%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP655+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 10:11:35 AM UTC 2026
% Result : Theorem 17.20s 2.81s
% Output : Proof 17.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP655+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n005.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Sun Sep 27 10:31:47 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.20/2.81 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 17.20/2.81
% 17.20/2.81 % SZS status Theorem
% 17.20/2.81
% 17.99/2.95 % SZS output start Proof
% 17.99/2.95 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 17.99/2.95 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 17.99/2.95 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 17.99/2.95 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 17.99/2.95 Axiom 5 (f05): mult(X, mult(Y, mult(Z, Y))) = mult(mult(mult(X, Y), Z), Y).
% 17.99/2.95
% 17.99/2.95 Lemma 6: mult(rd(X, Y), mult(Y, mult(Z, Y))) = mult(mult(X, Z), Y).
% 17.99/2.95 Proof:
% 17.99/2.95 mult(rd(X, Y), mult(Y, mult(Z, Y)))
% 17.99/2.95 = { by axiom 5 (f05) }
% 17.99/2.95 mult(mult(mult(rd(X, Y), Y), Z), Y)
% 17.99/2.95 = { by axiom 2 (f03) }
% 17.99/2.95 mult(mult(X, Z), Y)
% 17.99/2.95
% 17.99/2.95 Lemma 7: ld(rd(X, Y), mult(mult(X, Z), Y)) = mult(Y, mult(Z, Y)).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(rd(X, Y), mult(mult(X, Z), Y))
% 17.99/2.95 = { by lemma 6 R->L }
% 17.99/2.95 ld(rd(X, Y), mult(rd(X, Y), mult(Y, mult(Z, Y))))
% 17.99/2.95 = { by axiom 3 (f02) }
% 17.99/2.95 mult(Y, mult(Z, Y))
% 17.99/2.95
% 17.99/2.95 Lemma 8: ld(rd(X, Y), mult(Z, Y)) = mult(Y, mult(ld(X, Z), Y)).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(rd(X, Y), mult(Z, Y))
% 17.99/2.95 = { by axiom 1 (f01) R->L }
% 17.99/2.95 ld(rd(X, Y), mult(mult(X, ld(X, Z)), Y))
% 17.99/2.95 = { by lemma 7 }
% 17.99/2.95 mult(Y, mult(ld(X, Z), Y))
% 17.99/2.95
% 17.99/2.95 Lemma 9: ld(rd(X, Y), X) = Y.
% 17.99/2.95 Proof:
% 17.99/2.95 ld(rd(X, Y), X)
% 17.99/2.95 = { by axiom 2 (f03) R->L }
% 17.99/2.95 ld(rd(X, Y), mult(rd(X, Y), Y))
% 17.99/2.95 = { by axiom 3 (f02) }
% 17.99/2.95 Y
% 17.99/2.95
% 17.99/2.95 Lemma 10: mult(X, mult(ld(Y, rd(Y, X)), X)) = X.
% 17.99/2.95 Proof:
% 17.99/2.95 mult(X, mult(ld(Y, rd(Y, X)), X))
% 17.99/2.95 = { by lemma 8 R->L }
% 17.99/2.95 ld(rd(Y, X), mult(rd(Y, X), X))
% 17.99/2.95 = { by axiom 3 (f02) }
% 17.99/2.95 X
% 17.99/2.95
% 17.99/2.95 Lemma 11: mult(ld(X, rd(X, Y)), Y) = ld(Y, Y).
% 17.99/2.95 Proof:
% 17.99/2.95 mult(ld(X, rd(X, Y)), Y)
% 17.99/2.95 = { by axiom 3 (f02) R->L }
% 17.99/2.95 ld(Y, mult(Y, mult(ld(X, rd(X, Y)), Y)))
% 17.99/2.95 = { by lemma 10 }
% 17.99/2.95 ld(Y, Y)
% 17.99/2.95
% 17.99/2.95 Lemma 12: ld(Z, rd(Z, Y)) = ld(X, rd(X, Y)).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(Z, rd(Z, Y))
% 17.99/2.95 = { by axiom 4 (f04) R->L }
% 17.99/2.95 rd(mult(ld(Z, rd(Z, Y)), Y), Y)
% 17.99/2.95 = { by lemma 11 }
% 17.99/2.95 rd(ld(Y, Y), Y)
% 17.99/2.95 = { by lemma 11 R->L }
% 17.99/2.95 rd(mult(ld(X, rd(X, Y)), Y), Y)
% 17.99/2.95 = { by axiom 4 (f04) }
% 17.99/2.95 ld(X, rd(X, Y))
% 17.99/2.95
% 17.99/2.95 Lemma 13: mult(X, ld(Y, rd(Y, Z))) = rd(X, Z).
