%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP654+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:34 AM UTC 2026
% Result : Theorem 8.67s 1.58s
% Output : Proof 9.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP654+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:27:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.67/1.58 Command-line arguments: --no-flatten-goal
% 8.67/1.58
% 8.67/1.58 % SZS status Theorem
% 8.67/1.58
% 9.46/1.66 % SZS output start Proof
% 9.46/1.66 Axiom 1 (f04): rd(mult(X, Y), Y) = X.
% 9.46/1.66 Axiom 2 (f02): ld(X, mult(X, Y)) = Y.
% 9.46/1.66 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 9.46/1.66 Axiom 4 (f03): mult(rd(X, Y), Y) = X.
% 9.46/1.66 Axiom 5 (f05): mult(X, mult(Y, mult(X, Z))) = mult(mult(mult(X, Y), X), Z).
% 9.46/1.66
% 9.46/1.66 Lemma 6: rd(X, ld(Y, X)) = Y.
% 9.46/1.66 Proof:
% 9.46/1.66 rd(X, ld(Y, X))
% 9.46/1.66 = { by axiom 3 (f01) R->L }
% 9.46/1.66 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 9.46/1.66 = { by axiom 1 (f04) }
% 9.46/1.66 Y
% 9.46/1.66
% 9.46/1.66 Lemma 7: rd(mult(X, mult(Y, mult(X, Z))), Z) = mult(mult(X, Y), X).
% 9.46/1.66 Proof:
% 9.46/1.66 rd(mult(X, mult(Y, mult(X, Z))), Z)
% 9.46/1.66 = { by axiom 5 (f05) }
% 9.46/1.66 rd(mult(mult(mult(X, Y), X), Z), Z)
% 9.46/1.66 = { by axiom 1 (f04) }
% 9.46/1.66 mult(mult(X, Y), X)
% 9.46/1.66
% 9.46/1.66 Lemma 8: rd(mult(X, mult(Y, Z)), ld(X, Z)) = mult(mult(X, Y), X).
% 9.46/1.66 Proof:
% 9.46/1.66 rd(mult(X, mult(Y, Z)), ld(X, Z))
% 9.46/1.66 = { by axiom 3 (f01) R->L }
% 9.46/1.66 rd(mult(X, mult(Y, mult(X, ld(X, Z)))), ld(X, Z))
% 9.46/1.66 = { by lemma 7 }
% 9.46/1.66 mult(mult(X, Y), X)
% 9.46/1.66
% 9.46/1.66 Lemma 9: mult(mult(X, rd(Y, Z)), X) = rd(mult(X, Y), ld(X, Z)).
% 9.46/1.66 Proof:
% 9.46/1.66 mult(mult(X, rd(Y, Z)), X)
% 9.46/1.66 = { by lemma 8 R->L }
% 9.46/1.66 rd(mult(X, mult(rd(Y, Z), Z)), ld(X, Z))
% 9.46/1.66 = { by axiom 4 (f03) }
% 9.46/1.66 rd(mult(X, Y), ld(X, Z))
% 9.46/1.66
% 9.46/1.66 Lemma 10: rd(rd(mult(X, Y), ld(X, Z)), X) = mult(X, rd(Y, Z)).
% 9.46/1.66 Proof:
% 9.46/1.66 rd(rd(mult(X, Y), ld(X, Z)), X)
% 9.46/1.66 = { by lemma 9 R->L }
% 9.46/1.66 rd(mult(mult(X, rd(Y, Z)), X), X)
% 9.46/1.66 = { by axiom 1 (f04) }
% 9.46/1.66 mult(X, rd(Y, Z))
% 9.46/1.66
% 9.46/1.66 Lemma 11: mult(X, rd(ld(X, Y), Y)) = rd(X, X).
% 9.46/1.66 Proof:
% 9.46/1.66 mult(X, rd(ld(X, Y), Y))
% 9.46/1.66 = { by lemma 10 R->L }
% 9.46/1.66 rd(rd(mult(X, ld(X, Y)), ld(X, Y)), X)
% 9.46/1.66 = { by axiom 1 (f04) }
% 9.46/1.66 rd(X, X)
% 9.46/1.66
% 9.46/1.66 Lemma 12: rd(ld(X, Z), Z) = rd(ld(X, Y), Y).
