TSTP Solution File: GRP667+6 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP667+6 : 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 : n024.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 01:19:37 EDT 2023
% Result : Theorem 43.90s 5.96s
% Output : Proof 44.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP667+6 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 02:02:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 43.90/5.96 Command-line arguments: --no-flatten-goal
% 43.90/5.96
% 43.90/5.96 % SZS status Theorem
% 43.90/5.96
% 43.90/6.01 % SZS output start Proof
% 43.90/6.01 Axiom 1 (f05): mult(X, unit) = X.
% 43.90/6.01 Axiom 2 (f06): mult(unit, X) = X.
% 43.90/6.01 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 43.90/6.01 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 43.90/6.01 Axiom 5 (f01): mult(X, ld(X, Y)) = Y.
% 43.90/6.01 Axiom 6 (f09): mult(f(X), f(X)) = X.
% 43.90/6.01 Axiom 7 (f03): mult(rd(X, Y), Y) = X.
% 43.90/6.01 Axiom 8 (f08): mult(mult(X, Y), X) = mult(X, mult(Y, X)).
% 43.90/6.01 Axiom 9 (f07): mult(mult(X, Y), mult(mult(Z, Y), Z)) = mult(mult(X, mult(mult(Y, Z), Y)), Z).
% 43.90/6.01
% 43.90/6.01 Lemma 10: rd(X, X) = unit.
% 43.90/6.01 Proof:
% 43.90/6.01 rd(X, X)
% 43.90/6.01 = { by axiom 2 (f06) R->L }
% 43.90/6.01 rd(mult(unit, X), X)
% 43.90/6.01 = { by axiom 4 (f04) }
% 43.90/6.01 unit
% 43.90/6.01
% 43.90/6.01 Lemma 11: mult(f(X), X) = mult(X, f(X)).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(f(X), X)
% 43.90/6.01 = { by axiom 6 (f09) R->L }
% 43.90/6.01 mult(f(X), mult(f(X), f(X)))
% 43.90/6.01 = { by axiom 8 (f08) R->L }
% 43.90/6.01 mult(mult(f(X), f(X)), f(X))
% 43.90/6.01 = { by axiom 6 (f09) }
% 43.90/6.01 mult(X, f(X))
% 43.90/6.01
% 43.90/6.01 Lemma 12: rd(mult(X, mult(Y, X)), X) = mult(X, Y).
% 43.90/6.01 Proof:
% 43.90/6.01 rd(mult(X, mult(Y, X)), X)
% 43.90/6.01 = { by axiom 8 (f08) R->L }
% 43.90/6.01 rd(mult(mult(X, Y), X), X)
% 43.90/6.01 = { by axiom 4 (f04) }
% 43.90/6.01 mult(X, Y)
% 43.90/6.01
% 43.90/6.01 Lemma 13: mult(X, rd(Y, X)) = rd(mult(X, Y), X).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(X, rd(Y, X))
% 43.90/6.01 = { by lemma 12 R->L }
% 43.90/6.01 rd(mult(X, mult(rd(Y, X), X)), X)
% 43.90/6.01 = { by axiom 7 (f03) }
% 43.90/6.01 rd(mult(X, Y), X)
% 43.90/6.01
% 43.90/6.01 Lemma 14: ld(X, rd(mult(X, Y), X)) = rd(Y, X).
% 43.90/6.01 Proof:
% 43.90/6.01 ld(X, rd(mult(X, Y), X))
% 43.90/6.01 = { by lemma 13 R->L }
% 43.90/6.01 ld(X, mult(X, rd(Y, X)))
% 43.90/6.01 = { by axiom 3 (f02) }
% 43.90/6.01 rd(Y, X)
% 43.90/6.01
% 43.90/6.01 Lemma 15: rd(mult(X, f(X)), X) = f(X).
% 43.90/6.01 Proof:
% 43.90/6.01 rd(mult(X, f(X)), X)
% 43.90/6.01 = { by lemma 11 R->L }
% 43.90/6.01 rd(mult(f(X), X), X)
% 43.90/6.01 = { by axiom 4 (f04) }
% 43.90/6.01 f(X)
% 43.90/6.01
% 43.90/6.01 Lemma 16: rd(f(X), X) = ld(X, f(X)).