% 17.99/2.95 Proof:
% 17.99/2.95 mult(X, ld(Y, rd(Y, Z)))
% 17.99/2.95 = { by lemma 12 }
% 17.99/2.95 mult(X, ld(X, rd(X, Z)))
% 17.99/2.95 = { by axiom 1 (f01) }
% 17.99/2.95 rd(X, Z)
% 17.99/2.95
% 17.99/2.95 Lemma 14: rd(X, ld(Y, X)) = Y.
% 17.99/2.95 Proof:
% 17.99/2.95 rd(X, ld(Y, X))
% 17.99/2.95 = { by axiom 1 (f01) R->L }
% 17.99/2.95 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 17.99/2.95 = { by axiom 4 (f04) }
% 17.99/2.95 Y
% 17.99/2.95
% 17.99/2.95 Lemma 15: rd(X, ld(Y, Z)) = mult(X, ld(Z, Y)).
% 17.99/2.95 Proof:
% 17.99/2.95 rd(X, ld(Y, Z))
% 17.99/2.95 = { by lemma 13 R->L }
% 17.99/2.95 mult(X, ld(Z, rd(Z, ld(Y, Z))))
% 17.99/2.95 = { by lemma 14 }
% 17.99/2.95 mult(X, ld(Z, Y))
% 17.99/2.95
% 17.99/2.95 Lemma 16: rd(mult(X, mult(Y, mult(Z, Y))), Y) = mult(mult(X, Y), Z).
% 17.99/2.95 Proof:
% 17.99/2.95 rd(mult(X, mult(Y, mult(Z, Y))), Y)
% 17.99/2.95 = { by axiom 5 (f05) }
% 17.99/2.95 rd(mult(mult(mult(X, Y), Z), Y), Y)
% 17.99/2.95 = { by axiom 4 (f04) }
% 17.99/2.95 mult(mult(X, Y), Z)
% 17.99/2.95
% 17.99/2.95 Lemma 17: mult(mult(X, Y), rd(ld(Y, Z), Y)) = rd(mult(X, Z), Y).
% 17.99/2.95 Proof:
% 17.99/2.95 mult(mult(X, Y), rd(ld(Y, Z), Y))
% 17.99/2.95 = { by lemma 16 R->L }
% 17.99/2.95 rd(mult(X, mult(Y, mult(rd(ld(Y, Z), Y), Y))), Y)
% 17.99/2.95 = { by axiom 2 (f03) }
% 17.99/2.95 rd(mult(X, mult(Y, ld(Y, Z))), Y)
% 17.99/2.95 = { by axiom 1 (f01) }
% 17.99/2.95 rd(mult(X, Z), Y)
% 17.99/2.95
% 17.99/2.95 Lemma 18: ld(mult(X, Y), rd(mult(X, Z), Y)) = rd(ld(Y, Z), Y).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(mult(X, Y), rd(mult(X, Z), Y))
% 17.99/2.95 = { by lemma 17 R->L }
% 17.99/2.95 ld(mult(X, Y), mult(mult(X, Y), rd(ld(Y, Z), Y)))
% 17.99/2.95 = { by axiom 3 (f02) }
% 17.99/2.95 rd(ld(Y, Z), Y)
% 17.99/2.95
% 17.99/2.95 Lemma 19: rd(ld(X, ld(Y, Z)), X) = ld(mult(Y, X), rd(Z, X)).
% 17.99/2.95 Proof:
% 17.99/2.95 rd(ld(X, ld(Y, Z)), X)
% 17.99/2.95 = { by lemma 18 R->L }
% 17.99/2.95 ld(mult(Y, X), rd(mult(Y, ld(Y, Z)), X))
% 17.99/2.95 = { by axiom 1 (f01) }
% 17.99/2.95 ld(mult(Y, X), rd(Z, X))
% 17.99/2.95
% 17.99/2.95 Lemma 20: ld(ld(X, rd(X, Y)), ld(Y, Y)) = Y.
% 17.99/2.95 Proof:
% 17.99/2.95 ld(ld(X, rd(X, Y)), ld(Y, Y))
% 17.99/2.95 = { by lemma 11 R->L }
% 17.99/2.95 ld(ld(X, rd(X, Y)), mult(ld(X, rd(X, Y)), Y))
% 17.99/2.95 = { by axiom 3 (f02) }
% 17.99/2.95 Y
% 17.99/2.95
% 17.99/2.95 Lemma 21: mult(ld(X, X), X) = X.
