TSTP Solution File: GRP721-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP721-1 : 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 : n012.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 01:19:53 EDT 2023
% Result : Unsatisfiable 228.33s 29.85s
% Output : Proof 230.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP721-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 00:07:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 228.33/29.85 Command-line arguments: --no-flatten-goal
% 228.33/29.85
% 228.33/29.85 % SZS status Unsatisfiable
% 228.33/29.85
% 229.94/29.98 % SZS output start Proof
% 229.94/29.98 Axiom 1 (c05): mult(X, Y) = mult(Y, X).
% 229.94/29.98 Axiom 2 (c01): mult(X, unit) = X.
% 229.94/29.98 Axiom 3 (c02): mult(unit, X) = X.
% 229.94/29.98 Axiom 4 (c04): ld(X, mult(X, Y)) = Y.
% 229.94/29.98 Axiom 5 (c03): mult(X, ld(X, Y)) = Y.
% 229.94/29.98 Axiom 6 (c07): ld(X, mult(mult(Y, Z), X)) = mult(ld(X, mult(Y, X)), ld(X, mult(Z, X))).
% 229.94/29.98 Axiom 7 (c08): f(X, Y) = ld(mult(ld(mult(X, Y), X), ld(mult(X, Y), Y)), unit).
% 229.94/29.98 Axiom 8 (c06): ld(mult(X, Y), mult(X, mult(Y, mult(Z, W)))) = mult(ld(mult(X, Y), mult(X, mult(Y, Z))), ld(mult(X, Y), mult(X, mult(Y, W)))).
% 229.94/29.98
% 229.94/29.98 Lemma 9: ld(X, mult(Y, X)) = Y.
% 229.94/29.98 Proof:
% 229.94/29.98 ld(X, mult(Y, X))
% 229.94/29.98 = { by axiom 1 (c05) R->L }
% 229.94/29.98 ld(X, mult(X, Y))
% 229.94/29.98 = { by axiom 4 (c04) }
% 229.94/29.98 Y
% 229.94/29.98
% 229.94/29.98 Lemma 10: mult(X, ld(mult(X, X), mult(X, Y))) = ld(mult(X, X), mult(X, mult(X, Y))).
% 229.94/29.98 Proof:
% 229.94/29.98 mult(X, ld(mult(X, X), mult(X, Y)))
% 229.94/29.98 = { by axiom 5 (c03) R->L }
% 229.94/29.98 mult(X, ld(mult(X, X), mult(X, mult(X, ld(X, Y)))))
% 229.94/29.98 = { by lemma 9 R->L }
% 229.94/29.98 mult(ld(mult(X, X), mult(X, mult(X, X))), ld(mult(X, X), mult(X, mult(X, ld(X, Y)))))
% 229.94/29.98 = { by axiom 8 (c06) R->L }
% 229.94/29.98 ld(mult(X, X), mult(X, mult(X, mult(X, ld(X, Y)))))
% 229.94/29.98 = { by axiom 5 (c03) }
% 229.94/29.98 ld(mult(X, X), mult(X, mult(X, Y)))
% 229.94/29.98
% 229.94/29.98 Lemma 11: ld(X, X) = unit.
% 229.94/29.98 Proof:
% 229.94/29.98 ld(X, X)
% 229.94/29.98 = { by axiom 2 (c01) R->L }
% 229.94/29.98 ld(X, mult(X, unit))
% 229.94/29.98 = { by axiom 4 (c04) }
% 229.94/29.98 unit
% 229.94/29.98
% 229.94/29.98 Lemma 12: mult(X, ld(mult(X, X), X)) = unit.
% 229.94/29.98 Proof:
% 229.94/29.98 mult(X, ld(mult(X, X), X))
% 229.94/29.98 = { by axiom 2 (c01) R->L }
% 229.94/29.98 mult(X, ld(mult(X, X), mult(X, unit)))
% 229.94/29.98 = { by lemma 10 }
% 229.94/29.98 ld(mult(X, X), mult(X, mult(X, unit)))
% 229.94/29.98 = { by axiom 2 (c01) }
% 229.94/29.98 ld(mult(X, X), mult(X, X))
% 229.94/29.98 = { by lemma 11 }
% 229.94/29.98 unit
% 229.94/29.98
% 229.94/29.98 Lemma 13: ld(mult(X, X), X) = ld(X, unit).
% 229.94/29.98 Proof:
% 229.94/29.98 ld(mult(X, X), X)
% 229.94/29.98 = { by axiom 4 (c04) R->L }
% 229.94/29.98 ld(X, mult(X, ld(mult(X, X), X)))
% 229.94/29.98 = { by lemma 12 }
% 229.94/29.98 ld(X, unit)
% 229.94/29.98
% 229.94/29.98 Lemma 14: ld(ld(X, Y), Y) = X.
% 229.94/29.98 Proof:
% 229.94/29.98 ld(ld(X, Y), Y)
% 229.94/29.98 = { by axiom 5 (c03) R->L }
% 229.94/29.98 ld(ld(X, Y), mult(X, ld(X, Y)))
% 229.94/29.98 = { by lemma 9 }
% 229.94/29.98 X
% 229.94/29.98
% 229.94/29.98 Lemma 15: ld(ld(X, unit), X) = mult(X, X).
% 229.94/29.98 Proof:
% 229.94/29.98 ld(ld(X, unit), X)
% 229.94/29.98 = { by lemma 13 R->L }
% 229.94/29.98 ld(ld(mult(X, X), X), X)
% 229.94/29.98 = { by lemma 14 }
% 229.94/29.98 mult(X, X)
% 229.94/29.98
% 229.94/29.98 Lemma 16: mult(ld(mult(X, Y), X), ld(mult(X, Y), Y)) = ld(f(X, Y), unit).
% 229.94/29.98 Proof:
% 229.94/29.98 mult(ld(mult(X, Y), X), ld(mult(X, Y), Y))
% 229.94/29.98 = { by lemma 14 R->L }
% 229.94/29.98 ld(ld(mult(ld(mult(X, Y), X), ld(mult(X, Y), Y)), unit), unit)
% 229.94/29.98 = { by axiom 7 (c08) R->L }
% 229.94/29.98 ld(f(X, Y), unit)
% 229.94/29.98
% 229.94/29.98 Lemma 17: ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), unit)) = f(X, X).
% 229.94/29.98 Proof:
% 229.94/29.98 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), unit))
% 229.94/29.98 = { by lemma 11 R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), ld(ld(f(X, X), unit), ld(f(X, X), unit))))
% 229.94/29.99 = { by lemma 16 R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), ld(ld(f(X, X), unit), mult(ld(mult(X, X), X), ld(mult(X, X), X)))))
% 229.94/29.99 = { by axiom 2 (c01) R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), ld(ld(f(X, X), unit), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), unit)))))
% 229.94/29.99 = { by lemma 16 R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), unit)))))
% 229.94/29.99 = { by axiom 5 (c03) R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), mult(mult(ld(mult(X, X), X), ld(mult(X, X), X)), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), unit)))))))
% 229.94/29.99 = { by axiom 8 (c06) }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), mult(ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(X, X), X))))), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), unit)))))))
% 229.94/29.99 = { by axiom 8 (c06) }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), mult(mult(ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(X, X), X)))), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(X, X), X))))), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), unit)))))))
% 229.94/29.99 = { by axiom 6 (c07) R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), mult(ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), ld(mult(X, X), X)))), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), unit)))))))
% 229.94/29.99 = { by axiom 4 (c04) }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), mult(mult(ld(mult(X, X), X), ld(mult(X, X), X)), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), unit)))))))
% 229.94/29.99 = { by axiom 5 (c03) }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), unit)))))
% 229.94/29.99 = { by axiom 7 (c08) R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), mult(ld(mult(X, X), X), mult(ld(mult(X, X), X), f(X, X)))))
% 229.94/29.99 = { by axiom 1 (c05) }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), mult(ld(mult(X, X), X), mult(f(X, X), ld(mult(X, X), X)))))
% 229.94/29.99 = { by axiom 4 (c04) }
% 229.94/29.99 ld(ld(mult(X, X), X), mult(f(X, X), ld(mult(X, X), X)))
% 229.94/29.99 = { by lemma 9 }
% 229.94/29.99 f(X, X)
% 229.94/29.99
% 229.94/29.99 Lemma 18: mult(X, X) = f(X, X).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(X, X)
% 229.94/29.99 = { by lemma 15 R->L }
% 229.94/29.99 ld(ld(X, unit), X)
% 229.94/29.99 = { by lemma 14 R->L }
% 229.94/29.99 ld(ld(X, unit), ld(ld(X, unit), unit))
% 229.94/29.99 = { by lemma 13 R->L }
% 229.94/29.99 ld(ld(X, unit), ld(ld(mult(X, X), X), unit))
% 229.94/29.99 = { by lemma 13 R->L }
% 229.94/29.99 ld(ld(mult(X, X), X), ld(ld(mult(X, X), X), unit))
% 229.94/29.99 = { by lemma 17 }
% 229.94/29.99 f(X, X)
% 229.94/29.99
% 229.94/29.99 Lemma 19: ld(unit, X) = X.
% 229.94/29.99 Proof:
% 229.94/29.99 ld(unit, X)
% 229.94/29.99 = { by axiom 3 (c02) R->L }
% 229.94/29.99 ld(unit, mult(unit, X))
% 229.94/29.99 = { by axiom 4 (c04) }
% 229.94/29.99 X
% 229.94/29.99
% 229.94/29.99 Lemma 20: ld(mult(ld(X, Y), ld(X, ld(Y, X))), unit) = f(Y, ld(Y, X)).