% 43.90/6.01 Proof:
% 43.90/6.01 rd(f(X), X)
% 43.90/6.01 = { by lemma 14 R->L }
% 43.90/6.01 ld(X, rd(mult(X, f(X)), X))
% 43.90/6.01 = { by lemma 15 }
% 43.90/6.01 ld(X, f(X))
% 43.90/6.01
% 43.90/6.01 Lemma 17: mult(mult(X, mult(Y, mult(Z, Y))), Z) = mult(mult(X, Y), mult(Z, mult(Y, Z))).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(mult(X, mult(Y, mult(Z, Y))), Z)
% 43.90/6.01 = { by axiom 8 (f08) R->L }
% 43.90/6.01 mult(mult(X, mult(mult(Y, Z), Y)), Z)
% 43.90/6.01 = { by axiom 9 (f07) R->L }
% 43.90/6.01 mult(mult(X, Y), mult(mult(Z, Y), Z))
% 43.90/6.01 = { by axiom 8 (f08) }
% 43.90/6.01 mult(mult(X, Y), mult(Z, mult(Y, Z)))
% 43.90/6.01
% 43.90/6.01 Lemma 18: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(mult(X, Y), Y)
% 43.90/6.01 = { by axiom 1 (f05) R->L }
% 43.90/6.01 mult(mult(X, Y), mult(Y, unit))
% 43.90/6.01 = { by axiom 2 (f06) R->L }
% 43.90/6.01 mult(mult(X, Y), mult(unit, mult(Y, unit)))
% 43.90/6.01 = { by lemma 17 R->L }
% 43.90/6.01 mult(mult(X, mult(Y, mult(unit, Y))), unit)
% 43.90/6.01 = { by axiom 1 (f05) }
% 43.90/6.01 mult(X, mult(Y, mult(unit, Y)))
% 43.90/6.01 = { by axiom 2 (f06) }
% 43.90/6.01 mult(X, mult(Y, Y))
% 43.90/6.01
% 43.90/6.01 Lemma 19: mult(X, mult(ld(X, Y), X)) = mult(Y, X).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(X, mult(ld(X, Y), X))
% 43.90/6.01 = { by axiom 8 (f08) R->L }
% 43.90/6.01 mult(mult(X, ld(X, Y)), X)
% 43.90/6.01 = { by axiom 5 (f01) }
% 43.90/6.01 mult(Y, X)
% 43.90/6.01
% 43.90/6.01 Lemma 20: mult(f(X), mult(X, f(X))) = mult(X, X).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(f(X), mult(X, f(X)))
% 43.90/6.01 = { by axiom 3 (f02) R->L }
% 43.90/6.01 mult(f(X), mult(ld(f(X), mult(f(X), X)), f(X)))
% 43.90/6.01 = { by lemma 11 }
% 43.90/6.01 mult(f(X), mult(ld(f(X), mult(X, f(X))), f(X)))
% 43.90/6.01 = { by lemma 19 }
% 43.90/6.01 mult(mult(X, f(X)), f(X))
% 43.90/6.01 = { by lemma 18 }
% 43.90/6.01 mult(X, mult(f(X), f(X)))
% 43.90/6.01 = { by axiom 6 (f09) }
% 43.90/6.01 mult(X, X)
% 43.90/6.01
% 43.90/6.01 Lemma 21: mult(rd(X, Y), mult(Y, Y)) = mult(X, Y).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(rd(X, Y), mult(Y, Y))
% 43.90/6.01 = { by lemma 18 R->L }
% 43.90/6.01 mult(mult(rd(X, Y), Y), Y)
% 43.90/6.01 = { by axiom 7 (f03) }
% 43.90/6.01 mult(X, Y)
% 43.90/6.01
% 43.90/6.01 Lemma 22: ld(rd(X, Y), mult(X, Y)) = mult(Y, Y).
% 43.90/6.01 Proof:
% 43.90/6.01 ld(rd(X, Y), mult(X, Y))
% 43.90/6.01 = { by lemma 21 R->L }
% 43.90/6.01 ld(rd(X, Y), mult(rd(X, Y), mult(Y, Y)))
% 43.90/6.01 = { by axiom 3 (f02) }
% 43.90/6.01 mult(Y, Y)
% 43.90/6.01
% 43.90/6.01 Lemma 23: mult(rd(X, Y), rd(mult(Y, X), Y)) = mult(X, rd(X, Y)).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(rd(X, Y), rd(mult(Y, X), Y))
% 43.90/6.01 = { by lemma 13 R->L }
% 43.90/6.01 mult(rd(X, Y), mult(Y, rd(X, Y)))
% 43.90/6.01 = { by axiom 8 (f08) R->L }
% 43.90/6.01 mult(mult(rd(X, Y), Y), rd(X, Y))
% 43.90/6.01 = { by axiom 7 (f03) }
% 43.90/6.01 mult(X, rd(X, Y))
% 43.90/6.01
% 43.90/6.01 Lemma 24: rd(mult(X, mult(Y, Y)), Y) = mult(X, Y).
% 43.90/6.01 Proof:
% 43.90/6.01 rd(mult(X, mult(Y, Y)), Y)
% 43.90/6.01 = { by lemma 18 R->L }
% 43.90/6.01 rd(mult(mult(X, Y), Y), Y)
% 43.90/6.01 = { by axiom 4 (f04) }
% 43.90/6.01 mult(X, Y)
% 43.90/6.01
% 43.90/6.01 Lemma 25: mult(rd(X, Y), f(Y)) = rd(X, f(Y)).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(rd(X, Y), f(Y))
% 43.90/6.01 = { by lemma 24 R->L }
% 43.90/6.01 rd(mult(rd(X, Y), mult(f(Y), f(Y))), f(Y))
% 43.90/6.01 = { by axiom 6 (f09) }
% 43.90/6.01 rd(mult(rd(X, Y), Y), f(Y))
% 43.90/6.01 = { by axiom 7 (f03) }
% 43.90/6.01 rd(X, f(Y))
% 43.90/6.01
% 43.90/6.01 Lemma 26: mult(f(X), ld(X, f(X))) = unit.
% 43.90/6.01 Proof:
% 43.90/6.01 mult(f(X), ld(X, f(X)))
% 43.90/6.01 = { by lemma 16 R->L }
% 43.90/6.01 mult(f(X), rd(f(X), X))
% 43.90/6.01 = { by lemma 23 R->L }
% 43.90/6.01 mult(rd(f(X), X), rd(mult(X, f(X)), X))
% 43.90/6.01 = { by lemma 15 }
% 43.90/6.01 mult(rd(f(X), X), f(X))
% 43.90/6.01 = { by lemma 25 }
% 43.90/6.01 rd(f(X), f(X))
% 43.90/6.01 = { by lemma 10 }
% 43.90/6.01 unit
% 43.90/6.01
% 43.90/6.01 Lemma 27: rd(X, ld(Y, X)) = Y.