% 9.46/1.66 Proof:
% 9.46/1.66 rd(ld(X, Z), Z)
% 9.46/1.66 = { by axiom 2 (f02) R->L }
% 9.46/1.66 ld(X, mult(X, rd(ld(X, Z), Z)))
% 9.46/1.66 = { by lemma 11 }
% 9.46/1.66 ld(X, rd(X, X))
% 9.46/1.66 = { by lemma 11 R->L }
% 9.46/1.66 ld(X, mult(X, rd(ld(X, Y), Y)))
% 9.46/1.66 = { by axiom 2 (f02) }
% 9.46/1.67 rd(ld(X, Y), Y)
% 9.46/1.67
% 9.46/1.67 Lemma 13: rd(ld(X, Y), Y) = rd(Z, mult(X, Z)).
% 9.46/1.67 Proof:
% 9.46/1.67 rd(ld(X, Y), Y)
% 9.46/1.67 = { by lemma 12 }
% 9.46/1.67 rd(ld(X, mult(X, Z)), mult(X, Z))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 rd(Z, mult(X, Z))
% 9.46/1.67
% 9.46/1.67 Lemma 14: mult(X, mult(ld(X, Y), mult(X, Z))) = mult(mult(Y, X), Z).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(X, mult(ld(X, Y), mult(X, Z)))
% 9.46/1.67 = { by axiom 5 (f05) }
% 9.46/1.67 mult(mult(mult(X, ld(X, Y)), X), Z)
% 9.46/1.67 = { by axiom 3 (f01) }
% 9.46/1.67 mult(mult(Y, X), Z)
% 9.46/1.67
% 9.46/1.67 Lemma 15: mult(mult(X, Y), ld(Y, Z)) = mult(Y, mult(ld(Y, X), Z)).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(mult(X, Y), ld(Y, Z))
% 9.46/1.67 = { by lemma 14 R->L }
% 9.46/1.67 mult(Y, mult(ld(Y, X), mult(Y, ld(Y, Z))))
% 9.46/1.67 = { by axiom 3 (f01) }
% 9.46/1.67 mult(Y, mult(ld(Y, X), Z))
% 9.46/1.67
% 9.46/1.67 Lemma 16: mult(X, mult(ld(X, rd(Y, X)), Z)) = mult(Y, ld(X, Z)).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(X, mult(ld(X, rd(Y, X)), Z))
% 9.46/1.67 = { by lemma 15 R->L }
% 9.46/1.67 mult(mult(rd(Y, X), X), ld(X, Z))
% 9.46/1.67 = { by axiom 4 (f03) }
% 9.46/1.67 mult(Y, ld(X, Z))
% 9.46/1.67
% 9.46/1.67 Lemma 17: mult(ld(X, rd(Y, X)), Z) = ld(X, mult(Y, ld(X, Z))).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(ld(X, rd(Y, X)), Z)
% 9.46/1.67 = { by axiom 2 (f02) R->L }
% 9.46/1.67 ld(X, mult(X, mult(ld(X, rd(Y, X)), Z)))
% 9.46/1.67 = { by lemma 16 }
% 9.46/1.67 ld(X, mult(Y, ld(X, Z)))
% 9.46/1.67
% 9.46/1.67 Lemma 18: mult(rd(X, mult(Y, X)), Z) = ld(Y, Z).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(rd(X, mult(Y, X)), Z)
% 9.46/1.67 = { by lemma 13 R->L }
% 9.46/1.67 mult(rd(ld(Y, W), W), Z)
% 9.46/1.67 = { by axiom 2 (f02) R->L }
% 9.46/1.67 mult(ld(Y, mult(Y, rd(ld(Y, W), W))), Z)
% 9.46/1.67 = { by lemma 11 }
% 9.46/1.67 mult(ld(Y, rd(Y, Y)), Z)
% 9.46/1.67 = { by lemma 17 }
% 9.46/1.67 ld(Y, mult(Y, ld(Y, Z)))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 ld(Y, Z)
% 9.46/1.67
% 9.46/1.67 Lemma 19: ld(rd(X, Y), X) = Y.
% 9.46/1.67 Proof:
% 9.46/1.67 ld(rd(X, Y), X)
% 9.46/1.67 = { by axiom 4 (f03) R->L }
% 9.46/1.67 ld(rd(X, Y), mult(rd(X, Y), Y))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 Y
% 9.46/1.67
% 9.46/1.67 Lemma 20: rd(X, mult(rd(Y, Z), X)) = rd(Z, Y).