% 229.94/29.99 Proof:
% 229.94/29.99 ld(mult(ld(X, Y), ld(X, ld(Y, X))), unit)
% 229.94/29.99 = { by axiom 5 (c03) R->L }
% 229.94/29.99 ld(mult(ld(X, Y), ld(mult(Y, ld(Y, X)), ld(Y, X))), unit)
% 229.94/29.99 = { by axiom 5 (c03) R->L }
% 229.94/29.99 ld(mult(ld(mult(Y, ld(Y, X)), Y), ld(mult(Y, ld(Y, X)), ld(Y, X))), unit)
% 229.94/29.99 = { by axiom 7 (c08) R->L }
% 229.94/29.99 f(Y, ld(Y, X))
% 229.94/29.99
% 229.94/29.99 Lemma 21: f(Y, X) = f(X, Y).
% 229.94/29.99 Proof:
% 229.94/29.99 f(Y, X)
% 229.94/29.99 = { by axiom 7 (c08) }
% 229.94/29.99 ld(mult(ld(mult(Y, X), Y), ld(mult(Y, X), X)), unit)
% 229.94/29.99 = { by axiom 1 (c05) }
% 229.94/29.99 ld(mult(ld(mult(Y, X), X), ld(mult(Y, X), Y)), unit)
% 229.94/29.99 = { by lemma 9 R->L }
% 229.94/29.99 ld(mult(ld(mult(Y, X), X), ld(mult(Y, X), ld(X, mult(Y, X)))), unit)
% 229.94/29.99 = { by lemma 20 }
% 229.94/29.99 f(X, ld(X, mult(Y, X)))
% 229.94/29.99 = { by lemma 9 }
% 229.94/29.99 f(X, Y)
% 229.94/29.99
% 229.94/29.99 Lemma 22: f(unit, X) = X.
% 229.94/29.99 Proof:
% 229.94/29.99 f(unit, X)
% 229.94/29.99 = { by axiom 7 (c08) }
% 229.94/29.99 ld(mult(ld(mult(unit, X), unit), ld(mult(unit, X), X)), unit)
% 229.94/29.99 = { by axiom 3 (c02) }
% 229.94/29.99 ld(mult(ld(X, unit), ld(mult(unit, X), X)), unit)
% 229.94/29.99 = { by axiom 3 (c02) }
% 229.94/29.99 ld(mult(ld(X, unit), ld(X, X)), unit)
% 229.94/29.99 = { by lemma 11 }
% 229.94/29.99 ld(mult(ld(X, unit), unit), unit)
% 229.94/29.99 = { by axiom 2 (c01) }
% 229.94/29.99 ld(ld(X, unit), unit)
% 229.94/29.99 = { by lemma 14 }
% 229.94/29.99 X
% 229.94/29.99
% 229.94/29.99 Lemma 23: mult(ld(mult(X, Y), mult(X, Z)), ld(mult(X, Y), mult(X, mult(Y, W)))) = ld(mult(X, Y), mult(X, mult(Y, mult(W, ld(Y, Z))))).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(ld(mult(X, Y), mult(X, Z)), ld(mult(X, Y), mult(X, mult(Y, W))))
% 229.94/29.99 = { by axiom 5 (c03) R->L }
% 229.94/29.99 mult(ld(mult(X, Y), mult(X, mult(Y, ld(Y, Z)))), ld(mult(X, Y), mult(X, mult(Y, W))))
% 229.94/29.99 = { by axiom 8 (c06) R->L }
% 229.94/29.99 ld(mult(X, Y), mult(X, mult(Y, mult(ld(Y, Z), W))))
% 229.94/29.99 = { by axiom 1 (c05) }
% 229.94/29.99 ld(mult(X, Y), mult(X, mult(Y, mult(W, ld(Y, Z)))))
% 229.94/29.99
% 229.94/29.99 Lemma 24: mult(X, ld(mult(X, Y), mult(X, mult(Y, Z)))) = ld(mult(X, Y), mult(X, mult(Y, mult(X, Z)))).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(X, ld(mult(X, Y), mult(X, mult(Y, Z))))
% 229.94/29.99 = { by lemma 9 R->L }
% 229.94/29.99 mult(ld(mult(X, Y), mult(X, mult(X, Y))), ld(mult(X, Y), mult(X, mult(Y, Z))))
% 229.94/29.99 = { by lemma 23 }
% 229.94/29.99 ld(mult(X, Y), mult(X, mult(Y, mult(Z, ld(Y, mult(X, Y))))))
% 229.94/29.99 = { by lemma 9 }
% 229.94/29.99 ld(mult(X, Y), mult(X, mult(Y, mult(Z, X))))
% 229.94/29.99 = { by axiom 1 (c05) }
% 229.94/29.99 ld(mult(X, Y), mult(X, mult(Y, mult(X, Z))))
% 229.94/29.99
% 229.94/29.99 Lemma 25: mult(ld(X, unit), mult(X, Y)) = mult(X, mult(Y, ld(X, unit))).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(ld(X, unit), mult(X, Y))
% 229.94/29.99 = { by axiom 4 (c04) R->L }
% 229.94/29.99 ld(X, mult(X, mult(ld(X, unit), mult(X, Y))))
% 229.94/29.99 = { by lemma 13 R->L }
% 229.94/29.99 ld(X, mult(X, mult(ld(mult(X, X), X), mult(X, Y))))
% 229.94/29.99 = { by lemma 19 R->L }
% 229.94/29.99 ld(X, ld(unit, mult(X, mult(ld(mult(X, X), X), mult(X, Y)))))
% 229.94/29.99 = { by lemma 12 R->L }
% 229.94/29.99 ld(X, ld(mult(X, ld(mult(X, X), X)), mult(X, mult(ld(mult(X, X), X), mult(X, Y)))))
% 229.94/29.99 = { by lemma 24 R->L }
% 229.94/29.99 ld(X, mult(X, ld(mult(X, ld(mult(X, X), X)), mult(X, mult(ld(mult(X, X), X), Y)))))
% 229.94/29.99 = { by lemma 12 }
% 229.94/29.99 ld(X, mult(X, ld(unit, mult(X, mult(ld(mult(X, X), X), Y)))))
% 229.94/29.99 = { by lemma 19 }
% 229.94/29.99 ld(X, mult(X, mult(X, mult(ld(mult(X, X), X), Y))))
% 229.94/29.99 = { by lemma 13 }
% 229.94/29.99 ld(X, mult(X, mult(X, mult(ld(X, unit), Y))))
% 229.94/29.99 = { by axiom 1 (c05) }
% 229.94/29.99 ld(X, mult(X, mult(X, mult(Y, ld(X, unit)))))
% 229.94/29.99 = { by axiom 4 (c04) }
% 229.94/29.99 mult(X, mult(Y, ld(X, unit)))
% 229.94/29.99
% 229.94/29.99 Lemma 26: mult(ld(X, Y), ld(X, unit)) = ld(X, mult(Y, ld(X, unit))).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(ld(X, Y), ld(X, unit))
% 229.94/29.99 = { by axiom 4 (c04) R->L }
% 229.94/29.99 ld(X, mult(X, mult(ld(X, Y), ld(X, unit))))
% 229.94/29.99 = { by lemma 25 R->L }
% 229.94/29.99 ld(X, mult(ld(X, unit), mult(X, ld(X, Y))))
% 229.94/29.99 = { by axiom 5 (c03) }
% 229.94/29.99 ld(X, mult(ld(X, unit), Y))
% 229.94/29.99 = { by axiom 1 (c05) }
% 229.94/29.99 ld(X, mult(Y, ld(X, unit)))
% 229.94/29.99
% 229.94/29.99 Lemma 27: mult(X, ld(ld(X, unit), Y)) = ld(ld(X, unit), mult(X, Y)).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(X, ld(ld(X, unit), Y))
% 229.94/29.99 = { by axiom 1 (c05) R->L }
% 229.94/29.99 mult(ld(ld(X, unit), Y), X)
% 229.94/29.99 = { by lemma 14 R->L }
% 229.94/29.99 mult(ld(ld(X, unit), Y), ld(ld(X, unit), unit))
% 229.94/29.99 = { by lemma 26 }
% 229.94/29.99 ld(ld(X, unit), mult(Y, ld(ld(X, unit), unit)))
% 229.94/29.99 = { by lemma 14 }
% 229.94/29.99 ld(ld(X, unit), mult(Y, X))
% 229.94/29.99 = { by axiom 1 (c05) }
% 229.94/29.99 ld(ld(X, unit), mult(X, Y))
% 229.94/29.99
% 229.94/29.99 Lemma 28: mult(X, ld(f(X, X), Y)) = ld(f(X, X), mult(X, Y)).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(X, ld(f(X, X), Y))
% 229.94/29.99 = { by lemma 18 R->L }
% 229.94/29.99 mult(X, ld(mult(X, X), Y))
% 229.94/29.99 = { by axiom 5 (c03) R->L }
% 229.94/29.99 mult(X, ld(mult(X, X), mult(X, ld(X, Y))))
% 229.94/29.99 = { by lemma 10 }
% 229.94/29.99 ld(mult(X, X), mult(X, mult(X, ld(X, Y))))
% 229.94/29.99 = { by lemma 18 }
% 229.94/29.99 ld(f(X, X), mult(X, mult(X, ld(X, Y))))
% 229.94/29.99 = { by axiom 5 (c03) }
% 229.94/29.99 ld(f(X, X), mult(X, Y))
% 229.94/29.99
% 229.94/29.99 Lemma 29: mult(ld(X, unit), mult(Y, X)) = mult(X, mult(Y, ld(X, unit))).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(ld(X, unit), mult(Y, X))
% 229.94/29.99 = { by axiom 1 (c05) R->L }
% 229.94/29.99 mult(ld(X, unit), mult(X, Y))
% 229.94/29.99 = { by lemma 25 }
% 229.94/29.99 mult(X, mult(Y, ld(X, unit)))
% 229.94/29.99
% 229.94/29.99 Lemma 30: ld(X, mult(Y, mult(Z, ld(ld(Y, X), unit)))) = mult(ld(X, Y), ld(X, mult(Y, Z))).