% 43.90/6.01 Proof:
% 43.90/6.01 rd(X, ld(Y, X))
% 43.90/6.01 = { by axiom 5 (f01) R->L }
% 43.90/6.01 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 43.90/6.01 = { by axiom 4 (f04) }
% 43.90/6.01 Y
% 43.90/6.01
% 43.90/6.01 Lemma 28: mult(ld(X, f(X)), ld(X, f(X))) = ld(X, unit).
% 43.90/6.01 Proof:
% 43.90/6.01 mult(ld(X, f(X)), ld(X, f(X)))
% 43.90/6.01 = { by lemma 22 R->L }
% 43.90/6.01 ld(rd(f(X), ld(X, f(X))), mult(f(X), ld(X, f(X))))
% 43.90/6.01 = { by lemma 26 }
% 43.90/6.01 ld(rd(f(X), ld(X, f(X))), unit)
% 43.90/6.01 = { by lemma 27 }
% 43.90/6.01 ld(X, unit)
% 43.90/6.01
% 43.90/6.01 Lemma 29: mult(ld(X, f(X)), f(X)) = unit.
% 43.90/6.01 Proof:
% 43.90/6.01 mult(ld(X, f(X)), f(X))
% 43.90/6.01 = { by lemma 16 R->L }
% 43.90/6.01 mult(rd(f(X), X), f(X))
% 43.90/6.01 = { by lemma 25 }
% 43.90/6.01 rd(f(X), f(X))
% 43.90/6.01 = { by lemma 10 }
% 43.90/6.01 unit
% 43.90/6.02
% 43.90/6.02 Lemma 30: mult(mult(X, mult(Y, X)), Y) = mult(X, mult(Y, mult(X, Y))).
% 43.90/6.02 Proof:
% 43.90/6.02 mult(mult(X, mult(Y, X)), Y)
% 43.90/6.02 = { by axiom 2 (f06) R->L }
% 43.90/6.02 mult(mult(unit, mult(X, mult(Y, X))), Y)
% 43.90/6.02 = { by lemma 17 }
% 43.90/6.02 mult(mult(unit, X), mult(Y, mult(X, Y)))
% 43.90/6.02 = { by axiom 2 (f06) }
% 43.90/6.02 mult(X, mult(Y, mult(X, Y)))
% 43.90/6.02
% 43.90/6.02 Lemma 31: mult(mult(X, Y), ld(Y, X)) = mult(Y, mult(ld(Y, X), X)).
% 43.90/6.02 Proof:
% 43.90/6.02 mult(mult(X, Y), ld(Y, X))
% 43.90/6.02 = { by lemma 19 R->L }
% 43.90/6.02 mult(mult(Y, mult(ld(Y, X), Y)), ld(Y, X))
% 43.90/6.02 = { by lemma 30 }
% 43.90/6.02 mult(Y, mult(ld(Y, X), mult(Y, ld(Y, X))))
% 43.90/6.02 = { by axiom 5 (f01) }
% 43.90/6.02 mult(Y, mult(ld(Y, X), X))
% 43.90/6.02
% 43.90/6.02 Lemma 32: ld(mult(X, f(X)), X) = ld(X, f(X)).
% 43.90/6.02 Proof:
% 43.90/6.02 ld(mult(X, f(X)), X)
% 43.90/6.02 = { by axiom 1 (f05) R->L }
% 43.90/6.02 ld(mult(X, f(X)), mult(X, unit))
% 43.90/6.02 = { by lemma 29 R->L }
% 43.90/6.02 ld(mult(X, f(X)), mult(X, mult(ld(X, f(X)), f(X))))
% 43.90/6.02 = { by lemma 31 R->L }
% 43.90/6.02 ld(mult(X, f(X)), mult(mult(f(X), X), ld(X, f(X))))
% 43.90/6.02 = { by lemma 11 }
% 43.90/6.02 ld(mult(X, f(X)), mult(mult(X, f(X)), ld(X, f(X))))
% 43.90/6.02 = { by axiom 3 (f02) }
% 43.90/6.02 ld(X, f(X))
% 43.90/6.02
% 43.90/6.02 Lemma 33: mult(ld(X, Y), X) = ld(X, mult(Y, X)).
% 43.90/6.02 Proof:
% 43.90/6.02 mult(ld(X, Y), X)
% 43.90/6.02 = { by axiom 3 (f02) R->L }
% 43.90/6.02 ld(X, mult(X, mult(ld(X, Y), X)))
% 43.90/6.02 = { by lemma 19 }
% 43.90/6.02 ld(X, mult(Y, X))
% 43.90/6.02
% 43.90/6.02 Lemma 34: ld(ld(X, Y), ld(X, mult(Y, X))) = X.
% 43.90/6.02 Proof:
% 43.90/6.02 ld(ld(X, Y), ld(X, mult(Y, X)))
% 43.90/6.02 = { by lemma 33 R->L }
% 43.90/6.02 ld(ld(X, Y), mult(ld(X, Y), X))
% 43.90/6.02 = { by axiom 3 (f02) }
% 43.90/6.02 X
% 43.90/6.02
% 43.90/6.02 Lemma 35: ld(ld(X, unit), f(X)) = mult(X, f(X)).