% 17.99/2.95 Proof:
% 17.99/2.95 mult(ld(X, X), X)
% 17.99/2.95 = { by axiom 3 (f02) R->L }
% 17.99/2.95 ld(X, mult(X, mult(ld(X, X), X)))
% 17.99/2.95 = { by lemma 8 R->L }
% 17.99/2.95 ld(X, ld(rd(X, X), mult(X, X)))
% 17.99/2.95 = { by lemma 9 R->L }
% 17.99/2.95 ld(X, ld(rd(X, X), mult(X, ld(rd(Y, X), Y))))
% 17.99/2.95 = { by lemma 15 R->L }
% 17.99/2.95 ld(X, ld(rd(X, X), rd(X, ld(Y, rd(Y, X)))))
% 17.99/2.95 = { by lemma 13 R->L }
% 17.99/2.95 ld(X, ld(mult(X, ld(Y, rd(Y, X))), rd(X, ld(Y, rd(Y, X)))))
% 17.99/2.95 = { by lemma 19 R->L }
% 17.99/2.95 ld(X, rd(ld(ld(Y, rd(Y, X)), ld(X, X)), ld(Y, rd(Y, X))))
% 17.99/2.95 = { by lemma 20 }
% 17.99/2.95 ld(X, rd(X, ld(Y, rd(Y, X))))
% 17.99/2.95 = { by lemma 15 }
% 17.99/2.95 ld(X, mult(X, ld(rd(Y, X), Y)))
% 17.99/2.95 = { by lemma 9 }
% 17.99/2.95 ld(X, mult(X, X))
% 17.99/2.95 = { by axiom 3 (f02) }
% 17.99/2.95 X
% 17.99/2.95
% 17.99/2.95 Lemma 22: rd(X, X) = ld(X, X).
% 17.99/2.95 Proof:
% 17.99/2.95 rd(X, X)
% 17.99/2.95 = { by lemma 21 R->L }
% 17.99/2.95 rd(mult(ld(X, X), X), X)
% 17.99/2.95 = { by axiom 4 (f04) }
% 17.99/2.95 ld(X, X)
% 17.99/2.95
% 17.99/2.95 Lemma 23: ld(mult(X, Y), X) = ld(Z, rd(Z, Y)).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(mult(X, Y), X)
% 17.99/2.95 = { by axiom 4 (f04) R->L }
% 17.99/2.95 ld(mult(X, Y), rd(mult(X, Y), Y))
% 17.99/2.95 = { by lemma 12 R->L }
% 17.99/2.95 ld(Z, rd(Z, Y))
% 17.99/2.95
% 17.99/2.95 Lemma 24: ld(ld(X, Y), ld(X, Y)) = mult(ld(X, Y), ld(Y, X)).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(ld(X, Y), ld(X, Y))
% 17.99/2.95 = { by lemma 22 R->L }
% 17.99/2.95 rd(ld(X, Y), ld(X, Y))
% 17.99/2.95 = { by lemma 15 }
% 17.99/2.95 mult(ld(X, Y), ld(Y, X))
% 17.99/2.95
% 17.99/2.95 Lemma 25: ld(ld(X, Y), ld(X, Y)) = mult(ld(Y, X), ld(X, Y)).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(ld(X, Y), ld(X, Y))
% 17.99/2.95 = { by lemma 11 R->L }
% 17.99/2.95 mult(ld(Y, rd(Y, ld(X, Y))), ld(X, Y))
% 17.99/2.95 = { by lemma 14 }
% 17.99/2.95 mult(ld(Y, X), ld(X, Y))
% 17.99/2.95
% 17.99/2.95 Lemma 26: mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))) = mult(mult(Y, Z), ld(X, Y)).
% 17.99/2.95 Proof:
% 17.99/2.95 mult(X, mult(ld(X, Y), mult(Z, ld(X, Y))))
% 17.99/2.95 = { by axiom 5 (f05) }
% 17.99/2.95 mult(mult(mult(X, ld(X, Y)), Z), ld(X, Y))
% 17.99/2.95 = { by axiom 1 (f01) }
% 17.99/2.95 mult(mult(Y, Z), ld(X, Y))
% 17.99/2.95
% 17.99/2.95 Lemma 27: ld(X, mult(mult(Y, Z), ld(X, Y))) = mult(ld(X, Y), mult(Z, ld(X, Y))).
% 17.99/2.95 Proof:
% 17.99/2.95 ld(X, mult(mult(Y, Z), ld(X, Y)))
% 17.99/2.95 = { by lemma 26 R->L }
% 17.99/2.95 ld(X, mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))))
% 17.99/2.95 = { by axiom 3 (f02) }
% 17.99/2.95 mult(ld(X, Y), mult(Z, ld(X, Y)))
% 17.99/2.95
% 17.99/2.95 Lemma 28: mult(ld(X, X), ld(X, X)) = ld(X, X).