% 9.46/1.67 Proof:
% 9.46/1.67 rd(X, mult(rd(Y, Z), X))
% 9.46/1.67 = { by lemma 13 R->L }
% 9.46/1.67 rd(ld(rd(Y, Z), Y), Y)
% 9.46/1.67 = { by lemma 19 }
% 9.46/1.67 rd(Z, Y)
% 9.46/1.67
% 9.46/1.67 Lemma 21: rd(rd(X, mult(Y, X)), rd(X, mult(Y, X))) = ld(Y, Y).
% 9.46/1.67 Proof:
% 9.46/1.67 rd(rd(X, mult(Y, X)), rd(X, mult(Y, X)))
% 9.46/1.67 = { by lemma 11 R->L }
% 9.46/1.67 mult(rd(X, mult(Y, X)), rd(ld(rd(X, mult(Y, X)), Z), Z))
% 9.46/1.67 = { by lemma 18 }
% 9.46/1.67 ld(Y, rd(ld(rd(X, mult(Y, X)), Z), Z))
% 9.46/1.67 = { by lemma 13 }
% 9.46/1.67 ld(Y, rd(W, mult(rd(X, mult(Y, X)), W)))
% 9.46/1.67 = { by lemma 20 }
% 9.46/1.67 ld(Y, rd(mult(Y, X), X))
% 9.46/1.67 = { by axiom 1 (f04) }
% 9.46/1.67 ld(Y, Y)
% 9.46/1.67
% 9.46/1.67 Lemma 22: mult(rd(X, Y), Z) = ld(rd(Y, X), Z).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(rd(X, Y), Z)
% 9.46/1.67 = { by lemma 20 R->L }
% 9.46/1.67 mult(rd(W, mult(rd(Y, X), W)), Z)
% 9.46/1.67 = { by lemma 18 }
% 9.46/1.67 ld(rd(Y, X), Z)
% 9.46/1.67
% 9.46/1.67 Lemma 23: mult(ld(X, X), Y) = ld(ld(X, X), Y).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(ld(X, X), Y)
% 9.46/1.67 = { by lemma 21 R->L }
% 9.46/1.67 mult(rd(rd(Z, mult(X, Z)), rd(Z, mult(X, Z))), Y)
% 9.46/1.67 = { by lemma 22 }
% 9.46/1.67 ld(rd(rd(Z, mult(X, Z)), rd(Z, mult(X, Z))), Y)
% 9.46/1.67 = { by lemma 21 }
% 9.46/1.67 ld(ld(X, X), Y)
% 9.46/1.67
% 9.46/1.67 Lemma 24: ld(rd(X, mult(Y, X)), Z) = mult(Y, Z).
% 9.46/1.67 Proof:
% 9.46/1.67 ld(rd(X, mult(Y, X)), Z)
% 9.46/1.67 = { by axiom 2 (f02) R->L }
% 9.46/1.67 ld(rd(ld(Y, mult(Y, X)), mult(Y, X)), Z)
% 9.46/1.67 = { by lemma 12 R->L }
% 9.46/1.67 ld(rd(ld(Y, mult(Y, Z)), mult(Y, Z)), Z)
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 ld(rd(Z, mult(Y, Z)), Z)
% 9.46/1.67 = { by lemma 19 }
% 9.46/1.67 mult(Y, Z)
% 9.46/1.67
% 9.46/1.67 Lemma 25: mult(ld(X, Y), mult(X, Z)) = ld(X, mult(mult(Y, X), Z)).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(ld(X, Y), mult(X, Z))
% 9.46/1.67 = { by axiom 2 (f02) R->L }
% 9.46/1.67 ld(X, mult(X, mult(ld(X, Y), mult(X, Z))))
% 9.46/1.67 = { by lemma 14 }
% 9.46/1.67 ld(X, mult(mult(Y, X), Z))
% 9.46/1.67
% 9.46/1.67 Lemma 26: mult(X, ld(ld(X, X), Y)) = mult(X, ld(rd(X, X), Y)).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(X, ld(ld(X, X), Y))
% 9.46/1.67 = { by lemma 23 R->L }
% 9.46/1.67 mult(X, mult(ld(X, X), Y))
% 9.46/1.67 = { by lemma 15 R->L }
% 9.46/1.67 mult(mult(X, X), ld(X, Y))
% 9.46/1.67 = { by lemma 24 R->L }
% 9.46/1.67 mult(ld(rd(Z, mult(X, Z)), X), ld(X, Y))
% 9.46/1.67 = { by lemma 13 R->L }
% 9.46/1.67 mult(ld(rd(ld(X, Y), Y), X), ld(X, Y))
% 9.46/1.67 = { by axiom 4 (f03) R->L }
% 9.46/1.67 mult(ld(rd(ld(X, Y), Y), X), mult(rd(ld(X, Y), Y), Y))
% 9.46/1.67 = { by lemma 25 }
% 9.46/1.67 ld(rd(ld(X, Y), Y), mult(mult(X, rd(ld(X, Y), Y)), Y))
% 9.46/1.67 = { by lemma 11 }
% 9.46/1.67 ld(rd(ld(X, Y), Y), mult(rd(X, X), Y))
% 9.46/1.67 = { by lemma 12 R->L }
% 9.46/1.67 ld(rd(ld(X, W), W), mult(rd(X, X), Y))
% 9.46/1.67 = { by lemma 13 }
% 9.46/1.67 ld(rd(V, mult(X, V)), mult(rd(X, X), Y))
% 9.46/1.67 = { by lemma 24 }
% 9.46/1.67 mult(X, mult(rd(X, X), Y))
% 9.46/1.67 = { by lemma 22 }
% 9.46/1.67 mult(X, ld(rd(X, X), Y))
% 9.46/1.67
% 9.46/1.67 Lemma 27: ld(ld(X, X), Y) = ld(rd(X, X), Y).