% 43.90/6.02 Proof:
% 43.90/6.02 ld(ld(X, unit), f(X))
% 43.90/6.02 = { by axiom 3 (f02) R->L }
% 43.90/6.02 ld(ld(X, unit), ld(mult(f(X), X), mult(mult(f(X), X), f(X))))
% 43.90/6.02 = { by axiom 8 (f08) }
% 43.90/6.02 ld(ld(X, unit), ld(mult(f(X), X), mult(f(X), mult(X, f(X)))))
% 43.90/6.02 = { by lemma 11 }
% 43.90/6.02 ld(ld(X, unit), ld(mult(X, f(X)), mult(f(X), mult(X, f(X)))))
% 43.90/6.02 = { by lemma 20 }
% 43.90/6.02 ld(ld(X, unit), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by lemma 28 R->L }
% 43.90/6.02 ld(mult(ld(X, f(X)), ld(X, f(X))), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by lemma 32 R->L }
% 43.90/6.02 ld(mult(ld(X, f(X)), ld(mult(X, f(X)), X)), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by lemma 32 R->L }
% 43.90/6.02 ld(mult(ld(mult(X, f(X)), X), ld(mult(X, f(X)), X)), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by axiom 3 (f02) R->L }
% 43.90/6.02 ld(ld(mult(X, f(X)), mult(mult(X, f(X)), mult(ld(mult(X, f(X)), X), ld(mult(X, f(X)), X)))), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by lemma 18 R->L }
% 43.90/6.02 ld(ld(mult(X, f(X)), mult(mult(mult(X, f(X)), ld(mult(X, f(X)), X)), ld(mult(X, f(X)), X))), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by axiom 5 (f01) }
% 43.90/6.02 ld(ld(mult(X, f(X)), mult(X, ld(mult(X, f(X)), X))), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by lemma 32 }
% 43.90/6.02 ld(ld(mult(X, f(X)), mult(X, ld(X, f(X)))), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by axiom 5 (f01) }
% 43.90/6.02 ld(ld(mult(X, f(X)), f(X)), ld(mult(X, f(X)), mult(X, X)))
% 43.90/6.02 = { by lemma 20 R->L }
% 43.90/6.02 ld(ld(mult(X, f(X)), f(X)), ld(mult(X, f(X)), mult(f(X), mult(X, f(X)))))
% 43.90/6.02 = { by lemma 34 }
% 43.90/6.02 mult(X, f(X))
% 43.90/6.02
% 43.90/6.02 Lemma 36: rd(ld(X, Y), X) = ld(X, rd(Y, X)).
% 43.90/6.02 Proof:
% 43.90/6.02 rd(ld(X, Y), X)
% 43.90/6.02 = { by lemma 14 R->L }
% 43.90/6.02 ld(X, rd(mult(X, ld(X, Y)), X))
% 43.90/6.02 = { by axiom 5 (f01) }
% 43.90/6.02 ld(X, rd(Y, X))
% 43.90/6.02
% 43.90/6.02 Lemma 37: mult(mult(X, mult(Y, Z)), ld(Z, Y)) = mult(mult(X, Z), mult(ld(Z, Y), Y)).
% 43.90/6.02 Proof:
% 43.90/6.02 mult(mult(X, mult(Y, Z)), ld(Z, Y))
% 43.90/6.02 = { by lemma 19 R->L }
% 43.90/6.02 mult(mult(X, mult(Z, mult(ld(Z, Y), Z))), ld(Z, Y))
% 43.90/6.02 = { by lemma 17 }
% 43.90/6.02 mult(mult(X, Z), mult(ld(Z, Y), mult(Z, ld(Z, Y))))
% 43.90/6.02 = { by axiom 5 (f01) }
% 43.90/6.02 mult(mult(X, Z), mult(ld(Z, Y), Y))
% 43.90/6.02
% 43.90/6.02 Lemma 38: mult(rd(X, mult(Y, Y)), Y) = rd(X, Y).
% 43.90/6.02 Proof:
% 43.90/6.02 mult(rd(X, mult(Y, Y)), Y)
% 43.90/6.02 = { by lemma 24 R->L }
% 43.90/6.02 rd(mult(rd(X, mult(Y, Y)), mult(Y, Y)), Y)
% 43.90/6.02 = { by axiom 7 (f03) }
% 43.90/6.02 rd(X, Y)
% 43.90/6.02
% 43.90/6.02 Lemma 39: mult(X, ld(Y, unit)) = rd(X, Y).