% 17.99/2.95 Proof:
% 17.99/2.95 mult(ld(X, X), ld(X, X))
% 17.99/2.95 = { by lemma 22 R->L }
% 17.99/2.95 mult(rd(X, X), ld(X, X))
% 17.99/2.95 = { by lemma 13 R->L }
% 17.99/2.95 mult(mult(X, ld(Y, rd(Y, X))), ld(X, X))
% 17.99/2.95 = { by lemma 26 R->L }
% 17.99/2.95 mult(X, mult(ld(X, X), mult(ld(Y, rd(Y, X)), ld(X, X))))
% 17.99/2.95 = { by lemma 22 R->L }
% 17.99/2.95 mult(X, mult(ld(X, X), mult(ld(Y, rd(Y, X)), rd(X, X))))
% 17.99/2.96 = { by lemma 13 R->L }
% 17.99/2.96 mult(X, mult(ld(X, X), mult(ld(Y, rd(Y, X)), mult(X, ld(Z, rd(Z, X))))))
% 17.99/2.96 = { by lemma 23 R->L }
% 17.99/2.96 mult(X, mult(ld(X, X), mult(ld(mult(W, X), W), mult(X, ld(Z, rd(Z, X))))))
% 17.99/2.96 = { by lemma 23 R->L }
% 17.99/2.96 mult(X, mult(ld(X, X), mult(ld(mult(W, X), W), mult(X, ld(mult(W, X), W)))))
% 17.99/2.96 = { by lemma 27 R->L }
% 17.99/2.96 mult(X, mult(ld(X, X), ld(mult(W, X), mult(mult(W, X), ld(mult(W, X), W)))))
% 17.99/2.96 = { by axiom 1 (f01) }
% 17.99/2.96 mult(X, mult(ld(X, X), ld(mult(W, X), W)))
% 17.99/2.96 = { by lemma 23 }
% 17.99/2.96 mult(X, mult(ld(X, X), ld(V, rd(V, X))))
% 17.99/2.96 = { by lemma 13 }
% 17.99/2.96 mult(X, rd(ld(X, X), X))
% 17.99/2.96 = { by lemma 11 R->L }
% 17.99/2.96 mult(X, rd(mult(ld(U, rd(U, X)), X), X))
% 17.99/2.96 = { by axiom 4 (f04) }
% 17.99/2.96 mult(X, ld(U, rd(U, X)))
% 17.99/2.96 = { by lemma 13 }
% 17.99/2.96 rd(X, X)
% 17.99/2.96 = { by lemma 22 }
% 17.99/2.96 ld(X, X)
% 17.99/2.96
% 17.99/2.96 Lemma 29: mult(ld(X, Y), ld(Y, X)) = mult(ld(Y, X), ld(X, Y)).
% 17.99/2.96 Proof:
% 17.99/2.96 mult(ld(X, Y), ld(Y, X))
% 17.99/2.96 = { by lemma 25 R->L }
% 17.99/2.96 ld(ld(Y, X), ld(Y, X))
% 17.99/2.96 = { by lemma 24 }
% 17.99/2.96 mult(ld(Y, X), ld(X, Y))
% 17.99/2.96
% 17.99/2.96 Lemma 30: mult(ld(ld(X, X), Y), ld(X, X)) = mult(ld(X, X), mult(Y, ld(X, X))).
% 17.99/2.96 Proof:
% 17.99/2.96 mult(ld(ld(X, X), Y), ld(X, X))
% 17.99/2.96 = { by lemma 15 R->L }
% 17.99/2.96 rd(ld(ld(X, X), Y), ld(X, X))
% 17.99/2.96 = { by lemma 11 R->L }
% 17.99/2.96 rd(ld(mult(ld(Z, rd(Z, X)), X), Y), ld(X, X))
% 17.99/2.96 = { by lemma 11 R->L }
% 17.99/2.96 rd(ld(mult(ld(Z, rd(Z, X)), X), Y), mult(ld(Z, rd(Z, X)), X))
% 17.99/2.96 = { by lemma 18 R->L }
% 17.99/2.96 ld(mult(X, mult(ld(Z, rd(Z, X)), X)), rd(mult(X, Y), mult(ld(Z, rd(Z, X)), X)))
% 17.99/2.96 = { by lemma 10 }
% 17.99/2.96 ld(X, rd(mult(X, Y), mult(ld(Z, rd(Z, X)), X)))
% 17.99/2.96 = { by lemma 11 }
% 17.99/2.96 ld(X, rd(mult(X, Y), ld(X, X)))
% 17.99/2.96 = { by lemma 15 }
% 17.99/2.96 ld(X, mult(mult(X, Y), ld(X, X)))
% 17.99/2.96 = { by lemma 27 }
% 17.99/2.96 mult(ld(X, X), mult(Y, ld(X, X)))
% 17.99/2.96
% 17.99/2.96 Lemma 31: mult(mult(X, ld(Y, Z)), ld(Z, Y)) = X.