% 229.94/29.99 Proof:
% 229.94/29.99 ld(X, mult(Y, mult(Z, ld(ld(Y, X), unit))))
% 229.94/29.99 = { by axiom 5 (c03) R->L }
% 229.94/29.99 ld(mult(Y, ld(Y, X)), mult(Y, mult(Z, ld(ld(Y, X), unit))))
% 229.94/29.99 = { by axiom 5 (c03) R->L }
% 229.94/29.99 ld(mult(Y, ld(Y, X)), mult(Y, mult(ld(Y, X), ld(ld(Y, X), mult(Z, ld(ld(Y, X), unit))))))
% 229.94/29.99 = { by lemma 26 R->L }
% 229.94/29.99 ld(mult(Y, ld(Y, X)), mult(Y, mult(ld(Y, X), mult(ld(ld(Y, X), Z), ld(ld(Y, X), unit)))))
% 229.94/29.99 = { by lemma 23 R->L }
% 229.94/29.99 mult(ld(mult(Y, ld(Y, X)), mult(Y, unit)), ld(mult(Y, ld(Y, X)), mult(Y, mult(ld(Y, X), ld(ld(Y, X), Z)))))
% 229.94/29.99 = { by axiom 2 (c01) }
% 229.94/29.99 mult(ld(mult(Y, ld(Y, X)), Y), ld(mult(Y, ld(Y, X)), mult(Y, mult(ld(Y, X), ld(ld(Y, X), Z)))))
% 229.94/29.99 = { by axiom 5 (c03) }
% 229.94/29.99 mult(ld(mult(Y, ld(Y, X)), Y), ld(mult(Y, ld(Y, X)), mult(Y, Z)))
% 229.94/29.99 = { by axiom 5 (c03) }
% 229.94/29.99 mult(ld(X, Y), ld(mult(Y, ld(Y, X)), mult(Y, Z)))
% 229.94/29.99 = { by axiom 5 (c03) }
% 229.94/29.99 mult(ld(X, Y), ld(X, mult(Y, Z)))
% 229.94/29.99
% 229.94/29.99 Lemma 31: mult(X, mult(ld(X, Y), ld(X, mult(Z, Y)))) = mult(Y, mult(Z, ld(ld(Y, X), unit))).
% 229.94/29.99 Proof:
% 229.94/29.99 mult(X, mult(ld(X, Y), ld(X, mult(Z, Y))))
% 229.94/29.99 = { by axiom 1 (c05) R->L }
% 229.94/30.00 mult(X, mult(ld(X, Y), ld(X, mult(Y, Z))))
% 229.94/30.00 = { by lemma 30 R->L }
% 229.94/30.00 mult(X, ld(X, mult(Y, mult(Z, ld(ld(Y, X), unit)))))
% 229.94/30.00 = { by axiom 5 (c03) }
% 229.94/30.00 mult(Y, mult(Z, ld(ld(Y, X), unit)))
% 229.94/30.00
% 229.94/30.00 Lemma 32: mult(X, ld(Y, mult(X, mult(ld(X, Y), Z)))) = ld(Y, mult(X, mult(ld(X, Y), mult(X, Z)))).
% 229.94/30.00 Proof:
% 229.94/30.00 mult(X, ld(Y, mult(X, mult(ld(X, Y), Z))))
% 229.94/30.00 = { by axiom 5 (c03) R->L }
% 229.94/30.00 mult(X, ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), Z))))
% 229.94/30.00 = { by lemma 24 }
% 229.94/30.00 ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), mult(X, Z))))
% 229.94/30.00 = { by axiom 5 (c03) }
% 229.94/30.00 ld(Y, mult(X, mult(ld(X, Y), mult(X, Z))))
% 229.94/30.00
% 229.94/30.00 Lemma 33: ld(f(X, X), mult(X, mult(Y, f(X, X)))) = mult(X, Y).
% 229.94/30.00 Proof:
% 229.94/30.00 ld(f(X, X), mult(X, mult(Y, f(X, X))))
% 229.94/30.00 = { by axiom 1 (c05) R->L }
% 229.94/30.00 ld(f(X, X), mult(X, mult(f(X, X), Y)))
% 229.94/30.00 = { by lemma 28 R->L }
% 229.94/30.00 mult(X, ld(f(X, X), mult(f(X, X), Y)))
% 229.94/30.00 = { by axiom 4 (c04) }
% 229.94/30.00 mult(X, Y)
% 229.94/30.00
% 229.94/30.00 Lemma 34: mult(ld(X, Y), ld(X, ld(Y, X))) = ld(f(Y, ld(Y, X)), unit).
% 229.94/30.00 Proof:
% 229.94/30.00 mult(ld(X, Y), ld(X, ld(Y, X)))
% 229.94/30.00 = { by lemma 19 R->L }
% 229.94/30.00 ld(unit, mult(ld(X, Y), ld(X, ld(Y, X))))
% 229.94/30.00 = { by lemma 22 R->L }
% 229.94/30.00 f(unit, ld(unit, mult(ld(X, Y), ld(X, ld(Y, X)))))
% 229.94/30.00 = { by lemma 20 R->L }
% 229.94/30.00 ld(mult(ld(mult(ld(X, Y), ld(X, ld(Y, X))), unit), ld(mult(ld(X, Y), ld(X, ld(Y, X))), ld(unit, mult(ld(X, Y), ld(X, ld(Y, X)))))), unit)
% 229.94/30.00 = { by lemma 20 }
% 229.94/30.00 ld(mult(f(Y, ld(Y, X)), ld(mult(ld(X, Y), ld(X, ld(Y, X))), ld(unit, mult(ld(X, Y), ld(X, ld(Y, X)))))), unit)
% 229.94/30.00 = { by lemma 19 }
% 229.94/30.00 ld(mult(f(Y, ld(Y, X)), ld(mult(ld(X, Y), ld(X, ld(Y, X))), mult(ld(X, Y), ld(X, ld(Y, X))))), unit)
% 229.94/30.00 = { by lemma 11 }
% 229.94/30.00 ld(mult(f(Y, ld(Y, X)), unit), unit)
% 229.94/30.00 = { by axiom 2 (c01) }
% 229.94/30.00 ld(f(Y, ld(Y, X)), unit)
% 229.94/30.00
% 229.94/30.00 Lemma 35: ld(X, mult(Y, mult(ld(ld(Y, X), unit), Z))) = mult(ld(X, Y), ld(X, mult(Y, Z))).
% 229.94/30.00 Proof:
% 229.94/30.00 ld(X, mult(Y, mult(ld(ld(Y, X), unit), Z)))
% 229.94/30.00 = { by axiom 1 (c05) R->L }
% 229.94/30.00 ld(X, mult(Y, mult(Z, ld(ld(Y, X), unit))))
% 229.94/30.00 = { by lemma 30 }
% 229.94/30.00 mult(ld(X, Y), ld(X, mult(Y, Z)))
% 229.94/30.00
% 229.94/30.00 Lemma 36: ld(X, mult(Y, ld(f(unit, ld(Y, X)), unit))) = f(ld(X, Y), ld(X, Y)).
% 229.94/30.00 Proof:
% 229.94/30.00 ld(X, mult(Y, ld(f(unit, ld(Y, X)), unit)))
% 229.94/30.00 = { by lemma 19 R->L }
% 229.94/30.00 ld(X, mult(Y, ld(f(unit, ld(unit, ld(Y, X))), unit)))
% 229.94/30.00 = { by lemma 34 R->L }
% 229.94/30.00 ld(X, mult(Y, mult(ld(ld(Y, X), unit), ld(ld(Y, X), ld(unit, ld(Y, X))))))
% 229.94/30.00 = { by lemma 35 }
% 229.94/30.00 mult(ld(X, Y), ld(X, mult(Y, ld(ld(Y, X), ld(unit, ld(Y, X))))))
% 229.94/30.00 = { by lemma 19 }
% 229.94/30.00 mult(ld(X, Y), ld(X, mult(Y, ld(ld(Y, X), ld(Y, X)))))
% 229.94/30.00 = { by lemma 11 }
% 229.94/30.00 mult(ld(X, Y), ld(X, mult(Y, unit)))
% 229.94/30.00 = { by axiom 2 (c01) }
% 229.94/30.00 mult(ld(X, Y), ld(X, Y))
% 229.94/30.00 = { by lemma 18 }
% 229.94/30.00 f(ld(X, Y), ld(X, Y))
% 229.94/30.00
% 229.94/30.00 Lemma 37: mult(X, ld(f(unit, ld(X, unit)), unit)) = f(X, X).
% 229.94/30.00 Proof:
% 229.94/30.00 mult(X, ld(f(unit, ld(X, unit)), unit))
% 229.94/30.00 = { by lemma 19 R->L }
% 229.94/30.00 ld(unit, mult(X, ld(f(unit, ld(X, unit)), unit)))
% 229.94/30.00 = { by lemma 36 }
% 229.94/30.00 f(ld(unit, X), ld(unit, X))
% 229.94/30.00 = { by lemma 19 }
% 229.94/30.00 f(X, ld(unit, X))
% 229.94/30.00 = { by lemma 19 }
% 229.94/30.00 f(X, X)
% 229.94/30.00
% 229.94/30.00 Lemma 38: mult(X, ld(mult(X, Y), mult(X, mult(Z, Y)))) = ld(mult(X, Y), mult(X, mult(Y, mult(X, Z)))).