% 9.46/1.67 Proof:
% 9.46/1.67 ld(ld(X, X), Y)
% 9.46/1.67 = { by axiom 2 (f02) R->L }
% 9.46/1.67 ld(X, mult(X, ld(ld(X, X), Y)))
% 9.46/1.67 = { by lemma 26 }
% 9.46/1.67 ld(X, mult(X, ld(rd(X, X), Y)))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 ld(rd(X, X), Y)
% 9.46/1.67
% 9.46/1.67 Lemma 28: ld(X, X) = rd(X, X).
% 9.46/1.67 Proof:
% 9.46/1.67 ld(X, X)
% 9.46/1.67 = { by lemma 6 R->L }
% 9.46/1.67 rd(Y, ld(ld(X, X), Y))
% 9.46/1.67 = { by lemma 27 }
% 9.46/1.67 rd(Y, ld(rd(X, X), Y))
% 9.46/1.67 = { by lemma 6 }
% 9.46/1.67 rd(X, X)
% 9.46/1.67
% 9.46/1.67 Lemma 29: ld(X, rd(ld(X, Y), ld(X, Y))) = ld(mult(Y, X), Y).
% 9.46/1.67 Proof:
% 9.46/1.67 ld(X, rd(ld(X, Y), ld(X, Y)))
% 9.46/1.67 = { by lemma 28 R->L }
% 9.46/1.67 ld(X, ld(ld(X, Y), ld(X, Y)))
% 9.46/1.67 = { by axiom 3 (f01) R->L }
% 9.46/1.67 ld(X, ld(ld(X, Y), ld(X, mult(mult(Y, X), ld(mult(Y, X), Y)))))
% 9.46/1.67 = { by lemma 25 R->L }
% 9.46/1.67 ld(X, ld(ld(X, Y), mult(ld(X, Y), mult(X, ld(mult(Y, X), Y)))))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 ld(X, mult(X, ld(mult(Y, X), Y)))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 ld(mult(Y, X), Y)
% 9.46/1.67
% 9.46/1.67 Lemma 30: rd(ld(X, mult(Y, Z)), mult(X, Z)) = ld(X, rd(Y, X)).