% 17.99/2.96 Proof:
% 17.99/2.96 mult(mult(X, ld(Y, Z)), ld(Z, Y))
% 17.99/2.96 = { by axiom 4 (f04) R->L }
% 17.99/2.96 mult(mult(X, ld(Y, Z)), rd(mult(ld(Z, Y), ld(Y, Z)), ld(Y, Z)))
% 17.99/2.96 = { by lemma 25 R->L }
% 17.99/2.96 mult(mult(X, ld(Y, Z)), rd(ld(ld(Y, Z), ld(Y, Z)), ld(Y, Z)))
% 17.99/2.96 = { by lemma 17 }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), ld(Y, Z))
% 17.99/2.96 = { by axiom 4 (f04) }
% 17.99/2.96 X
% 17.99/2.96
% 17.99/2.96 Lemma 32: rd(mult(X, ld(Y, Z)), mult(ld(Y, Z), W)) = mult(rd(X, mult(W, ld(Z, Y))), ld(Z, Y)).
% 17.99/2.96 Proof:
% 17.99/2.96 rd(mult(X, ld(Y, Z)), mult(ld(Y, Z), W))
% 17.99/2.96 = { by lemma 31 R->L }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), mult(ld(Y, Z), mult(mult(W, ld(Z, Y)), ld(Y, Z))))
% 17.99/2.96 = { by axiom 3 (f02) R->L }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), mult(ld(Y, Z), mult(mult(W, ld(Z, Y)), ld(X, mult(X, ld(Y, Z))))))
% 17.99/2.96 = { by axiom 3 (f02) R->L }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), mult(ld(X, mult(X, ld(Y, Z))), mult(mult(W, ld(Z, Y)), ld(X, mult(X, ld(Y, Z))))))
% 17.99/2.96 = { by axiom 2 (f03) R->L }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), mult(ld(X, mult(X, ld(Y, Z))), mult(mult(W, ld(Z, Y)), ld(mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))), mult(X, ld(Y, Z))))))
% 17.99/2.96 = { by axiom 2 (f03) R->L }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), mult(ld(mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))), mult(X, ld(Y, Z))), mult(mult(W, ld(Z, Y)), ld(mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))), mult(X, ld(Y, Z))))))
% 17.99/2.96 = { by lemma 7 R->L }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), ld(rd(rd(X, mult(W, ld(Z, Y))), ld(mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))), mult(X, ld(Y, Z)))), mult(mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))), ld(mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))), mult(X, ld(Y, Z))))))
% 17.99/2.96 = { by axiom 1 (f01) }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), ld(rd(rd(X, mult(W, ld(Z, Y))), ld(mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))), mult(X, ld(Y, Z)))), mult(X, ld(Y, Z))))
% 17.99/2.96 = { by lemma 15 }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), ld(mult(rd(X, mult(W, ld(Z, Y))), ld(mult(X, ld(Y, Z)), mult(rd(X, mult(W, ld(Z, Y))), mult(W, ld(Z, Y))))), mult(X, ld(Y, Z))))
% 17.99/2.96 = { by axiom 2 (f03) }
% 17.99/2.96 rd(mult(X, ld(Y, Z)), ld(mult(rd(X, mult(W, ld(Z, Y))), ld(mult(X, ld(Y, Z)), X)), mult(X, ld(Y, Z))))
% 17.99/2.96 = { by lemma 14 }
% 17.99/2.96 mult(rd(X, mult(W, ld(Z, Y))), ld(mult(X, ld(Y, Z)), X))
% 17.99/2.96 = { by lemma 23 }
% 17.99/2.96 mult(rd(X, mult(W, ld(Z, Y))), ld(V, rd(V, ld(Y, Z))))
% 17.99/2.96 = { by lemma 13 }
% 17.99/2.96 rd(rd(X, mult(W, ld(Z, Y))), ld(Y, Z))
% 17.99/2.96 = { by lemma 15 }
% 17.99/2.96 mult(rd(X, mult(W, ld(Z, Y))), ld(Z, Y))
% 17.99/2.96
% 17.99/2.96 Lemma 33: mult(ld(X, X), mult(mult(ld(X, X), Y), ld(X, X))) = mult(Y, ld(X, X)).