% 43.90/6.02 Proof:
% 43.90/6.02 mult(X, ld(Y, unit))
% 43.90/6.02 = { by axiom 7 (f03) R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, Y)), ld(Y, unit))
% 43.90/6.02 = { by axiom 6 (f09) R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, mult(f(Y), f(Y)))), ld(Y, unit))
% 43.90/6.02 = { by lemma 18 R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(mult(Y, f(Y)), f(Y))), ld(Y, unit))
% 43.90/6.02 = { by lemma 35 R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(ld(ld(Y, unit), f(Y)), f(Y))), ld(Y, unit))
% 43.90/6.02 = { by lemma 34 R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(ld(ld(Y, unit), f(Y)), f(Y))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by axiom 4 (f04) R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(ld(ld(Y, unit), f(Y)), rd(mult(f(Y), ld(Y, unit)), ld(Y, unit)))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by axiom 4 (f04) R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(rd(mult(ld(ld(Y, unit), f(Y)), ld(Y, unit)), ld(Y, unit)), rd(mult(f(Y), ld(Y, unit)), ld(Y, unit)))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by lemma 19 R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(rd(mult(ld(ld(Y, unit), f(Y)), ld(Y, unit)), ld(Y, unit)), rd(mult(ld(Y, unit), mult(ld(ld(Y, unit), f(Y)), ld(Y, unit))), ld(Y, unit)))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by lemma 23 }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(mult(ld(ld(Y, unit), f(Y)), ld(Y, unit)), rd(mult(ld(ld(Y, unit), f(Y)), ld(Y, unit)), ld(Y, unit)))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by lemma 33 }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(mult(ld(ld(Y, unit), f(Y)), ld(Y, unit)), rd(ld(ld(Y, unit), mult(f(Y), ld(Y, unit))), ld(Y, unit)))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by lemma 33 }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(ld(ld(Y, unit), mult(f(Y), ld(Y, unit))), rd(ld(ld(Y, unit), mult(f(Y), ld(Y, unit))), ld(Y, unit)))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by lemma 36 }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(ld(ld(Y, unit), mult(f(Y), ld(Y, unit))), ld(ld(Y, unit), rd(mult(f(Y), ld(Y, unit)), ld(Y, unit))))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by axiom 4 (f04) }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(ld(ld(Y, unit), mult(f(Y), ld(Y, unit))), ld(ld(Y, unit), f(Y)))), ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by lemma 37 }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), ld(ld(Y, unit), f(Y))), mult(ld(ld(ld(Y, unit), f(Y)), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by lemma 34 }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), ld(ld(Y, unit), f(Y))), mult(ld(Y, unit), ld(ld(Y, unit), mult(f(Y), ld(Y, unit)))))
% 43.90/6.02 = { by axiom 5 (f01) }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), ld(ld(Y, unit), f(Y))), mult(f(Y), ld(Y, unit)))
% 43.90/6.02 = { by lemma 35 }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, f(Y))), mult(f(Y), ld(Y, unit)))
% 43.90/6.02 = { by lemma 28 R->L }
% 43.90/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, f(Y))), mult(f(Y), mult(ld(Y, f(Y)), ld(Y, f(Y)))))
% 44.62/6.02 = { by axiom 3 (f02) R->L }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, f(Y))), ld(unit, mult(unit, mult(f(Y), mult(ld(Y, f(Y)), ld(Y, f(Y)))))))
% 44.62/6.02 = { by axiom 2 (f06) }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, f(Y))), ld(unit, mult(f(Y), mult(ld(Y, f(Y)), ld(Y, f(Y))))))
% 44.62/6.02 = { by lemma 26 R->L }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, f(Y))), ld(mult(f(Y), ld(Y, f(Y))), mult(f(Y), mult(ld(Y, f(Y)), ld(Y, f(Y))))))
% 44.62/6.02 = { by lemma 18 R->L }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, f(Y))), ld(mult(f(Y), ld(Y, f(Y))), mult(mult(f(Y), ld(Y, f(Y))), ld(Y, f(Y)))))
% 44.62/6.02 = { by axiom 3 (f02) }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), mult(Y, f(Y))), ld(Y, f(Y)))
% 44.62/6.02 = { by lemma 11 R->L }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), mult(f(Y), Y)), ld(Y, f(Y)))
% 44.62/6.02 = { by lemma 37 }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), Y), mult(ld(Y, f(Y)), f(Y)))
% 44.62/6.02 = { by lemma 29 }
% 44.62/6.02 mult(mult(rd(X, mult(Y, Y)), Y), unit)
% 44.62/6.02 = { by axiom 1 (f05) }
% 44.62/6.02 mult(rd(X, mult(Y, Y)), Y)
% 44.62/6.02 = { by lemma 38 }
% 44.62/6.02 rd(X, Y)
% 44.62/6.02
% 44.62/6.02 Lemma 40: ld(ld(X, Y), unit) = ld(Y, X).
% 44.62/6.02 Proof:
% 44.62/6.02 ld(ld(X, Y), unit)
% 44.62/6.02 = { by axiom 3 (f02) R->L }
% 44.62/6.02 ld(Y, mult(Y, ld(ld(X, Y), unit)))
% 44.62/6.02 = { by lemma 39 }
% 44.62/6.02 ld(Y, rd(Y, ld(X, Y)))
% 44.62/6.02 = { by lemma 27 }
% 44.62/6.02 ld(Y, X)
% 44.62/6.02
% 44.62/6.02 Lemma 41: rd(X, ld(Y, unit)) = mult(X, Y).
% 44.62/6.02 Proof:
% 44.62/6.02 rd(X, ld(Y, unit))
% 44.62/6.02 = { by lemma 10 R->L }
% 44.62/6.02 rd(X, ld(Y, rd(Y, Y)))
% 44.62/6.02 = { by axiom 1 (f05) R->L }
% 44.62/6.02 rd(X, ld(Y, rd(mult(Y, unit), Y)))
% 44.62/6.02 = { by lemma 14 }
% 44.62/6.02 rd(X, rd(unit, Y))
% 44.62/6.02 = { by lemma 39 R->L }
% 44.62/6.02 mult(X, ld(rd(unit, Y), unit))
% 44.62/6.02 = { by axiom 7 (f03) R->L }
% 44.62/6.02 mult(X, ld(rd(unit, Y), mult(rd(unit, Y), Y)))
% 44.62/6.02 = { by axiom 3 (f02) }
% 44.62/6.02 mult(X, Y)
% 44.62/6.02
% 44.62/6.02 Lemma 42: ld(ld(X, unit), Y) = mult(X, Y).