% 9.46/1.67 Proof:
% 9.46/1.67 rd(ld(X, mult(Y, Z)), mult(X, Z))
% 9.46/1.67 = { by lemma 24 R->L }
% 9.46/1.67 rd(ld(X, mult(Y, Z)), ld(rd(W, mult(X, W)), Z))
% 9.46/1.67 = { by lemma 13 R->L }
% 9.46/1.67 rd(ld(X, mult(Y, Z)), ld(rd(ld(X, mult(Y, Z)), mult(Y, Z)), Z))
% 9.46/1.67 = { by axiom 4 (f03) R->L }
% 9.46/1.67 rd(mult(rd(ld(X, mult(Y, Z)), mult(Y, Z)), mult(Y, Z)), ld(rd(ld(X, mult(Y, Z)), mult(Y, Z)), Z))
% 9.46/1.67 = { by lemma 8 }
% 9.46/1.67 mult(mult(rd(ld(X, mult(Y, Z)), mult(Y, Z)), Y), rd(ld(X, mult(Y, Z)), mult(Y, Z)))
% 9.46/1.67 = { by lemma 7 R->L }
% 9.46/1.67 rd(mult(rd(ld(X, mult(Y, Z)), mult(Y, Z)), mult(Y, mult(rd(ld(X, mult(Y, Z)), mult(Y, Z)), mult(Y, Z)))), mult(Y, Z))
% 9.46/1.67 = { by axiom 4 (f03) }
% 9.46/1.67 rd(mult(rd(ld(X, mult(Y, Z)), mult(Y, Z)), mult(Y, ld(X, mult(Y, Z)))), mult(Y, Z))
% 9.46/1.67 = { by lemma 22 }
% 9.46/1.67 rd(ld(rd(mult(Y, Z), ld(X, mult(Y, Z))), mult(Y, ld(X, mult(Y, Z)))), mult(Y, Z))
% 9.46/1.67 = { by lemma 6 }
% 9.46/1.67 rd(ld(X, mult(Y, ld(X, mult(Y, Z)))), mult(Y, Z))
% 9.46/1.67 = { by lemma 17 R->L }
% 9.46/1.67 rd(mult(ld(X, rd(Y, X)), mult(Y, Z)), mult(Y, Z))
% 9.46/1.67 = { by axiom 1 (f04) }
% 9.46/1.67 ld(X, rd(Y, X))
% 9.46/1.67
% 9.46/1.67 Lemma 31: mult(mult(X, rd(X, Y)), Y) = mult(rd(X, Y), mult(Y, X)).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(mult(X, rd(X, Y)), Y)
% 9.46/1.67 = { by axiom 4 (f03) R->L }
% 9.46/1.67 mult(mult(mult(rd(X, Y), Y), rd(X, Y)), Y)
% 9.46/1.67 = { by axiom 5 (f05) R->L }
% 9.46/1.67 mult(rd(X, Y), mult(Y, mult(rd(X, Y), Y)))
% 9.46/1.67 = { by axiom 4 (f03) }
% 9.46/1.67 mult(rd(X, Y), mult(Y, X))
% 9.46/1.67
% 9.46/1.67 Lemma 32: mult(rd(X, X), mult(X, X)) = rd(mult(X, X), ld(X, X)).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(rd(X, X), mult(X, X))
% 9.46/1.67 = { by lemma 31 R->L }
% 9.46/1.67 mult(mult(X, rd(X, X)), X)
% 9.46/1.67 = { by lemma 9 }
% 9.46/1.67 rd(mult(X, X), ld(X, X))
% 9.46/1.67
% 9.46/1.67 Lemma 33: ld(rd(X, X), mult(X, Y)) = ld(X, mult(mult(X, X), Y)).
% 9.46/1.67 Proof:
% 9.46/1.67 ld(rd(X, X), mult(X, Y))
% 9.46/1.67 = { by lemma 24 R->L }
% 9.46/1.67 ld(rd(X, X), ld(rd(Z, mult(X, Z)), Y))
% 9.46/1.67 = { by lemma 22 R->L }
% 9.46/1.67 mult(rd(X, X), ld(rd(Z, mult(X, Z)), Y))
% 9.46/1.67 = { by lemma 16 R->L }
% 9.46/1.67 mult(rd(Z, mult(X, Z)), mult(ld(rd(Z, mult(X, Z)), rd(rd(X, X), rd(Z, mult(X, Z)))), Y))
% 9.46/1.67 = { by lemma 13 R->L }
% 9.46/1.67 mult(rd(Z, mult(X, Z)), mult(ld(rd(Z, mult(X, Z)), rd(rd(X, X), rd(ld(X, W), W))), Y))
% 9.46/1.67 = { by lemma 11 R->L }
% 9.46/1.67 mult(rd(Z, mult(X, Z)), mult(ld(rd(Z, mult(X, Z)), rd(mult(X, rd(ld(X, W), W)), rd(ld(X, W), W))), Y))
% 9.46/1.67 = { by axiom 1 (f04) }
% 9.46/1.67 mult(rd(Z, mult(X, Z)), mult(ld(rd(Z, mult(X, Z)), X), Y))
% 9.46/1.67 = { by lemma 18 }
% 9.46/1.67 ld(X, mult(ld(rd(Z, mult(X, Z)), X), Y))
% 9.46/1.67 = { by lemma 24 }
% 9.46/1.67 ld(X, mult(mult(X, X), Y))
% 9.46/1.67
% 9.46/1.67 Lemma 34: mult(mult(X, X), rd(X, X)) = mult(X, X).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(mult(X, X), rd(X, X))
% 9.46/1.67 = { by axiom 3 (f01) R->L }
% 9.46/1.67 mult(X, ld(X, mult(mult(X, X), rd(X, X))))
% 9.46/1.67 = { by lemma 33 R->L }
% 9.46/1.67 mult(X, ld(rd(X, X), mult(X, rd(X, X))))
% 9.46/1.67 = { by lemma 22 R->L }
% 9.46/1.67 mult(X, mult(rd(X, X), mult(X, rd(X, X))))
% 9.46/1.67 = { by axiom 5 (f05) }
% 9.46/1.67 mult(mult(mult(X, rd(X, X)), X), rd(X, X))
% 9.46/1.67 = { by lemma 31 }
% 9.46/1.67 mult(mult(rd(X, X), mult(X, X)), rd(X, X))