% 17.99/2.96 Proof:
% 17.99/2.96 mult(ld(X, X), mult(mult(ld(X, X), Y), ld(X, X)))
% 17.99/2.96 = { by lemma 30 R->L }
% 17.99/2.96 mult(ld(ld(X, X), mult(ld(X, X), Y)), ld(X, X))
% 17.99/2.96 = { by axiom 3 (f02) }
% 17.99/2.96 mult(Y, ld(X, X))
% 17.99/2.96
% 17.99/2.96 Lemma 34: mult(ld(X, X), mult(ld(Y, Y), ld(X, X))) = ld(X, X).
% 17.99/2.96 Proof:
% 17.99/2.96 mult(ld(X, X), mult(ld(Y, Y), ld(X, X)))
% 17.99/2.96 = { by lemma 30 R->L }
% 17.99/2.96 mult(ld(ld(X, X), ld(Y, Y)), ld(X, X))
% 17.99/2.96 = { by axiom 1 (f01) R->L }
% 17.99/2.96 mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(Y, Y), ld(X, X))))
% 17.99/2.96 = { by lemma 28 R->L }
% 17.99/2.96 mult(ld(ld(X, X), ld(Y, Y)), mult(mult(ld(Y, Y), ld(Y, Y)), ld(ld(Y, Y), ld(X, X))))
% 17.99/2.97 = { by lemma 15 R->L }
% 17.99/2.97 mult(ld(ld(X, X), ld(Y, Y)), mult(rd(ld(Y, Y), ld(Y, Y)), ld(ld(Y, Y), ld(X, X))))
% 17.99/2.97 = { by lemma 31 R->L }
% 17.99/2.97 mult(ld(ld(X, X), ld(Y, Y)), mult(rd(ld(Y, Y), mult(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), ld(ld(Y, Y), ld(X, X)))), ld(ld(Y, Y), ld(X, X))))
% 17.99/2.97 = { by lemma 32 R->L }
% 17.99/2.97 mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))
% 17.99/2.97 = { by axiom 4 (f04) R->L }
% 17.99/2.97 mult(rd(mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))
% 17.99/2.97 = { by lemma 9 R->L }
% 17.99/2.97 mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))
% 17.99/2.97 = { by lemma 13 R->L }
% 17.99/2.97 mult(mult(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), ld(Z, rd(Z, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))
% 17.99/2.97 = { by lemma 23 R->L }
% 17.99/2.97 mult(mult(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))
% 17.99/2.97 = { by lemma 6 R->L }
% 17.99/2.97 mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))))
% 17.99/2.97 = { by lemma 8 R->L }
% 17.99/2.97 mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))))
% 17.99/2.97 = { by lemma 18 R->L }
% 17.99/2.97 mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))))
% 17.99/2.97 = { by lemma 29 R->L }
% 17.99/2.97 mult(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))))
% 17.99/2.97 = { by lemma 24 R->L }
% 17.99/2.97 ld(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))))
% 17.99/2.98 = { by lemma 28 R->L }
% 17.99/2.98 mult(ld(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), ld(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/2.98 = { by lemma 25 R->L }
% 17.99/2.98 ld(ld(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), ld(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/2.98 = { by lemma 25 }
% 17.99/2.98 ld(mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), ld(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/2.99 = { by lemma 24 }
% 17.99/2.99 ld(mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), mult(ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/2.99 = { by lemma 29 }
% 17.99/2.99 ld(mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/2.99 = { by lemma 18 }
% 17.99/2.99 ld(mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/2.99 = { by lemma 8 }
% 17.99/2.99 ld(mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), ld(rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/2.99 = { by lemma 8 }
% 17.99/2.99 ld(mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/3.00 = { by lemma 6 }
% 17.99/3.00 ld(mult(mult(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/3.00 = { by lemma 23 }
% 17.99/3.00 ld(mult(mult(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), ld(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), W)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(V, rd(V, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/3.01 = { by lemma 23 }
% 17.99/3.01 ld(mult(mult(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), ld(U, rd(U, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(V, rd(V, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/3.01 = { by lemma 13 }
% 17.99/3.01 ld(mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(ld(mult(W, rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(W, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(V, rd(V, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/3.01 = { by lemma 18 }
% 17.99/3.01 ld(mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(V, rd(V, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))))
% 17.99/3.02 = { by lemma 6 }