% 44.62/6.02 Proof:
% 44.62/6.02 ld(ld(X, unit), Y)
% 44.62/6.02 = { by axiom 3 (f02) R->L }
% 44.62/6.02 ld(ld(Y, mult(Y, ld(X, unit))), Y)
% 44.62/6.02 = { by axiom 3 (f02) R->L }
% 44.62/6.02 ld(mult(Y, ld(X, unit)), mult(mult(Y, ld(X, unit)), ld(ld(Y, mult(Y, ld(X, unit))), Y)))
% 44.62/6.02 = { by axiom 5 (f01) R->L }
% 44.62/6.02 ld(mult(Y, ld(X, unit)), mult(mult(Y, ld(Y, mult(Y, ld(X, unit)))), ld(ld(Y, mult(Y, ld(X, unit))), Y)))
% 44.62/6.02 = { by lemma 31 }
% 44.62/6.02 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), Y)))
% 44.62/6.02 = { by axiom 4 (f04) R->L }
% 44.62/6.02 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(mult(mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), Y), ld(Y, mult(Y, ld(X, unit)))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by axiom 5 (f01) R->L }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(mult(mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), mult(ld(Y, mult(Y, ld(X, unit))), ld(ld(Y, mult(Y, ld(X, unit))), Y))), ld(Y, mult(Y, ld(X, unit)))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by lemma 30 }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), ld(Y, mult(Y, ld(X, unit)))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by lemma 19 }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), mult(Y, ld(Y, mult(Y, ld(X, unit))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by axiom 3 (f02) R->L }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(ld(ld(Y, mult(Y, ld(X, unit))), mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), mult(Y, ld(Y, mult(Y, ld(X, unit))))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by lemma 19 R->L }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(ld(ld(Y, mult(Y, ld(X, unit))), mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), ld(Y, mult(Y, ld(X, unit)))))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by lemma 30 R->L }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(ld(ld(Y, mult(Y, ld(X, unit))), mult(ld(Y, mult(Y, ld(X, unit))), mult(mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), mult(ld(Y, mult(Y, ld(X, unit))), ld(ld(Y, mult(Y, ld(X, unit))), Y))), ld(Y, mult(Y, ld(X, unit)))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by axiom 8 (f08) R->L }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(ld(ld(Y, mult(Y, ld(X, unit))), mult(mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), mult(ld(Y, mult(Y, ld(X, unit))), ld(ld(Y, mult(Y, ld(X, unit))), Y)))), ld(Y, mult(Y, ld(X, unit))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by lemma 17 }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(ld(ld(Y, mult(Y, ld(X, unit))), mult(mult(ld(Y, mult(Y, ld(X, unit))), ld(ld(Y, mult(Y, ld(X, unit))), Y)), mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), ld(Y, mult(Y, ld(X, unit))))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by axiom 5 (f01) }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(ld(ld(Y, mult(Y, ld(X, unit))), mult(Y, mult(ld(Y, mult(Y, ld(X, unit))), mult(ld(ld(Y, mult(Y, ld(X, unit))), Y), ld(Y, mult(Y, ld(X, unit))))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by lemma 19 }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), rd(ld(ld(Y, mult(Y, ld(X, unit))), mult(Y, mult(Y, ld(Y, mult(Y, ld(X, unit)))))), ld(Y, mult(Y, ld(X, unit))))))
% 44.62/6.03 = { by lemma 36 }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(ld(Y, mult(Y, ld(X, unit))), ld(ld(Y, mult(Y, ld(X, unit))), rd(mult(Y, mult(Y, ld(Y, mult(Y, ld(X, unit))))), ld(Y, mult(Y, ld(X, unit)))))))
% 44.62/6.03 = { by axiom 5 (f01) }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), rd(mult(Y, mult(Y, ld(Y, mult(Y, ld(X, unit))))), ld(Y, mult(Y, ld(X, unit)))))
% 44.62/6.03 = { by axiom 5 (f01) }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), rd(mult(Y, mult(Y, ld(X, unit))), ld(Y, mult(Y, ld(X, unit)))))
% 44.62/6.03 = { by axiom 3 (f02) }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), rd(mult(Y, mult(Y, ld(X, unit))), ld(X, unit)))
% 44.62/6.03 = { by lemma 41 }
% 44.62/6.03 ld(mult(Y, ld(X, unit)), mult(mult(Y, mult(Y, ld(X, unit))), X))
% 44.62/6.03 = { by lemma 39 }
% 44.62/6.03 ld(rd(Y, X), mult(mult(Y, mult(Y, ld(X, unit))), X))
% 44.62/6.03 = { by lemma 39 }
% 44.62/6.03 ld(rd(Y, X), mult(mult(Y, rd(Y, X)), X))
% 44.62/6.03 = { by lemma 23 R->L }
% 44.62/6.03 ld(rd(Y, X), mult(mult(rd(Y, X), rd(mult(X, Y), X)), X))
% 44.62/6.03 = { by lemma 13 R->L }
% 44.62/6.03 ld(rd(Y, X), mult(mult(rd(Y, X), mult(X, rd(Y, X))), X))
% 44.62/6.03 = { by lemma 30 }
% 44.62/6.03 ld(rd(Y, X), mult(rd(Y, X), mult(X, mult(rd(Y, X), X))))
% 44.62/6.03 = { by axiom 7 (f03) }
% 44.62/6.03 ld(rd(Y, X), mult(rd(Y, X), mult(X, Y)))
% 44.62/6.03 = { by axiom 3 (f02) }
% 44.62/6.03 mult(X, Y)
% 44.62/6.03
% 44.62/6.03 Lemma 43: rd(X, mult(Y, X)) = ld(Y, unit).