% 9.46/1.67 = { by lemma 32 }
% 9.46/1.67 mult(rd(mult(X, X), ld(X, X)), rd(X, X))
% 9.46/1.67 = { by lemma 22 }
% 9.46/1.67 ld(rd(ld(X, X), mult(X, X)), rd(X, X))
% 9.46/1.67 = { by lemma 28 }
% 9.46/1.67 ld(rd(rd(X, X), mult(X, X)), rd(X, X))
% 9.46/1.67 = { by lemma 19 }
% 9.46/1.67 mult(X, X)
% 9.46/1.67
% 9.46/1.67 Lemma 35: ld(rd(X, X), ld(rd(X, X), Y)) = Y.
% 9.46/1.67 Proof:
% 9.46/1.67 ld(rd(X, X), ld(rd(X, X), Y))
% 9.46/1.67 = { by lemma 27 R->L }
% 9.46/1.67 ld(rd(X, X), ld(ld(X, X), Y))
% 9.46/1.67 = { by lemma 23 R->L }
% 9.46/1.67 ld(rd(X, X), mult(ld(X, X), Y))
% 9.46/1.67 = { by lemma 27 R->L }
% 9.46/1.67 ld(ld(X, X), mult(ld(X, X), Y))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 Y
% 9.46/1.67
% 9.46/1.67 Lemma 36: rd(mult(X, X), mult(X, X)) = rd(X, X).
% 9.46/1.67 Proof:
% 9.46/1.67 rd(mult(X, X), mult(X, X))
% 9.46/1.67 = { by lemma 28 R->L }
% 9.46/1.67 ld(mult(X, X), mult(X, X))
% 9.46/1.67 = { by lemma 34 R->L }
% 9.46/1.67 ld(mult(X, X), mult(mult(X, X), rd(X, X)))
% 9.46/1.67 = { by axiom 2 (f02) }
% 9.46/1.67 rd(X, X)
% 9.46/1.67
% 9.46/1.67 Lemma 37: ld(mult(X, rd(Y, Y)), X) = rd(rd(X, X), rd(Y, Y)).
% 9.46/1.67 Proof:
% 9.46/1.67 ld(mult(X, rd(Y, Y)), X)
% 9.46/1.67 = { by lemma 29 R->L }
% 9.46/1.67 ld(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))
% 9.46/1.67 = { by lemma 22 R->L }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))
% 9.46/1.67 = { by lemma 27 R->L }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(ld(Y, Y), X)))
% 9.46/1.67 = { by lemma 23 R->L }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(rd(Y, Y), X), mult(ld(Y, Y), X)))
% 9.46/1.67 = { by lemma 27 R->L }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(ld(Y, Y), X), mult(ld(Y, Y), X)))
% 9.46/1.67 = { by axiom 4 (f03) R->L }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(ld(Y, Y), mult(rd(X, X), X)), mult(ld(Y, Y), X)))
% 9.46/1.67 = { by lemma 30 }
% 9.46/1.67 mult(rd(Y, Y), ld(ld(Y, Y), rd(rd(X, X), ld(Y, Y))))
% 9.46/1.67 = { by lemma 30 R->L }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(ld(Y, Y), mult(rd(X, X), mult(X, X))), mult(ld(Y, Y), mult(X, X))))
% 9.46/1.67 = { by lemma 32 }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(ld(Y, Y), rd(mult(X, X), ld(X, X))), mult(ld(Y, Y), mult(X, X))))
% 9.46/1.67 = { by lemma 28 }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(ld(Y, Y), rd(mult(X, X), rd(X, X))), mult(ld(Y, Y), mult(X, X))))
% 9.46/1.67 = { by lemma 34 R->L }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(ld(Y, Y), rd(mult(mult(X, X), rd(X, X)), rd(X, X))), mult(ld(Y, Y), mult(X, X))))
% 9.46/1.67 = { by axiom 1 (f04) }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(ld(Y, Y), mult(X, X)), mult(ld(Y, Y), mult(X, X))))
% 9.46/1.67 = { by lemma 27 }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(rd(Y, Y), mult(X, X)), mult(ld(Y, Y), mult(X, X))))
% 9.46/1.67 = { by lemma 23 }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(rd(Y, Y), mult(X, X)), ld(ld(Y, Y), mult(X, X))))
% 9.46/1.67 = { by lemma 27 }
% 9.46/1.67 mult(rd(Y, Y), rd(ld(rd(Y, Y), mult(X, X)), ld(rd(Y, Y), mult(X, X))))
% 9.46/1.67 = { by lemma 10 R->L }
% 9.46/1.67 rd(rd(mult(rd(Y, Y), ld(rd(Y, Y), mult(X, X))), ld(rd(Y, Y), ld(rd(Y, Y), mult(X, X)))), rd(Y, Y))
% 9.46/1.67 = { by axiom 3 (f01) }
% 9.46/1.67 rd(rd(mult(X, X), ld(rd(Y, Y), ld(rd(Y, Y), mult(X, X)))), rd(Y, Y))
% 9.46/1.67 = { by lemma 35 }
% 9.46/1.67 rd(rd(mult(X, X), mult(X, X)), rd(Y, Y))
% 9.46/1.67 = { by lemma 36 }