% 229.94/30.00 Proof:
% 229.94/30.00 mult(X, ld(mult(X, Y), mult(X, mult(Z, Y))))
% 229.94/30.00 = { by axiom 1 (c05) R->L }
% 229.94/30.00 mult(X, ld(mult(X, Y), mult(X, mult(Y, Z))))
% 229.94/30.00 = { by lemma 24 }
% 229.94/30.00 ld(mult(X, Y), mult(X, mult(Y, mult(X, Z))))
% 229.94/30.00
% 229.94/30.00 Lemma 39: mult(ld(X, unit), ld(ld(X, Y), unit)) = ld(Y, unit).
% 229.94/30.00 Proof:
% 229.94/30.00 mult(ld(X, unit), ld(ld(X, Y), unit))
% 229.94/30.00 = { by axiom 4 (c04) R->L }
% 229.94/30.00 ld(Y, mult(Y, mult(ld(X, unit), ld(ld(X, Y), unit))))
% 229.94/30.00 = { by lemma 22 R->L }
% 229.94/30.00 ld(Y, mult(Y, mult(f(unit, ld(X, unit)), ld(ld(X, Y), unit))))
% 229.94/30.00 = { by axiom 4 (c04) R->L }
% 229.94/30.00 ld(Y, mult(Y, ld(X, mult(X, mult(f(unit, ld(X, unit)), ld(ld(X, Y), unit))))))
% 229.94/30.00 = { by lemma 31 R->L }
% 229.94/30.00 ld(Y, mult(Y, ld(X, mult(Y, mult(ld(Y, X), ld(Y, mult(f(unit, ld(X, unit)), X)))))))
% 229.94/30.00 = { by lemma 32 }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(Y, ld(Y, mult(f(unit, ld(X, unit)), X)))))))
% 229.94/30.00 = { by axiom 5 (c03) }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(f(unit, ld(X, unit)), X)))))
% 229.94/30.00 = { by axiom 1 (c05) }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(X, f(unit, ld(X, unit)))))))
% 229.94/30.00 = { by lemma 33 R->L }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(f(X, X), mult(X, mult(f(unit, ld(X, unit)), f(X, X))))))))
% 229.94/30.00 = { by lemma 37 R->L }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(f(X, X), mult(X, mult(f(unit, ld(X, unit)), mult(X, ld(f(unit, ld(X, unit)), unit)))))))))
% 229.94/30.00 = { by lemma 37 R->L }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(mult(X, ld(f(unit, ld(X, unit)), unit)), mult(X, mult(f(unit, ld(X, unit)), mult(X, ld(f(unit, ld(X, unit)), unit)))))))))
% 229.94/30.00 = { by lemma 29 R->L }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(mult(X, ld(f(unit, ld(X, unit)), unit)), mult(X, mult(ld(f(unit, ld(X, unit)), unit), mult(X, f(unit, ld(X, unit))))))))))
% 229.94/30.00 = { by lemma 13 R->L }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(mult(X, ld(mult(f(unit, ld(X, unit)), f(unit, ld(X, unit))), f(unit, ld(X, unit)))), mult(X, mult(ld(f(unit, ld(X, unit)), unit), mult(X, f(unit, ld(X, unit))))))))))
% 229.94/30.00 = { by lemma 13 R->L }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(mult(X, ld(mult(f(unit, ld(X, unit)), f(unit, ld(X, unit))), f(unit, ld(X, unit)))), mult(X, mult(ld(mult(f(unit, ld(X, unit)), f(unit, ld(X, unit))), f(unit, ld(X, unit))), mult(X, f(unit, ld(X, unit))))))))))
% 229.94/30.00 = { by lemma 38 R->L }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(X, ld(mult(X, ld(mult(f(unit, ld(X, unit)), f(unit, ld(X, unit))), f(unit, ld(X, unit)))), mult(X, mult(f(unit, ld(X, unit)), ld(mult(f(unit, ld(X, unit)), f(unit, ld(X, unit))), f(unit, ld(X, unit)))))))))))
% 229.94/30.00 = { by lemma 12 }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(X, ld(mult(X, ld(mult(f(unit, ld(X, unit)), f(unit, ld(X, unit))), f(unit, ld(X, unit)))), mult(X, unit)))))))
% 229.94/30.00 = { by lemma 13 }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(X, ld(mult(X, ld(f(unit, ld(X, unit)), unit)), mult(X, unit)))))))
% 229.94/30.00 = { by axiom 2 (c01) }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(X, ld(mult(X, ld(f(unit, ld(X, unit)), unit)), X))))))
% 229.94/30.00 = { by lemma 37 }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), mult(X, ld(f(X, X), X))))))
% 229.94/30.00 = { by lemma 28 }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(f(X, X), mult(X, X))))))
% 229.94/30.00 = { by lemma 18 }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), ld(f(X, X), f(X, X))))))
% 229.94/30.00 = { by lemma 11 }
% 229.94/30.00 ld(Y, ld(X, mult(Y, mult(ld(Y, X), unit))))
% 229.94/30.00 = { by axiom 2 (c01) }
% 229.94/30.00 ld(Y, ld(X, mult(Y, ld(Y, X))))
% 229.94/30.00 = { by axiom 5 (c03) }
% 229.94/30.00 ld(Y, ld(X, X))
% 229.94/30.00 = { by lemma 11 }
% 229.94/30.00 ld(Y, unit)
% 229.94/30.00
% 229.94/30.00 Lemma 40: mult(ld(X, unit), ld(Y, unit)) = ld(mult(X, Y), unit).
% 229.94/30.00 Proof:
% 229.94/30.00 mult(ld(X, unit), ld(Y, unit))
% 229.94/30.00 = { by axiom 1 (c05) R->L }
% 229.94/30.00 mult(ld(Y, unit), ld(X, unit))
% 229.94/30.00 = { by axiom 4 (c04) R->L }
% 229.94/30.00 mult(ld(Y, unit), ld(ld(Y, mult(Y, X)), unit))
% 229.94/30.00 = { by lemma 39 }
% 229.94/30.00 ld(mult(Y, X), unit)
% 229.94/30.00 = { by axiom 1 (c05) }
% 229.94/30.00 ld(mult(X, Y), unit)
% 229.94/30.00
% 229.94/30.00 Lemma 41: ld(ld(X, unit), ld(Y, unit)) = ld(ld(X, Y), unit).
% 229.94/30.00 Proof:
% 230.62/30.00 ld(ld(X, unit), ld(Y, unit))
% 230.62/30.00 = { by lemma 39 R->L }
% 230.62/30.00 ld(ld(X, unit), mult(ld(X, unit), ld(ld(X, Y), unit)))
% 230.62/30.00 = { by axiom 4 (c04) }
% 230.62/30.00 ld(ld(X, Y), unit)
% 230.62/30.00
% 230.62/30.00 Lemma 42: ld(X, ld(mult(X, Y), mult(X, mult(Y, mult(X, Z))))) = ld(mult(X, Y), mult(X, mult(Y, Z))).
% 230.62/30.00 Proof:
% 230.62/30.00 ld(X, ld(mult(X, Y), mult(X, mult(Y, mult(X, Z)))))
% 230.62/30.00 = { by lemma 24 R->L }
% 230.62/30.00 ld(X, mult(X, ld(mult(X, Y), mult(X, mult(Y, Z)))))
% 230.62/30.00 = { by axiom 4 (c04) }
% 230.62/30.00 ld(mult(X, Y), mult(X, mult(Y, Z)))
% 230.62/30.00
% 230.62/30.00 Lemma 43: ld(X, mult(Y, mult(X, ld(Y, X)))) = mult(Y, ld(ld(X, Y), unit)).
% 230.62/30.00 Proof:
% 230.62/30.00 ld(X, mult(Y, mult(X, ld(Y, X))))
% 230.62/30.00 = { by axiom 2 (c01) R->L }
% 230.62/30.00 ld(X, mult(Y, mult(X, ld(Y, mult(X, unit)))))
% 230.62/30.00 = { by lemma 12 R->L }
% 230.62/30.00 ld(X, mult(Y, mult(X, ld(Y, mult(X, mult(ld(X, Y), ld(mult(ld(X, Y), ld(X, Y)), ld(X, Y))))))))
% 230.62/30.00 = { by lemma 32 }
% 230.62/30.00 ld(X, mult(Y, ld(Y, mult(X, mult(ld(X, Y), mult(X, ld(mult(ld(X, Y), ld(X, Y)), ld(X, Y))))))))
% 230.62/30.00 = { by lemma 13 }
% 230.62/30.00 ld(X, mult(Y, ld(Y, mult(X, mult(ld(X, Y), mult(X, ld(ld(X, Y), unit)))))))
% 230.62/30.01 = { by lemma 29 R->L }
% 230.62/30.01 ld(X, mult(Y, ld(Y, mult(X, mult(ld(ld(X, Y), unit), mult(X, ld(X, Y)))))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(X, mult(Y, ld(Y, mult(X, mult(ld(ld(X, Y), unit), Y)))))
% 230.62/30.01 = { by axiom 1 (c05) }
% 230.62/30.01 ld(X, mult(Y, ld(Y, mult(X, mult(Y, ld(ld(X, Y), unit))))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(X, mult(X, mult(Y, ld(ld(X, Y), unit))))
% 230.62/30.01 = { by axiom 4 (c04) }
% 230.62/30.01 mult(Y, ld(ld(X, Y), unit))
% 230.62/30.01
% 230.62/30.01 Lemma 44: mult(X, f(ld(X, Y), ld(X, Y))) = mult(Y, ld(ld(Y, X), unit)).