% 44.62/6.03 Proof:
% 44.62/6.03 rd(X, mult(Y, X))
% 44.62/6.03 = { by lemma 42 R->L }
% 44.62/6.03 rd(X, ld(ld(Y, unit), X))
% 44.62/6.03 = { by lemma 27 }
% 44.62/6.03 ld(Y, unit)
% 44.62/6.03
% 44.62/6.03 Lemma 44: ld(rd(X, Y), unit) = rd(Y, X).
% 44.62/6.03 Proof:
% 44.62/6.03 ld(rd(X, Y), unit)
% 44.62/6.03 = { by lemma 43 R->L }
% 44.62/6.03 rd(Y, mult(rd(X, Y), Y))
% 44.62/6.03 = { by axiom 7 (f03) }
% 44.62/6.03 rd(Y, X)
% 44.62/6.03
% 44.62/6.03 Lemma 45: mult(X, ld(Y, Z)) = rd(X, ld(Z, Y)).
% 44.62/6.03 Proof:
% 44.62/6.03 mult(X, ld(Y, Z))
% 44.62/6.03 = { by lemma 40 R->L }
% 44.62/6.03 mult(X, ld(ld(Z, Y), unit))
% 44.62/6.03 = { by lemma 39 }
% 44.62/6.03 rd(X, ld(Z, Y))
% 44.62/6.03
% 44.62/6.03 Lemma 46: mult(ld(X, Y), Z) = ld(ld(Y, X), Z).
% 44.62/6.03 Proof:
% 44.62/6.03 mult(ld(X, Y), Z)
% 44.62/6.03 = { by lemma 42 R->L }
% 44.62/6.03 ld(ld(ld(X, Y), unit), Z)
% 44.62/6.03 = { by lemma 40 }
% 44.62/6.03 ld(ld(Y, X), Z)
% 44.62/6.03
% 44.62/6.03 Lemma 47: mult(rd(X, Y), Z) = ld(rd(Y, X), Z).
% 44.62/6.03 Proof:
% 44.62/6.03 mult(rd(X, Y), Z)
% 44.62/6.03 = { by lemma 42 R->L }
% 44.62/6.03 ld(ld(rd(X, Y), unit), Z)
% 44.62/6.03 = { by lemma 44 }
% 44.62/6.03 ld(rd(Y, X), Z)
% 44.62/6.03
% 44.62/6.03 Lemma 48: rd(mult(X, mult(Y, Z)), rd(Y, Z)) = rd(mult(X, Y), rd(Y, mult(Z, Z))).
% 44.62/6.03 Proof:
% 44.62/6.03 rd(mult(X, mult(Y, Z)), rd(Y, Z))
% 44.62/6.03 = { by lemma 39 R->L }
% 44.62/6.03 mult(mult(X, mult(Y, Z)), ld(rd(Y, Z), unit))
% 44.62/6.03 = { by lemma 44 }
% 44.62/6.03 mult(mult(X, mult(Y, Z)), rd(Z, Y))
% 44.62/6.03 = { by axiom 7 (f03) R->L }
% 44.62/6.03 mult(mult(X, mult(Y, mult(rd(Z, Y), Y))), rd(Z, Y))
% 44.62/6.03 = { by lemma 17 }
% 44.62/6.03 mult(mult(X, Y), mult(rd(Z, Y), mult(Y, rd(Z, Y))))
% 44.62/6.03 = { by lemma 47 }
% 44.62/6.03 mult(mult(X, Y), ld(rd(Y, Z), mult(Y, rd(Z, Y))))
% 44.62/6.03 = { by lemma 45 }
% 44.62/6.03 rd(mult(X, Y), ld(mult(Y, rd(Z, Y)), rd(Y, Z)))
% 44.62/6.03 = { by lemma 12 R->L }
% 44.62/6.03 rd(mult(X, Y), ld(rd(mult(Y, mult(rd(Z, Y), Y)), Y), rd(Y, Z)))
% 44.62/6.03 = { by axiom 7 (f03) }
% 44.62/6.03 rd(mult(X, Y), ld(rd(mult(Y, Z), Y), rd(Y, Z)))
% 44.62/6.03 = { by lemma 27 R->L }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), ld(ld(rd(mult(Y, Z), Y), rd(Y, Z)), mult(Y, Y))))
% 44.62/6.03 = { by lemma 13 R->L }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), ld(ld(mult(Y, rd(Z, Y)), rd(Y, Z)), mult(Y, Y))))
% 44.62/6.03 = { by lemma 46 R->L }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), mult(ld(rd(Y, Z), mult(Y, rd(Z, Y))), mult(Y, Y))))
% 44.62/6.03 = { by lemma 47 R->L }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), mult(mult(rd(Z, Y), mult(Y, rd(Z, Y))), mult(Y, Y))))
% 44.62/6.03 = { by lemma 18 R->L }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), mult(mult(mult(rd(Z, Y), mult(Y, rd(Z, Y))), Y), Y)))
% 44.62/6.03 = { by lemma 30 }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), mult(mult(rd(Z, Y), mult(Y, mult(rd(Z, Y), Y))), Y)))
% 44.62/6.03 = { by axiom 7 (f03) }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), mult(mult(rd(Z, Y), mult(Y, Z)), Y)))
