult(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), ld(mult(rd(a, mult(i(b), i(a))), a), a)))), a)
% 7.28/2.21 = { by axiom 8 (c03) }
% 7.28/2.21 ld(ld(a, rd(mult(rd(a, mult(rd(a, mult(i(b), i(a))), a)), mult(rd(a, mult(i(b), i(a))), a)), mult(a, ld(mult(rd(a, mult(i(b), i(a))), a), a)))), a)
% 7.28/2.21 = { by axiom 8 (c03) }
% 7.28/2.21 ld(ld(a, rd(a, mult(a, ld(mult(rd(a, mult(i(b), i(a))), a), a)))), a)
% 7.28/2.21 = { by lemma 82 R->L }
% 7.28/2.21 ld(ld(a, rd(a, mult(a, ld(rd(a, i(ld(mult(i(b), i(a)), a))), a)))), a)
% 7.28/2.21 = { by lemma 22 }
% 7.28/2.21 ld(ld(a, rd(a, mult(a, i(ld(mult(i(b), i(a)), a))))), a)
% 7.28/2.21 = { by lemma 88 R->L }
% 7.28/2.21 ld(ld(a, rd(a, ld(rd(mult(a, ld(mult(i(b), i(a)), a)), a), a))), a)
% 7.28/2.21 = { by lemma 24 }
% 7.28/2.21 ld(ld(a, rd(mult(a, ld(mult(i(b), i(a)), a)), a)), a)
% 7.28/2.21 = { by lemma 97 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, ld(rd(ld(a, ld(i(a), i(b))), a), a)), a)), a)
% 7.28/2.21 = { by lemma 68 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(a, i(ld(a, ld(a, ld(i(a), i(b))))))), a)), a)
% 7.28/2.21 = { by lemma 98 }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(a, i(mult(i(a), i(b))))), a)), a)
% 7.28/2.21 = { by lemma 12 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(i(i(a)), i(mult(i(a), i(b))))), a)), a)
% 7.28/2.21 = { by lemma 98 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, ld(i(a), ld(i(a), ld(i(i(a)), i(mult(i(a), i(b))))))), a)), a)
% 7.28/2.21 = { by lemma 59 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, ld(i(a), ld(i(i(a)), ld(i(a), i(mult(i(a), i(b))))))), a)), a)
% 7.28/2.21 = { by lemma 84 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(rd(ld(i(a), i(mult(i(a), i(b)))), i(a)), i(i(a)))), a)), a)
% 7.28/2.21 = { by lemma 50 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(mult(ld(i(a), i(mult(i(a), i(b)))), i(a)), i(i(a)))), a)), a)
% 7.28/2.21 = { by lemma 94 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(rd(ld(i(a), mult(mult(i(mult(i(a), i(b))), i(a)), i(a))), i(a)), i(i(a)))), a)), a)
% 7.28/2.21 = { by lemma 70 }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(mult(ld(i(a), mult(mult(i(mult(i(a), i(b))), i(a)), i(a))), i(i(a))), i(a))), a)), a)
% 7.28/2.21 = { by lemma 78 }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(ld(i(a), mult(mult(i(mult(i(a), i(b))), i(a)), i(a))), mult(i(a), i(a)))), a)), a)
% 7.28/2.21 = { by axiom 7 (c01) R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(ld(i(a), mult(mult(i(a), ld(i(a), mult(i(mult(i(a), i(b))), i(a)))), i(a))), mult(i(a), i(a)))), a)), a)
% 7.28/2.21 = { by lemma 99 }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(ld(i(a), mult(mult(i(a), rd(i(i(a)), i(b))), i(a))), mult(i(a), i(a)))), a)), a)
% 7.28/2.21 = { by axiom 6 (c04) R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(ld(i(a), rd(mult(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(a)), i(a))), mult(i(a), i(a)))), a)), a)
% 7.28/2.21 = { by lemma 83 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(rd(mult(i(i(a)), mult(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(a))), i(a)), mult(i(a), i(a)))), a)), a)
% 7.28/2.21 = { by lemma 78 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(mult(rd(mult(i(i(a)), mult(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(a))), i(a)), i(i(a))), i(a))), a)), a)
% 7.28/2.21 = { by lemma 70 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(rd(rd(mult(i(i(a)), mult(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(a))), i(a)), i(a)), i(i(a)))), a)), a)
% 7.28/2.21 = { by lemma 96 }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(mult(i(i(a)), rd(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(a))), i(i(a)))), a)), a)
% 7.28/2.21 = { by lemma 93 }
% 7.28/2.21 ld(ld(a, rd(mult(a, mult(i(i(a)), rd(rd(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(a)), i(a)))), a)), a)
% 7.28/2.21 = { by lemma 96 R->L }
% 7.28/2.21 ld(ld(a, rd(mult(a, rd(rd(mult(i(i(a)), mult(rd(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(a)), i(a))), i(a)), i(a))), a)), a)
% 7.28/2.22 = { by axiom 8 (c03) }
% 7.28/2.22 ld(ld(a, rd(mult(a, rd(rd(mult(i(i(a)), mult(mult(i(a), rd(i(i(a)), i(b))), i(a))), i(a)), i(a))), a)), a)
% 7.28/2.22 = { by lemma 47 R->L }
% 7.28/2.22 ld(ld(a, rd(mult(a, rd(mult(i(i(a)), mult(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(i(a)))), i(a))), a)), a)
% 7.28/2.22 = { by lemma 83 }
% 7.28/2.22 ld(ld(a, rd(mult(a, ld(i(a), rd(mult(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), i(i(a))), i(a)))), a)), a)
% 7.28/2.22 = { by lemma 78 }
% 7.28/2.22 ld(ld(a, rd(mult(a, ld(i(a), rd(mult(mult(i(a), rd(i(i(a)), i(b))), i(a)), mult(i(a), i(a))))), a)), a)
% 7.28/2.22 = { by lemma 77 }
% 7.28/2.22 ld(ld(a, rd(mult(a, ld(i(a), mult(mult(i(a), rd(i(i(a)), i(b))), i(i(a))))), a)), a)
% 7.28/2.22 = { by lemma 32 }
% 7.28/2.22 ld(ld(a, rd(mult(a, rd(ld(i(a), mult(i(a), rd(i(i(a)), i(b)))), i(a))), a)), a)
% 7.28/2.22 = { by axiom 5 (c02) }
% 7.28/2.22 ld(ld(a, rd(mult(a, rd(rd(i(i(a)), i(b)), i(a))), a)), a)
% 7.28/2.22 = { by lemma 12 }
% 7.28/2.22 ld(ld(a, rd(mult(a, rd(rd(a, i(b)), i(a))), a)), a)
% 7.28/2.22 = { by lemma 43 }
% 7.28/2.22 ld(ld(a, mult(a, rd(a, i(b)))), a)
% 7.28/2.22 = { by axiom 5 (c02) }
% 7.28/2.22 ld(rd(a, i(b)), a)
% 7.28/2.22 = { by lemma 22 }
% 7.28/2.22 i(b)
% 7.28/2.22 % SZS output end Proof
% 7.28/2.22
% 7.28/2.22 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------