% 230.62/30.01 Proof:
% 230.62/30.01 mult(X, f(ld(X, Y), ld(X, Y)))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 mult(Y, ld(Y, mult(X, f(ld(X, Y), ld(X, Y)))))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 mult(Y, ld(mult(X, ld(X, Y)), mult(X, f(ld(X, Y), ld(X, Y)))))
% 230.62/30.01 = { by lemma 18 R->L }
% 230.62/30.01 mult(Y, ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), ld(X, Y)))))
% 230.62/30.01 = { by lemma 42 R->L }
% 230.62/30.01 mult(Y, ld(X, ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), mult(X, ld(X, Y)))))))
% 230.62/30.01 = { by axiom 1 (c05) R->L }
% 230.62/30.01 mult(Y, ld(X, ld(mult(X, ld(X, Y)), mult(X, mult(mult(X, ld(X, Y)), ld(X, Y))))))
% 230.62/30.01 = { by axiom 4 (c04) R->L }
% 230.62/30.01 mult(Y, ld(X, ld(mult(X, ld(X, Y)), mult(X, mult(mult(X, ld(X, Y)), ld(X, mult(X, ld(X, Y))))))))
% 230.62/30.01 = { by lemma 43 }
% 230.62/30.01 mult(Y, ld(X, mult(X, ld(ld(mult(X, ld(X, Y)), X), unit))))
% 230.62/30.01 = { by axiom 4 (c04) }
% 230.62/30.01 mult(Y, ld(ld(mult(X, ld(X, Y)), X), unit))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 mult(Y, ld(ld(Y, X), unit))
% 230.62/30.01
% 230.62/30.01 Lemma 45: ld(Y, mult(X, mult(ld(X, Y), ld(X, Z)))) = ld(X, ld(Y, mult(X, mult(Z, ld(X, Y))))).
% 230.62/30.01 Proof:
% 230.62/30.01 ld(Y, mult(X, mult(ld(X, Y), ld(X, Z))))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), ld(X, Z))))
% 230.62/30.01 = { by lemma 42 R->L }
% 230.62/30.01 ld(X, ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), mult(X, ld(X, Z))))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(X, ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), Z))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(X, ld(Y, mult(X, mult(ld(X, Y), Z))))
% 230.62/30.01 = { by axiom 1 (c05) }
% 230.62/30.01 ld(X, ld(Y, mult(X, mult(Z, ld(X, Y)))))
% 230.62/30.01
% 230.62/30.01 Lemma 46: mult(ld(X, mult(Y, Z)), ld(ld(X, Y), unit)) = ld(X, mult(Y, mult(Z, ld(Y, X)))).
% 230.62/30.01 Proof:
% 230.62/30.01 mult(ld(X, mult(Y, Z)), ld(ld(X, Y), unit))
% 230.62/30.01 = { by axiom 4 (c04) R->L }
% 230.62/30.01 mult(ld(X, mult(Y, Z)), ld(Y, mult(Y, ld(ld(X, Y), unit))))
% 230.62/30.01 = { by lemma 43 R->L }
% 230.62/30.01 mult(ld(X, mult(Y, Z)), ld(Y, ld(X, mult(Y, mult(X, ld(Y, X))))))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 mult(ld(mult(Y, ld(Y, X)), mult(Y, Z)), ld(Y, ld(X, mult(Y, mult(X, ld(Y, X))))))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 mult(ld(mult(Y, ld(Y, X)), mult(Y, Z)), ld(Y, ld(mult(Y, ld(Y, X)), mult(Y, mult(X, ld(Y, X))))))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 mult(ld(mult(Y, ld(Y, X)), mult(Y, Z)), ld(Y, ld(mult(Y, ld(Y, X)), mult(Y, mult(X, ld(Y, mult(Y, ld(Y, X))))))))
% 230.62/30.01 = { by lemma 45 R->L }
% 230.62/30.01 mult(ld(mult(Y, ld(Y, X)), mult(Y, Z)), ld(mult(Y, ld(Y, X)), mult(Y, mult(ld(Y, mult(Y, ld(Y, X))), ld(Y, X)))))
% 230.62/30.01 = { by axiom 1 (c05) }
% 230.62/30.01 mult(ld(mult(Y, ld(Y, X)), mult(Y, Z)), ld(mult(Y, ld(Y, X)), mult(Y, mult(ld(Y, X), ld(Y, mult(Y, ld(Y, X)))))))
% 230.62/30.01 = { by lemma 23 }
% 230.62/30.01 ld(mult(Y, ld(Y, X)), mult(Y, mult(ld(Y, X), mult(ld(Y, mult(Y, ld(Y, X))), ld(ld(Y, X), Z)))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(X, mult(Y, mult(ld(Y, X), mult(ld(Y, mult(Y, ld(Y, X))), ld(ld(Y, X), Z)))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(X, mult(Y, mult(ld(Y, X), mult(ld(Y, X), ld(ld(Y, X), Z)))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(X, mult(Y, mult(ld(Y, X), Z)))
% 230.62/30.01 = { by axiom 1 (c05) }
% 230.62/30.01 ld(X, mult(Y, mult(Z, ld(Y, X))))
% 230.62/30.01
% 230.62/30.01 Lemma 47: ld(ld(ld(X, Y), unit), Y) = ld(X, f(Y, Y)).
% 230.62/30.01 Proof:
% 230.62/30.01 ld(ld(ld(X, Y), unit), Y)
% 230.62/30.01 = { by lemma 9 R->L }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, X)))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, mult(Y, ld(Y, X)))))
% 230.62/30.01 = { by lemma 14 R->L }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, mult(ld(ld(Y, unit), unit), ld(Y, X)))))
% 230.62/30.01 = { by axiom 4 (c04) R->L }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, mult(ld(Y, mult(Y, ld(ld(Y, unit), unit))), ld(Y, X)))))
% 230.62/30.01 = { by lemma 44 R->L }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, mult(ld(Y, mult(unit, f(ld(unit, Y), ld(unit, Y)))), ld(Y, X)))))
% 230.62/30.01 = { by lemma 36 R->L }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, mult(ld(Y, mult(unit, ld(unit, mult(Y, ld(f(unit, ld(Y, unit)), unit))))), ld(Y, X)))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, mult(ld(Y, mult(Y, ld(f(unit, ld(Y, unit)), unit))), ld(Y, X)))))
% 230.62/30.01 = { by axiom 4 (c04) }
% 230.62/30.01 ld(ld(ld(X, Y), unit), ld(X, mult(Y, mult(ld(f(unit, ld(Y, unit)), unit), ld(Y, X)))))
% 230.62/30.01 = { by lemma 46 R->L }
% 230.62/30.01 ld(ld(ld(X, Y), unit), mult(ld(X, mult(Y, ld(f(unit, ld(Y, unit)), unit))), ld(ld(X, Y), unit)))
% 230.62/30.01 = { by lemma 37 }
% 230.62/30.01 ld(ld(ld(X, Y), unit), mult(ld(X, f(Y, Y)), ld(ld(X, Y), unit)))
% 230.62/30.01 = { by lemma 9 }
% 230.62/30.01 ld(X, f(Y, Y))
% 230.62/30.01
% 230.62/30.01 Lemma 48: ld(ld(ld(X, unit), Y), unit) = ld(X, ld(Y, unit)).
% 230.62/30.01 Proof:
% 230.62/30.01 ld(ld(ld(X, unit), Y), unit)
% 230.62/30.01 = { by lemma 41 R->L }
% 230.62/30.01 ld(ld(ld(X, unit), unit), ld(Y, unit))
% 230.62/30.01 = { by lemma 14 }
% 230.62/30.01 ld(X, ld(Y, unit))
% 230.62/30.01
% 230.62/30.01 Lemma 49: f(ld(X, unit), ld(X, unit)) = ld(X, ld(X, unit)).
% 230.62/30.01 Proof:
% 230.62/30.01 f(ld(X, unit), ld(X, unit))
% 230.62/30.01 = { by lemma 18 R->L }
% 230.62/30.01 mult(ld(X, unit), ld(X, unit))
% 230.62/30.01 = { by lemma 15 R->L }
% 230.62/30.01 ld(ld(ld(X, unit), unit), ld(X, unit))
% 230.62/30.01 = { by lemma 14 }
% 230.62/30.01 ld(X, ld(X, unit))
% 230.62/30.01
% 230.62/30.01 Lemma 50: ld(ld(X, ld(X, unit)), ld(Y, unit)) = ld(ld(f(X, X), Y), unit).
% 230.62/30.01 Proof:
% 230.62/30.01 ld(ld(X, ld(X, unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 49 R->L }
% 230.62/30.01 ld(f(ld(X, unit), ld(X, unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 17 R->L }
% 230.62/30.01 ld(ld(ld(mult(ld(X, unit), ld(X, unit)), ld(X, unit)), ld(ld(mult(ld(X, unit), ld(X, unit)), ld(X, unit)), unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 13 R->L }
% 230.62/30.01 ld(ld(ld(mult(ld(X, unit), ld(mult(X, X), X)), ld(X, unit)), ld(ld(mult(ld(X, unit), ld(X, unit)), ld(X, unit)), unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 13 R->L }
% 230.62/30.01 ld(ld(ld(mult(ld(mult(X, X), X), ld(mult(X, X), X)), ld(X, unit)), ld(ld(mult(ld(X, unit), ld(X, unit)), ld(X, unit)), unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 16 }
% 230.62/30.01 ld(ld(ld(ld(f(X, X), unit), ld(X, unit)), ld(ld(mult(ld(X, unit), ld(X, unit)), ld(X, unit)), unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 13 }
% 230.62/30.01 ld(ld(ld(ld(f(X, X), unit), ld(X, unit)), ld(ld(ld(X, unit), unit), unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 14 }
% 230.62/30.01 ld(ld(ld(ld(f(X, X), unit), ld(X, unit)), ld(X, unit)), ld(Y, unit))
% 230.62/30.01 = { by lemma 14 }
% 230.62/30.01 ld(ld(f(X, X), unit), ld(Y, unit))
% 230.62/30.01 = { by lemma 41 }
% 230.62/30.01 ld(ld(f(X, X), Y), unit)
% 230.62/30.01
% 230.62/30.01 Lemma 51: ld(ld(X, Y), ld(Y, mult(ld(X, Y), mult(X, Z)))) = ld(Y, ld(X, mult(Y, mult(X, ld(Y, mult(X, Z)))))).