% 44.62/6.03 = { by lemma 47 }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), mult(ld(rd(Y, Z), mult(Y, Z)), Y)))
% 44.62/6.03 = { by lemma 46 }
% 44.62/6.03 rd(mult(X, Y), rd(mult(Y, Y), ld(ld(mult(Y, Z), rd(Y, Z)), Y)))
% 44.62/6.03 = { by lemma 44 R->L }
% 44.62/6.03 rd(mult(X, Y), ld(rd(ld(ld(mult(Y, Z), rd(Y, Z)), Y), mult(Y, Y)), unit))
% 44.62/6.03 = { by axiom 4 (f04) R->L }
% 44.62/6.03 rd(mult(X, Y), ld(rd(mult(rd(ld(ld(mult(Y, Z), rd(Y, Z)), Y), mult(Y, Y)), Y), Y), unit))
% 44.62/6.03 = { by lemma 38 }
% 44.62/6.03 rd(mult(X, Y), ld(rd(rd(ld(ld(mult(Y, Z), rd(Y, Z)), Y), Y), Y), unit))
% 44.62/6.03 = { by lemma 44 }
% 44.62/6.03 rd(mult(X, Y), rd(Y, rd(ld(ld(mult(Y, Z), rd(Y, Z)), Y), Y)))
% 44.62/6.03 = { by axiom 5 (f01) R->L }
% 44.62/6.03 rd(mult(X, Y), rd(Y, rd(ld(ld(mult(Y, Z), rd(Y, Z)), Y), mult(ld(mult(Y, Z), rd(Y, Z)), ld(ld(mult(Y, Z), rd(Y, Z)), Y)))))
% 44.62/6.03 = { by lemma 43 }
% 44.62/6.03 rd(mult(X, Y), rd(Y, ld(ld(mult(Y, Z), rd(Y, Z)), unit)))
% 44.62/6.03 = { by lemma 41 }
% 44.62/6.03 rd(mult(X, Y), mult(Y, ld(mult(Y, Z), rd(Y, Z))))
% 44.62/6.03 = { by lemma 45 }
% 44.62/6.03 rd(mult(X, Y), rd(Y, ld(rd(Y, Z), mult(Y, Z))))
% 44.62/6.03 = { by lemma 22 }
% 44.62/6.03 rd(mult(X, Y), rd(Y, mult(Z, Z)))
% 44.62/6.03
% 44.62/6.03 Goal 1 (goals_1): mult(x3, mult(x5, mult(x4, x5))) = mult(mult(mult(x3, x5), x4), x5).
% 44.62/6.03 Proof:
% 44.62/6.03 mult(x3, mult(x5, mult(x4, x5)))
% 44.62/6.03 = { by axiom 4 (f04) R->L }
% 44.62/6.03 rd(mult(mult(x3, mult(x5, mult(x4, x5))), x4), x4)
% 44.62/6.03 = { by lemma 17 }
% 44.62/6.03 rd(mult(mult(x3, x5), mult(x4, mult(x5, x4))), x4)
% 44.62/6.03 = { by axiom 6 (f09) R->L }
% 44.62/6.03 rd(mult(mult(x3, x5), mult(x4, mult(f(mult(x5, x4)), f(mult(x5, x4))))), x4)
% 44.62/6.03 = { by lemma 18 R->L }
% 44.62/6.03 rd(mult(mult(x3, x5), mult(mult(x4, f(mult(x5, x4))), f(mult(x5, x4)))), x4)
% 44.62/6.03 = { by axiom 4 (f04) R->L }
% 44.62/6.03 rd(mult(mult(x3, x5), mult(mult(x4, f(mult(x5, x4))), f(mult(x5, x4)))), rd(mult(x4, f(mult(x5, x4))), f(mult(x5, x4))))
% 44.62/6.03 = { by lemma 48 }
% 44.62/6.03 rd(mult(mult(x3, x5), mult(x4, f(mult(x5, x4)))), rd(mult(x4, f(mult(x5, x4))), mult(f(mult(x5, x4)), f(mult(x5, x4)))))
% 44.62/6.03 = { by lemma 21 R->L }
% 44.62/6.03 rd(mult(mult(x3, x5), mult(x4, f(mult(x5, x4)))), rd(mult(rd(x4, f(mult(x5, x4))), mult(f(mult(x5, x4)), f(mult(x5, x4)))), mult(f(mult(x5, x4)), f(mult(x5, x4)))))
% 44.62/6.03 = { by axiom 4 (f04) }
% 44.62/6.03 rd(mult(mult(x3, x5), mult(x4, f(mult(x5, x4)))), rd(x4, f(mult(x5, x4))))
% 44.62/6.03 = { by lemma 48 }
% 44.62/6.03 rd(mult(mult(x3, x5), x4), rd(x4, mult(f(mult(x5, x4)), f(mult(x5, x4)))))
% 44.62/6.03 = { by axiom 6 (f09) }
% 44.62/6.03 rd(mult(mult(x3, x5), x4), rd(x4, mult(x5, x4)))
% 44.62/6.03 = { by lemma 43 }
% 44.62/6.03 rd(mult(mult(x3, x5), x4), ld(x5, unit))
% 44.62/6.03 = { by lemma 41 }
% 44.62/6.03 mult(mult(mult(x3, x5), x4), x5)
% 44.62/6.03 % SZS output end Proof
% 44.62/6.03
% 44.62/6.03 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------