% 17.99/3.02 ld(mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(mult(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), ld(V, rd(V, mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.02 = { by lemma 13 }
% 17.99/3.02 ld(mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.02 = { by lemma 9 }
% 17.99/3.02 ld(mult(rd(mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(ld(rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.02 = { by lemma 9 }
% 17.99/3.02 ld(mult(rd(mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.02 = { by axiom 4 (f04) }
% 17.99/3.02 ld(mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(rd(mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.02 = { by axiom 4 (f04) }
% 17.99/3.02 ld(mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.02 = { by lemma 27 R->L }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), ld(ld(X, X), mult(mult(ld(Y, Y), ld(Y, Y)), ld(ld(X, X), ld(Y, Y)))))), mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.03 = { by lemma 28 }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), ld(ld(X, X), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))), mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.03 = { by lemma 14 }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(ld(X, X), ld(Y, Y)), rd(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y)))))))
% 17.99/3.03 = { by lemma 32 }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(ld(X, X), ld(Y, Y)), mult(rd(ld(Y, Y), mult(mult(ld(Y, Y), ld(ld(X, X), ld(Y, Y))), ld(ld(Y, Y), ld(X, X)))), ld(ld(Y, Y), ld(X, X)))))
% 17.99/3.03 = { by lemma 31 }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(ld(X, X), ld(Y, Y)), mult(rd(ld(Y, Y), ld(Y, Y)), ld(ld(Y, Y), ld(X, X)))))
% 17.99/3.03 = { by lemma 15 }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(ld(X, X), ld(Y, Y)), mult(mult(ld(Y, Y), ld(Y, Y)), ld(ld(Y, Y), ld(X, X)))))
% 17.99/3.03 = { by lemma 28 }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), ld(ld(Y, Y), ld(X, X)))))
% 17.99/3.03 = { by axiom 1 (f01) }
% 17.99/3.03 ld(mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)))
% 17.99/3.03 = { by lemma 15 R->L }
% 17.99/3.03 ld(rd(ld(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)))
% 17.99/3.03 = { by lemma 18 R->L }
% 17.99/3.03 ld(ld(mult(X, ld(X, X)), rd(mult(X, ld(Y, Y)), ld(X, X))), mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)))
% 17.99/3.03 = { by axiom 1 (f01) }
% 17.99/3.03 ld(ld(X, rd(mult(X, ld(Y, Y)), ld(X, X))), mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)))
% 17.99/3.03 = { by lemma 15 }
% 17.99/3.03 ld(ld(X, mult(mult(X, ld(Y, Y)), ld(X, X))), mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)))
% 17.99/3.03 = { by lemma 27 }
% 17.99/3.03 ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), mult(ld(ld(X, X), ld(Y, Y)), ld(X, X)))
% 17.99/3.03 = { by lemma 30 }
% 17.99/3.03 ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), mult(ld(X, X), mult(ld(Y, Y), ld(X, X))))
% 17.99/3.03 = { by lemma 31 R->L }
% 17.99/3.03 ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), mult(ld(X, X), mult(ld(Y, Y), mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)))))
% 17.99/3.03 = { by axiom 5 (f05) }
% 17.99/3.03 ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), mult(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)))
% 17.99/3.03 = { by lemma 15 R->L }
% 17.99/3.03 ld(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)))
% 17.99/3.04 = { by lemma 31 R->L }
% 17.99/3.04 ld(mult(mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)), mult(ld(Y, Y), ld(X, X))), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)))
% 17.99/3.04 = { by lemma 16 R->L }
% 17.99/3.04 ld(rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(Y, Y), mult(mult(ld(Y, Y), ld(X, X)), ld(Y, Y)))), ld(Y, Y)), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)))
% 17.99/3.04 = { by lemma 33 }
% 17.99/3.04 ld(rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)))
% 17.99/3.04 = { by lemma 15 }
% 17.99/3.04 ld(mult(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)))
% 17.99/3.04 = { by lemma 19 R->L }