% 230.62/30.01 Proof:
% 230.62/30.01 ld(ld(X, Y), ld(Y, mult(ld(X, Y), mult(X, Z))))
% 230.62/30.01 = { by axiom 1 (c05) R->L }
% 230.62/30.01 ld(ld(X, Y), ld(Y, mult(ld(X, Y), mult(Z, X))))
% 230.62/30.01 = { by lemma 14 R->L }
% 230.62/30.01 ld(ld(X, Y), ld(Y, mult(ld(X, Y), mult(Z, ld(ld(X, Y), Y)))))
% 230.62/30.01 = { by lemma 45 R->L }
% 230.62/30.01 ld(Y, mult(ld(X, Y), mult(ld(ld(X, Y), Y), ld(ld(X, Y), Z))))
% 230.62/30.01 = { by lemma 14 }
% 230.62/30.01 ld(Y, mult(ld(X, Y), mult(X, ld(ld(X, Y), Z))))
% 230.62/30.01 = { by axiom 4 (c04) R->L }
% 230.62/30.01 ld(Y, ld(X, mult(X, mult(ld(X, Y), mult(X, ld(ld(X, Y), Z))))))
% 230.62/30.01 = { by axiom 5 (c03) R->L }
% 230.62/30.01 ld(Y, ld(X, mult(mult(X, ld(X, Y)), ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), mult(X, ld(ld(X, Y), Z))))))))
% 230.62/30.01 = { by lemma 24 R->L }
% 230.62/30.01 ld(Y, ld(X, mult(mult(X, ld(X, Y)), mult(X, ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), ld(ld(X, Y), Z))))))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(Y, ld(X, mult(mult(X, ld(X, Y)), mult(X, ld(mult(X, ld(X, Y)), mult(X, Z))))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(Y, ld(X, mult(Y, mult(X, ld(mult(X, ld(X, Y)), mult(X, Z))))))
% 230.62/30.01 = { by axiom 5 (c03) }
% 230.62/30.01 ld(Y, ld(X, mult(Y, mult(X, ld(Y, mult(X, Z))))))
% 230.62/30.01
% 230.62/30.01 Lemma 52: ld(X, f(mult(X, Y), mult(X, Y))) = ld(ld(Y, unit), mult(X, Y)).
% 230.62/30.01 Proof:
% 230.62/30.01 ld(X, f(mult(X, Y), mult(X, Y)))
% 230.62/30.01 = { by lemma 47 R->L }
% 230.62/30.01 ld(ld(ld(X, mult(X, Y)), unit), mult(X, Y))
% 230.62/30.01 = { by axiom 4 (c04) }
% 230.62/30.01 ld(ld(Y, unit), mult(X, Y))
% 230.62/30.01
% 230.62/30.01 Lemma 53: ld(mult(X, ld(ld(X, Y), unit)), mult(X, f(ld(Y, X), ld(Y, X)))) = ld(Y, X).
% 230.62/30.01 Proof:
% 230.62/30.01 ld(mult(X, ld(ld(X, Y), unit)), mult(X, f(ld(Y, X), ld(Y, X))))
% 230.62/30.02 = { by lemma 44 R->L }
% 230.62/30.02 ld(mult(Y, f(ld(Y, X), ld(Y, X))), mult(X, f(ld(Y, X), ld(Y, X))))
% 230.62/30.02 = { by axiom 1 (c05) R->L }
% 230.62/30.02 ld(mult(Y, f(ld(Y, X), ld(Y, X))), mult(f(ld(Y, X), ld(Y, X)), X))
% 230.62/30.02 = { by axiom 5 (c03) R->L }
% 230.62/30.02 ld(mult(Y, f(ld(Y, X), ld(Y, X))), mult(f(ld(Y, X), ld(Y, X)), mult(Y, ld(Y, X))))
% 230.62/30.02 = { by axiom 1 (c05) R->L }
% 230.62/30.02 ld(mult(Y, f(ld(Y, X), ld(Y, X))), mult(f(ld(Y, X), ld(Y, X)), mult(ld(Y, X), Y)))
% 230.62/30.02 = { by lemma 33 R->L }
% 230.62/30.02 ld(mult(Y, f(ld(Y, X), ld(Y, X))), mult(f(ld(Y, X), ld(Y, X)), ld(f(ld(Y, X), ld(Y, X)), mult(ld(Y, X), mult(Y, f(ld(Y, X), ld(Y, X)))))))
% 230.62/30.02 = { by axiom 5 (c03) }
% 230.62/30.02 ld(mult(Y, f(ld(Y, X), ld(Y, X))), mult(ld(Y, X), mult(Y, f(ld(Y, X), ld(Y, X)))))
% 230.62/30.02 = { by lemma 9 }
% 230.62/30.02 ld(Y, X)
% 230.62/30.02
% 230.62/30.02 Lemma 54: ld(ld(f(X, X), f(X, ld(X, Y))), unit) = ld(ld(X, unit), ld(Y, X)).
% 230.62/30.02 Proof:
% 230.62/30.02 ld(ld(f(X, X), f(X, ld(X, Y))), unit)
% 230.62/30.02 = { by lemma 50 R->L }
% 230.62/30.02 ld(ld(X, ld(X, unit)), ld(f(X, ld(X, Y)), unit))
% 230.62/30.02 = { by lemma 34 R->L }
% 230.62/30.02 ld(ld(X, ld(X, unit)), mult(ld(Y, X), ld(Y, ld(X, Y))))
% 230.62/30.02 = { by lemma 14 R->L }
% 230.62/30.02 ld(ld(X, ld(X, unit)), mult(ld(Y, X), ld(ld(ld(Y, ld(X, Y)), unit), unit)))
% 230.62/30.02 = { by lemma 49 R->L }
% 230.62/30.02 ld(f(ld(X, unit), ld(X, unit)), mult(ld(Y, X), ld(ld(ld(Y, ld(X, Y)), unit), unit)))
% 230.62/30.02 = { by lemma 14 R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(X, unit)), mult(ld(Y, X), ld(ld(ld(Y, ld(X, Y)), unit), unit)))
% 230.62/30.02 = { by lemma 14 R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, ld(X, Y)), unit), unit)))
% 230.62/30.02 = { by lemma 14 R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, ld(X, ld(ld(Y, X), X))), unit), unit)))
% 230.62/30.02 = { by lemma 14 R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(ld(ld(Y, X), X), ld(X, ld(ld(Y, X), X))), unit), unit)))
% 230.62/30.02 = { by axiom 4 (c04) R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), mult(ld(Y, X), ld(ld(ld(ld(Y, X), X), ld(X, ld(ld(Y, X), X))), unit))), unit)))
% 230.62/30.02 = { by axiom 4 (c04) R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), mult(ld(Y, X), ld(ld(ld(ld(Y, X), X), ld(X, ld(ld(Y, X), X))), unit))))), unit)))
% 230.62/30.02 = { by axiom 4 (c04) R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), ld(ld(ld(Y, X), X), mult(ld(ld(Y, X), X), mult(ld(Y, X), ld(ld(ld(ld(Y, X), X), ld(X, ld(ld(Y, X), X))), unit))))))), unit)))
% 230.62/30.02 = { by axiom 5 (c03) R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), ld(mult(ld(X, ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))), mult(ld(ld(Y, X), X), mult(ld(Y, X), ld(ld(ld(ld(Y, X), X), ld(X, ld(ld(Y, X), X))), unit))))))), unit)))
% 230.62/30.02 = { by lemma 31 R->L }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), ld(mult(ld(X, ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))), mult(ld(X, ld(ld(Y, X), X)), mult(ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), mult(ld(Y, X), ld(ld(Y, X), X))))))))), unit)))
% 230.62/30.02 = { by axiom 5 (c03) }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), ld(mult(ld(X, ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))), mult(ld(X, ld(ld(Y, X), X)), mult(ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), X))))))), unit)))
% 230.62/30.02 = { by axiom 1 (c05) }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), ld(mult(ld(X, ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))), mult(ld(X, ld(ld(Y, X), X)), mult(ld(ld(X, ld(ld(Y, X), X)), X), ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X)))))))), unit)))
% 230.62/30.02 = { by lemma 38 }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), ld(mult(ld(X, ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))), mult(ld(X, ld(ld(Y, X), X)), mult(ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), X))))))), unit)))
% 230.62/30.02 = { by axiom 5 (c03) }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), ld(ld(ld(Y, X), X), mult(ld(X, ld(ld(Y, X), X)), mult(ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X)), mult(ld(X, ld(ld(Y, X), X)), ld(ld(X, ld(ld(Y, X), X)), X))))))), unit)))
% 230.62/30.02 = { by axiom 5 (c03) }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), ld(ld(ld(Y, X), X), mult(ld(X, ld(ld(Y, X), X)), mult(ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X)), X))))), unit)))
% 230.62/30.02 = { by axiom 1 (c05) }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, ld(ld(Y, X), X)), ld(ld(ld(Y, X), X), mult(ld(X, ld(ld(Y, X), X)), mult(X, ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))))))), unit)))
% 230.62/30.02 = { by lemma 51 }
% 230.62/30.02 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(ld(Y, X), X), ld(X, mult(ld(ld(Y, X), X), mult(X, ld(ld(ld(Y, X), X), mult(X, ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))))))))), unit)))
% 230.62/30.02 = { by axiom 5 (c03) R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(ld(Y, X), X), ld(X, mult(ld(ld(Y, X), X), mult(ld(Y, X), ld(ld(Y, X), mult(X, ld(ld(ld(Y, X), X), mult(X, ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))))))))))), unit)))