% 9.46/1.67 rd(rd(X, X), rd(Y, Y))
% 9.46/1.67
% 9.46/1.67 Lemma 38: mult(rd(X, Y), rd(Y, X)) = rd(rd(X, Y), rd(X, Y)).
% 9.46/1.67 Proof:
% 9.46/1.67 mult(rd(X, Y), rd(Y, X))
% 9.46/1.67 = { by lemma 19 R->L }
% 9.46/1.67 mult(rd(X, Y), rd(ld(rd(X, Y), X), X))
% 9.46/1.67 = { by lemma 11 }
% 9.46/1.67 rd(rd(X, Y), rd(X, Y))
% 9.46/1.67
% 9.46/1.67 Lemma 39: rd(rd(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(Y, Y))) = rd(X, X).
% 9.46/1.67 Proof:
% 9.46/1.67 rd(rd(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(Y, Y)))
% 9.46/1.67 = { by lemma 37 R->L }
% 9.46/1.68 rd(rd(rd(X, X), rd(Y, Y)), ld(mult(X, rd(Y, Y)), X))
% 9.46/1.68 = { by lemma 29 R->L }
% 9.46/1.68 rd(rd(rd(X, X), rd(Y, Y)), ld(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 37 R->L }
% 9.46/1.68 rd(ld(mult(X, rd(Y, Y)), X), ld(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 29 R->L }
% 9.46/1.68 rd(ld(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 27 R->L }
% 9.46/1.68 rd(ld(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 23 R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 27 R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 9 R->L }
% 9.46/1.68 mult(mult(ld(Y, Y), rd(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))), ld(Y, Y))
% 9.46/1.68 = { by lemma 36 R->L }
% 9.46/1.68 mult(mult(ld(Y, Y), rd(mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))), ld(Y, Y))
% 9.46/1.68 = { by lemma 9 }
% 9.46/1.68 rd(mult(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 38 }
% 9.46/1.68 rd(mult(ld(Y, Y), rd(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by axiom 2 (f02) R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), mult(ld(rd(Y, Y), X), rd(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 28 R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), mult(ld(rd(Y, Y), X), ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 26 R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), mult(ld(rd(Y, Y), X), ld(ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by axiom 3 (f01) R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), mult(mult(ld(rd(Y, Y), X), ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 15 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), mult(ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), mult(ld(ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 27 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), mult(ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), mult(ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 23 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), ld(ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), mult(ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 27 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), mult(ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 19 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), mult(ld(rd(Y, Y), X), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 33 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), ld(ld(rd(Y, Y), X), mult(mult(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 34 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), ld(ld(rd(Y, Y), X), mult(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by axiom 2 (f02) }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 28 }
% 9.46/1.68 rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(ld(Y, Y), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 38 }