% 17.99/3.04 rd(ld(ld(Y, Y), ld(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 22 R->L }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by axiom 1 (f01) R->L }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(mult(mult(ld(X, X), ld(Y, Y)), ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 9 R->L }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(mult(mult(ld(X, X), ld(Y, Y)), ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), ld(rd(T, mult(ld(X, X), ld(Y, Y))), T)), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 15 R->L }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(rd(mult(mult(ld(X, X), ld(Y, Y)), ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), ld(T, rd(T, mult(ld(X, X), ld(Y, Y))))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 17 R->L }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(mult(mult(ld(X, X), ld(Y, Y)), ld(T, rd(T, mult(ld(X, X), ld(Y, Y))))), rd(ld(ld(T, rd(T, mult(ld(X, X), ld(Y, Y)))), ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), ld(T, rd(T, mult(ld(X, X), ld(Y, Y)))))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 20 }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(mult(mult(ld(X, X), ld(Y, Y)), ld(T, rd(T, mult(ld(X, X), ld(Y, Y))))), rd(mult(ld(X, X), ld(Y, Y)), ld(T, rd(T, mult(ld(X, X), ld(Y, Y)))))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 13 }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(rd(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), rd(mult(ld(X, X), ld(Y, Y)), ld(T, rd(T, mult(ld(X, X), ld(Y, Y)))))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 15 }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(rd(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), ld(rd(T, mult(ld(X, X), ld(Y, Y))), T))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 9 }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(rd(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by lemma 22 }
% 17.99/3.04 rd(ld(ld(Y, Y), rd(mult(ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))))), ld(Y, Y))
% 17.99/3.04 = { by axiom 4 (f04) }
% 17.99/3.04 rd(ld(ld(Y, Y), ld(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y)))), ld(Y, Y))
% 17.99/3.04 = { by lemma 19 }
% 17.99/3.04 ld(mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)), rd(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)))
% 17.99/3.04 = { by lemma 31 }
% 17.99/3.04 ld(ld(X, X), rd(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)))
% 17.99/3.04 = { by axiom 4 (f04) }
% 17.99/3.04 ld(ld(X, X), ld(X, X))
% 17.99/3.04 = { by lemma 24 }
% 17.99/3.04 mult(ld(X, X), ld(X, X))
% 17.99/3.04 = { by lemma 28 }
% 17.99/3.04 ld(X, X)
% 17.99/3.04
% 17.99/3.04 Goal 1 (goals): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 17.99/3.04 The goal is true when:
% 17.99/3.04 X = ld(X, X)
% 17.99/3.04
% 17.99/3.04 Proof:
% 17.99/3.04 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 17.99/3.04 = { by lemma 34 R->L }
% 17.99/3.04 tuple(mult(mult(ld(X, X), mult(ld(rd(x1(ld(X, X)), ld(X, X)), rd(x1(ld(X, X)), ld(X, X))), ld(X, X))), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 17.99/3.04 = { by lemma 8 R->L }
% 17.99/3.04 tuple(mult(ld(rd(rd(x1(ld(X, X)), ld(X, X)), ld(X, X)), mult(rd(x1(ld(X, X)), ld(X, X)), ld(X, X))), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 17.99/3.04 = { by axiom 2 (f03) }
% 17.99/3.04 tuple(mult(ld(rd(rd(x1(ld(X, X)), ld(X, X)), ld(X, X)), x1(ld(X, X))), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 17.99/3.04 = { by lemma 15 }
% 17.99/3.04 tuple(mult(ld(mult(rd(x1(ld(X, X)), ld(X, X)), ld(X, X)), x1(ld(X, X))), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 17.99/3.05 = { by axiom 2 (f03) }
% 17.99/3.05 tuple(mult(ld(x1(ld(X, X)), x1(ld(X, X))), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 17.99/3.05 = { by lemma 21 }
% 17.99/3.05 tuple(x1(ld(X, X)), mult(x1_2(ld(X, X)), ld(X, X)))
% 17.99/3.05 = { by lemma 31 R->L }
% 17.99/3.05 tuple(x1(ld(X, X)), mult(x1_2(ld(X, X)), mult(mult(ld(X, X), ld(x1_2(ld(X, X)), x1_2(ld(X, X)))), ld(x1_2(ld(X, X)), x1_2(ld(X, X))))))
% 17.99/3.05 = { by lemma 33 R->L }
% 17.99/3.05 tuple(x1(ld(X, X)), mult(x1_2(ld(X, X)), mult(ld(x1_2(ld(X, X)), x1_2(ld(X, X))), mult(mult(ld(x1_2(ld(X, X)), x1_2(ld(X, X))), mult(ld(X, X), ld(x1_2(ld(X, X)), x1_2(ld(X, X))))), ld(x1_2(ld(X, X)), x1_2(ld(X, X)))))))
% 17.99/3.05 = { by lemma 26 }
% 17.99/3.05 tuple(x1(ld(X, X)), mult(mult(x1_2(ld(X, X)), mult(ld(x1_2(ld(X, X)), x1_2(ld(X, X))), mult(ld(X, X), ld(x1_2(ld(X, X)), x1_2(ld(X, X)))))), ld(x1_2(ld(X, X)), x1_2(ld(X, X)))))
% 17.99/3.05 = { by lemma 34 }
% 17.99/3.05 tuple(x1(ld(X, X)), mult(mult(x1_2(ld(X, X)), ld(x1_2(ld(X, X)), x1_2(ld(X, X)))), ld(x1_2(ld(X, X)), x1_2(ld(X, X)))))
% 17.99/3.05 = { by lemma 31 }
% 17.99/3.05 tuple(x1(ld(X, X)), x1_2(ld(X, X)))
% 17.99/3.05 % SZS output end Proof
% 17.99/3.05
% 17.99/3.05 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------