% 230.62/30.03 = { by lemma 51 }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, mult(ld(Y, X), ld(X, mult(ld(Y, X), ld(ld(Y, X), mult(X, ld(ld(ld(Y, X), X), mult(X, ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))))))))))))), unit)))
% 230.62/30.03 = { by axiom 5 (c03) }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, mult(ld(Y, X), ld(X, mult(X, ld(ld(ld(Y, X), X), mult(X, ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))))))))))), unit)))
% 230.62/30.03 = { by axiom 4 (c04) }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, mult(ld(Y, X), ld(ld(ld(Y, X), X), mult(X, ld(ld(X, ld(ld(Y, X), X)), ld(ld(Y, X), X))))))))), unit)))
% 230.62/30.03 = { by lemma 14 }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, mult(ld(Y, X), ld(ld(ld(Y, X), X), mult(X, X))))))), unit)))
% 230.62/30.03 = { by lemma 18 }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, mult(ld(Y, X), ld(ld(ld(Y, X), X), f(X, X))))))), unit)))
% 230.62/30.03 = { by lemma 47 R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, mult(ld(Y, X), ld(ld(ld(ld(ld(Y, X), X), X), unit), X)))))), unit)))
% 230.62/30.03 = { by lemma 14 }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, mult(ld(Y, X), ld(ld(ld(Y, X), unit), X)))))), unit)))
% 230.62/30.03 = { by lemma 27 }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, ld(ld(ld(Y, X), unit), mult(ld(Y, X), X)))))), unit)))
% 230.62/30.03 = { by axiom 1 (c05) R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, ld(ld(ld(Y, X), unit), mult(X, ld(Y, X))))))), unit)))
% 230.62/30.03 = { by lemma 52 R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), mult(X, ld(X, f(mult(X, ld(Y, X)), mult(X, ld(Y, X)))))))), unit)))
% 230.62/30.03 = { by axiom 5 (c03) }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), f(mult(X, ld(Y, X)), mult(X, ld(Y, X)))))), unit)))
% 230.62/30.03 = { by axiom 1 (c05) R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), f(mult(X, ld(Y, X)), mult(ld(Y, X), X))))), unit)))
% 230.62/30.03 = { by axiom 1 (c05) R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(Y, X), f(mult(ld(Y, X), X), mult(ld(Y, X), X))))), unit)))
% 230.62/30.03 = { by lemma 52 }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(X, unit), mult(ld(Y, X), X)))), unit)))
% 230.62/30.03 = { by axiom 1 (c05) R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, ld(ld(X, unit), mult(X, ld(Y, X))))), unit)))
% 230.62/30.03 = { by lemma 27 R->L }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(X, mult(X, ld(ld(X, unit), ld(Y, X))))), unit)))
% 230.62/30.03 = { by axiom 4 (c04) }
% 230.62/30.03 ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)))
% 230.62/30.03 = { by lemma 53 R->L }
% 230.62/30.03 ld(f(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)))
% 230.62/30.03 = { by lemma 53 R->L }
% 230.62/30.03 ld(f(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)))))), mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)))
% 230.62/30.03 = { by lemma 14 R->L }
% 230.62/30.03 ld(f(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)))))), ld(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))))
% 230.62/30.03 = { by axiom 4 (c04) R->L }
% 230.62/30.03 ld(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), mult(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(f(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)))))), ld(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))))))
% 230.62/30.03 = { by lemma 28 }
% 230.62/30.03 ld(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(f(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)))))), mult(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))))))
% 230.62/30.04 = { by axiom 5 (c03) }
% 230.62/30.04 ld(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(f(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)))))), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))))
% 230.62/30.04 = { by lemma 53 }
% 230.62/30.04 ld(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(f(ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))), ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)))))), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))))
% 230.62/30.04 = { by lemma 53 }
% 230.62/30.04 ld(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(mult(ld(Y, X), ld(ld(ld(Y, X), ld(ld(X, unit), ld(Y, X))), unit)), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)))))), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))))
% 230.62/30.04 = { by lemma 53 }
% 230.62/30.04 ld(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))), mult(ld(Y, X), f(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X))))))
% 230.62/30.04 = { by lemma 9 }
% 230.62/30.04 ld(ld(ld(ld(X, unit), ld(Y, X)), ld(Y, X)), ld(Y, X))
% 230.62/30.04 = { by lemma 14 }
% 230.62/30.04 ld(ld(X, unit), ld(Y, X))
% 230.62/30.04
% 230.62/30.04 Lemma 55: ld(X, ld(ld(mult(X, Y), X), unit)) = ld(f(X, X), f(X, Y)).
% 230.62/30.04 Proof:
% 230.62/30.04 ld(X, ld(ld(mult(X, Y), X), unit))
% 230.62/30.04 = { by lemma 48 R->L }
% 230.62/30.04 ld(ld(ld(X, unit), ld(mult(X, Y), X)), unit)
% 230.62/30.04 = { by lemma 54 R->L }
% 230.62/30.04 ld(ld(ld(f(X, X), f(X, ld(X, mult(X, Y)))), unit), unit)
% 230.62/30.04 = { by lemma 14 }
% 230.62/30.04 ld(f(X, X), f(X, ld(X, mult(X, Y))))
% 230.62/30.04 = { by axiom 4 (c04) }
% 230.62/30.04 ld(f(X, X), f(X, Y))
% 230.62/30.04
% 230.62/30.04 Lemma 56: ld(ld(f(X, X), f(X, Y)), unit) = ld(ld(X, unit), ld(mult(X, Y), X)).
% 230.62/30.04 Proof:
% 230.62/30.04 ld(ld(f(X, X), f(X, Y)), unit)
% 230.62/30.04 = { by axiom 4 (c04) R->L }
% 230.62/30.04 ld(ld(f(X, X), f(X, ld(X, mult(X, Y)))), unit)
% 230.62/30.04 = { by lemma 54 }
% 230.62/30.04 ld(ld(X, unit), ld(mult(X, Y), X))
% 230.62/30.04
% 230.62/30.04 Lemma 57: mult(ld(mult(X, Y), Y), ld(mult(X, Y), X)) = ld(f(X, Y), unit).
% 230.62/30.04 Proof:
% 230.62/30.04 mult(ld(mult(X, Y), Y), ld(mult(X, Y), X))
% 230.62/30.04 = { by axiom 1 (c05) R->L }
% 230.62/30.04 mult(ld(mult(X, Y), X), ld(mult(X, Y), Y))
% 230.62/30.04 = { by lemma 16 }
% 230.62/30.04 ld(f(X, Y), unit)
% 230.62/30.04
% 230.62/30.04 Lemma 58: ld(f(ld(X, unit), ld(Y, unit)), unit) = f(X, Y).
% 230.62/30.04 Proof:
% 230.62/30.04 ld(f(ld(X, unit), ld(Y, unit)), unit)
% 230.62/30.04 = { by lemma 21 }
% 230.62/30.04 ld(f(ld(Y, unit), ld(X, unit)), unit)
% 230.62/30.04 = { by lemma 57 R->L }
% 230.62/30.04 mult(ld(mult(ld(Y, unit), ld(X, unit)), ld(X, unit)), ld(mult(ld(Y, unit), ld(X, unit)), ld(Y, unit)))
% 230.62/30.04 = { by lemma 40 }
% 230.62/30.04 mult(ld(ld(mult(Y, X), unit), ld(X, unit)), ld(mult(ld(Y, unit), ld(X, unit)), ld(Y, unit)))
% 230.62/30.04 = { by lemma 41 }
% 230.62/30.04 mult(ld(ld(mult(Y, X), X), unit), ld(mult(ld(Y, unit), ld(X, unit)), ld(Y, unit)))
% 230.62/30.04 = { by lemma 40 }
% 230.62/30.04 mult(ld(ld(mult(Y, X), X), unit), ld(ld(mult(Y, X), unit), ld(Y, unit)))
% 230.62/30.04 = { by lemma 41 }
% 230.62/30.04 mult(ld(ld(mult(Y, X), X), unit), ld(ld(mult(Y, X), Y), unit))
% 230.62/30.04 = { by lemma 40 }
% 230.62/30.04 ld(mult(ld(mult(Y, X), X), ld(mult(Y, X), Y)), unit)
% 230.62/30.04 = { by lemma 57 }
% 230.62/30.04 ld(ld(f(Y, X), unit), unit)
% 230.62/30.04 = { by lemma 14 }
% 230.62/30.04 f(Y, X)
% 230.62/30.04 = { by lemma 21 R->L }
% 230.62/30.04 f(X, Y)
% 230.62/30.04
% 230.62/30.04 Goal 1 (goals): mult(mult(a, a), mult(b, b)) = mult(f(a, b), f(a, b)).