% 9.46/1.68 rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(ld(Y, Y), rd(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by axiom 1 (f04) R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 28 R->L }
% 9.46/1.68 rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by axiom 4 (f03) R->L }
% 9.46/1.68 rd(mult(rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by axiom 3 (f01) R->L }
% 9.46/1.68 rd(mult(rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), mult(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))), ld(rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))))
% 9.46/1.68 = { by lemma 8 }
% 9.46/1.68 mult(mult(rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 22 }
% 9.46/1.68 mult(ld(rd(rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)), mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X)))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by lemma 19 }
% 9.46/1.68 mult(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))))
% 9.46/1.68 = { by axiom 1 (f04) }
% 9.46/1.68 mult(mult(ld(Y, Y), rd(ld(rd(Y, Y), X), ld(rd(Y, Y), X))), ld(Y, Y))
% 9.46/1.68 = { by lemma 9 }
% 9.46/1.68 rd(mult(ld(Y, Y), ld(rd(Y, Y), X)), ld(ld(Y, Y), ld(rd(Y, Y), X)))
% 9.46/1.68 = { by lemma 23 }
% 9.46/1.68 rd(ld(ld(Y, Y), ld(rd(Y, Y), X)), ld(ld(Y, Y), ld(rd(Y, Y), X)))
% 9.46/1.68 = { by lemma 27 }
% 9.46/1.69 rd(ld(rd(Y, Y), ld(rd(Y, Y), X)), ld(ld(Y, Y), ld(rd(Y, Y), X)))
% 9.46/1.69 = { by lemma 27 }
% 9.46/1.69 rd(ld(rd(Y, Y), ld(rd(Y, Y), X)), ld(rd(Y, Y), ld(rd(Y, Y), X)))
% 9.46/1.69 = { by lemma 35 }
% 9.46/1.69 rd(X, ld(rd(Y, Y), ld(rd(Y, Y), X)))
% 9.46/1.69 = { by lemma 35 }
% 9.46/1.69 rd(X, X)
% 9.46/1.69
% 9.46/1.69 Lemma 40: rd(Y, Y) = rd(X, X).
% 9.46/1.69 Proof:
% 9.46/1.69 rd(Y, Y)
% 9.46/1.69 = { by lemma 39 R->L }
% 9.46/1.69 rd(rd(rd(Y, Y), rd(X, X)), rd(rd(Y, Y), rd(X, X)))
% 9.46/1.69 = { by lemma 11 R->L }
% 9.46/1.69 mult(rd(rd(Y, Y), rd(X, X)), rd(ld(rd(rd(Y, Y), rd(X, X)), W), W))
% 9.46/1.69 = { by lemma 22 }
% 9.46/1.69 ld(rd(rd(X, X), rd(Y, Y)), rd(ld(rd(rd(Y, Y), rd(X, X)), W), W))
% 9.46/1.69 = { by lemma 13 }
% 9.46/1.69 ld(rd(rd(X, X), rd(Y, Y)), rd(Z, mult(rd(rd(Y, Y), rd(X, X)), Z)))
% 9.46/1.69 = { by lemma 20 }
% 9.46/1.69 ld(rd(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(Y, Y)))
% 9.46/1.69 = { by lemma 28 }
% 9.46/1.69 rd(rd(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(Y, Y)))
% 9.46/1.69 = { by lemma 39 }
% 9.46/1.69 rd(X, X)
% 9.46/1.69
% 9.46/1.69 Goal 1 (goals): tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2))) = tuple(x0, x0_2).
% 9.46/1.69 Proof:
% 9.46/1.69 tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2)))
% 9.46/1.69 = { by lemma 23 }
% 9.46/1.69 tuple(ld(ld(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2)))
% 9.46/1.69 = { by lemma 28 }
% 9.46/1.69 tuple(ld(rd(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2)))
% 9.46/1.69 = { by lemma 28 }
% 9.46/1.69 tuple(ld(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2)))
% 9.46/1.69 = { by lemma 40 }
% 9.46/1.69 tuple(ld(rd(x0, x0), x0), mult(x0_2, rd(x1_2, x1_2)))
% 9.46/1.69 = { by lemma 19 }
% 9.46/1.69 tuple(x0, mult(x0_2, rd(x1_2, x1_2)))
% 9.46/1.69 = { by lemma 40 }
% 9.46/1.69 tuple(x0, mult(x0_2, rd(x0_2, x0_2)))
% 9.46/1.69 = { by lemma 28 R->L }
% 9.46/1.69 tuple(x0, mult(x0_2, ld(x0_2, x0_2)))
% 9.46/1.69 = { by axiom 3 (f01) }
% 9.46/1.69 tuple(x0, x0_2)
% 9.46/1.69 % SZS output end Proof
% 9.46/1.69
% 9.46/1.69 RESULT: Theorem (the conjecture is true).
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