% 230.62/30.04 Proof:
% 230.62/30.04 mult(mult(a, a), mult(b, b))
% 230.62/30.04 = { by lemma 18 }
% 230.62/30.04 mult(f(a, a), mult(b, b))
% 230.62/30.04 = { by lemma 18 }
% 230.62/30.04 mult(f(a, a), f(b, b))
% 230.62/30.04 = { by axiom 1 (c05) R->L }
% 230.62/30.04 mult(f(b, b), f(a, a))
% 230.62/30.04 = { by lemma 14 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(f(a, a), f(a, b)), f(a, b)))
% 230.62/30.04 = { by lemma 55 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(a, ld(ld(mult(a, b), a), unit)), f(a, b)))
% 230.62/30.04 = { by lemma 48 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(mult(a, b), a)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 56 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(f(a, a), f(a, b)), unit), unit), f(a, b)))
% 230.62/30.04 = { by lemma 50 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, ld(a, unit)), ld(f(a, b), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 21 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, ld(a, unit)), ld(f(b, a), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 58 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, ld(a, unit)), ld(ld(f(ld(b, unit), ld(a, unit)), unit), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 14 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, ld(a, unit)), f(ld(b, unit), ld(a, unit))), unit), f(a, b)))
% 230.62/30.04 = { by lemma 21 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, ld(a, unit)), f(ld(a, unit), ld(b, unit))), unit), f(a, b)))
% 230.62/30.04 = { by lemma 49 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(f(ld(a, unit), ld(a, unit)), f(ld(a, unit), ld(b, unit))), unit), f(a, b)))
% 230.62/30.04 = { by lemma 21 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(f(ld(a, unit), ld(a, unit)), f(ld(b, unit), ld(a, unit))), unit), f(a, b)))
% 230.62/30.04 = { by lemma 58 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(f(ld(a, unit), ld(a, unit)), ld(f(ld(ld(b, unit), unit), ld(ld(a, unit), unit)), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 14 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(f(ld(a, unit), ld(a, unit)), ld(f(b, ld(ld(a, unit), unit)), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 21 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(f(ld(a, unit), ld(a, unit)), ld(f(ld(ld(a, unit), unit), b), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 18 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(mult(ld(a, unit), ld(a, unit)), ld(f(ld(ld(a, unit), unit), b), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 14 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(ld(mult(ld(a, unit), ld(a, unit)), ld(a, unit)), ld(a, unit)), ld(f(ld(ld(a, unit), unit), b), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 13 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(ld(ld(a, unit), unit), ld(a, unit)), ld(f(ld(ld(a, unit), unit), b), unit)), unit), f(a, b)))
% 230.62/30.04 = { by lemma 48 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(ld(ld(ld(ld(a, unit), unit), ld(a, unit)), unit), f(ld(ld(a, unit), unit), b)), unit), unit), f(a, b)))
% 230.62/30.04 = { by lemma 48 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(ld(ld(a, unit), ld(ld(a, unit), unit)), f(ld(ld(a, unit), unit), b)), unit), unit), f(a, b)))
% 230.62/30.04 = { by lemma 49 R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(f(ld(ld(a, unit), unit), ld(ld(a, unit), unit)), f(ld(ld(a, unit), unit), b)), unit), unit), f(a, b)))
% 230.62/30.04 = { by lemma 56 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(ld(ld(a, unit), unit), unit), ld(mult(ld(ld(a, unit), unit), b), ld(ld(a, unit), unit))), unit), f(a, b)))
% 230.62/30.04 = { by lemma 14 }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(mult(ld(ld(a, unit), unit), b), ld(ld(a, unit), unit))), unit), f(a, b)))
% 230.62/30.04 = { by axiom 4 (c04) R->L }
% 230.62/30.04 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(ld(a, unit), unit), ld(mult(ld(ld(a, unit), unit), b), ld(ld(a, unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 5 (c03) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(a, unit), mult(ld(ld(a, unit), unit), ld(mult(ld(ld(a, unit), unit), b), ld(ld(a, unit), unit))))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 14 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(ld(ld(a, unit), unit), unit), mult(ld(ld(a, unit), unit), ld(mult(ld(ld(a, unit), unit), b), ld(ld(a, unit), unit))))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 1 (c05) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(ld(ld(a, unit), unit), unit), mult(ld(ld(a, unit), unit), ld(mult(b, ld(ld(a, unit), unit)), ld(ld(a, unit), unit))))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 4 (c04) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(ld(ld(a, unit), unit), unit), mult(ld(ld(a, unit), unit), ld(mult(b, ld(ld(a, unit), unit)), ld(b, mult(b, ld(ld(a, unit), unit))))))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 4 (c04) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(ld(ld(a, unit), unit), unit), mult(ld(b, mult(b, ld(ld(a, unit), unit))), ld(mult(b, ld(ld(a, unit), unit)), ld(b, mult(b, ld(ld(a, unit), unit))))))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 4 (c04) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), mult(ld(b, mult(b, ld(ld(a, unit), unit))), ld(mult(b, ld(ld(a, unit), unit)), ld(b, mult(b, ld(ld(a, unit), unit))))))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 1 (c05) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), mult(ld(mult(b, ld(ld(a, unit), unit)), ld(b, mult(b, ld(ld(a, unit), unit)))), ld(b, mult(b, ld(ld(a, unit), unit)))))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 14 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), mult(ld(mult(b, ld(ld(a, unit), unit)), ld(b, mult(b, ld(ld(a, unit), unit)))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit)))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 26 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(mult(b, ld(ld(a, unit), unit)), ld(b, mult(b, ld(ld(a, unit), unit))))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 2 (c01) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(mult(b, ld(ld(a, unit), unit)), mult(ld(b, mult(b, ld(ld(a, unit), unit))), unit))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 11 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(mult(b, ld(ld(a, unit), unit)), mult(ld(b, mult(b, ld(ld(a, unit), unit))), ld(b, b)))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 5 (c03) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(mult(b, ld(ld(a, unit), unit)), mult(ld(b, mult(b, ld(ld(a, unit), unit))), ld(b, mult(mult(b, ld(ld(a, unit), unit)), ld(mult(b, ld(ld(a, unit), unit)), b)))))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 35 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(mult(b, ld(ld(a, unit), unit)), ld(b, mult(mult(b, ld(ld(a, unit), unit)), mult(ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit), ld(mult(b, ld(ld(a, unit), unit)), b)))))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 45 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(b, mult(mult(b, ld(ld(a, unit), unit)), mult(ld(mult(b, ld(ld(a, unit), unit)), b), ld(mult(b, ld(ld(a, unit), unit)), ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)))))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 1 (c05) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(b, mult(mult(b, ld(ld(a, unit), unit)), mult(ld(mult(b, ld(ld(a, unit), unit)), ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)), ld(mult(b, ld(ld(a, unit), unit)), b))))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 46 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), mult(ld(b, mult(mult(b, ld(ld(a, unit), unit)), ld(mult(b, ld(ld(a, unit), unit)), ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)))), ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 5 (c03) }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), mult(ld(b, ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)), ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 1 (c05) }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), mult(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), ld(b, ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)))), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 4 (c04) }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(b, ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)), ld(ld(ld(b, mult(b, ld(ld(a, unit), unit))), unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 14 }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(b, ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)), ld(b, mult(b, ld(ld(a, unit), unit))))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 1 (c05) }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(b, mult(b, ld(ld(a, unit), unit))), ld(b, ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 4 (c04) }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(a, unit), unit), ld(b, ld(ld(mult(b, ld(ld(a, unit), unit)), b), unit)))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 55 }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(a, unit), unit), ld(f(b, b), f(b, ld(ld(a, unit), unit))))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 21 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(ld(a, unit), unit), ld(f(b, b), f(ld(ld(a, unit), unit), b)))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 1 (c05) R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(a, unit), mult(ld(f(b, b), f(ld(ld(a, unit), unit), b)), ld(ld(a, unit), unit))))), unit), f(a, b)))
% 230.62/30.05 = { by lemma 25 R->L }
% 230.62/30.05 mult(f(b, b), ld(ld(ld(ld(a, unit), ld(ld(ld(a, unit), unit), mult(ld(ld(a, unit), unit), mult(ld(a, unit), ld(f(b, b), f(ld(ld(a, unit), unit), b)))))), unit), f(a, b)))
% 230.62/30.05 = { by axiom 4 (c04) }
% 230.62/30.06 mult(f(b, b), ld(ld(ld(ld(a, unit), mult(ld(a, unit), ld(f(b, b), f(ld(ld(a, unit), unit), b)))), unit), f(a, b)))
% 230.62/30.06 = { by lemma 21 R->L }
% 230.62/30.06 mult(f(b, b), ld(ld(ld(ld(a, unit), mult(ld(a, unit), ld(f(b, b), f(b, ld(ld(a, unit), unit))))), unit), f(a, b)))
% 230.62/30.06 = { by axiom 4 (c04) }
% 230.62/30.06 mult(f(b, b), ld(ld(ld(f(b, b), f(b, ld(ld(a, unit), unit))), unit), f(a, b)))
% 230.62/30.06 = { by lemma 14 }
% 230.62/30.06 mult(f(b, b), ld(ld(ld(f(b, b), f(b, a)), unit), f(a, b)))
% 230.62/30.06 = { by lemma 21 R->L }
% 230.62/30.06 mult(f(b, b), ld(ld(ld(f(b, b), f(a, b)), unit), f(a, b)))
% 230.62/30.06 = { by lemma 47 }
% 230.62/30.06 mult(f(b, b), ld(f(b, b), f(f(a, b), f(a, b))))
% 230.62/30.06 = { by lemma 21 R->L }
% 230.62/30.06 mult(f(b, b), ld(f(b, b), f(f(a, b), f(b, a))))
% 230.62/30.06 = { by lemma 21 R->L }
% 230.62/30.06 mult(f(b, b), ld(f(b, b), f(f(b, a), f(b, a))))
% 230.62/30.06 = { by axiom 5 (c03) }
% 230.62/30.06 f(f(b, a), f(b, a))
% 230.62/30.06 = { by lemma 21 R->L }
% 230.62/30.06 f(f(a, b), f(b, a))
% 230.62/30.06 = { by lemma 21 R->L }
% 230.62/30.06 f(f(a, b), f(a, b))
% 230.62/30.06 = { by lemma 18 R->L }
% 230.62/30.06 mult(f(a, b), f(a, b))
% 230.62/30.06 % SZS output end Proof
% 230.62/30.06
% 230.62/30.06 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------