%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP685+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:11:43 AM UTC 2026
% Result : Theorem 1.61s 0.65s
% Output : Proof 2.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP685+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 10:35:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.61/0.65 Command-line arguments: --no-flatten-goal
% 1.61/0.65
% 1.61/0.65 % SZS status Theorem
% 1.61/0.65
% 2.18/0.71 % SZS output start Proof
% 2.18/0.71 Axiom 1 (f01): ld(X, mult(X, X)) = X.
% 2.18/0.71 Axiom 2 (f02): rd(mult(X, X), X) = X.
% 2.18/0.71 Axiom 3 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 2.18/0.71 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 2.18/0.71 Axiom 5 (f07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 2.18/0.71 Axiom 6 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 2.18/0.71 Axiom 7 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 2.18/0.71
% 2.18/0.71 Lemma 8: rd(X, X) = ld(X, X).
% 2.18/0.71 Proof:
% 2.18/0.71 rd(X, X)
% 2.18/0.71 = { by axiom 2 (f02) R->L }
% 2.18/0.71 rd(rd(mult(X, X), X), X)
% 2.18/0.71 = { by axiom 4 (f04) R->L }
% 2.18/0.71 rd(mult(rd(X, X), X), X)
% 2.18/0.71 = { by axiom 5 (f07) R->L }
% 2.18/0.71 ld(X, mult(X, ld(X, X)))
% 2.18/0.71 = { by axiom 3 (f03) }
% 2.18/0.71 ld(X, ld(X, mult(X, X)))
% 2.18/0.71 = { by axiom 1 (f01) }
% 2.18/0.71 ld(X, X)
% 2.18/0.71
% 2.18/0.71 Lemma 9: mult(ld(X, mult(X, Y)), Z) = ld(X, mult(X, mult(Y, Z))).
% 2.18/0.71 Proof:
% 2.18/0.71 mult(ld(X, mult(X, Y)), Z)
% 2.18/0.71 = { by axiom 6 (f05) R->L }
% 2.18/0.71 ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), mult(Y, Z)))
% 2.18/0.71 = { by axiom 1 (f01) }
% 2.18/0.71 ld(X, mult(ld(X, mult(X, X)), mult(Y, Z)))
% 2.18/0.71 = { by axiom 1 (f01) }
% 2.18/0.71 ld(X, mult(X, mult(Y, Z)))
% 2.18/0.71
% 2.18/0.71 Lemma 10: ld(X, mult(X, mult(X, Y))) = mult(X, Y).
% 2.18/0.71 Proof:
% 2.18/0.71 ld(X, mult(X, mult(X, Y)))
% 2.18/0.71 = { by lemma 9 R->L }
% 2.18/0.71 mult(ld(X, mult(X, X)), Y)
% 2.18/0.71 = { by axiom 1 (f01) }
% 2.18/0.71 mult(X, Y)
% 2.18/0.71
% 2.18/0.71 Lemma 11: mult(X, rd(mult(Y, Z), Z)) = rd(mult(mult(X, Y), Z), Z).
% 2.18/0.71 Proof:
% 2.18/0.71 mult(X, rd(mult(Y, Z), Z))
% 2.18/0.71 = { by axiom 7 (f06) R->L }
% 2.18/0.71 rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 2.18/0.71 = { by axiom 2 (f02) }
% 2.18/0.71 rd(mult(mult(X, Y), Z), rd(mult(Z, Z), Z))
% 2.18/0.71 = { by axiom 2 (f02) }
% 2.18/0.71 rd(mult(mult(X, Y), Z), Z)
% 2.18/0.71
% 2.18/0.71 Lemma 12: mult(X, ld(Y, Y)) = rd(mult(X, Y), Y).
% 2.18/0.71 Proof:
% 2.18/0.71 mult(X, ld(Y, Y))
% 2.18/0.71 = { by lemma 10 R->L }
% 2.18/0.71 ld(X, mult(X, mult(X, ld(Y, Y))))
% 2.18/0.71 = { by axiom 3 (f03) R->L }
% 2.18/0.71 mult(X, ld(X, mult(X, ld(Y, Y))))
% 2.18/0.71 = { by axiom 5 (f07) }
% 2.18/0.71 mult(X, rd(mult(rd(X, X), Y), Y))
% 2.18/0.71 = { by lemma 11 }
% 2.18/0.71 rd(mult(mult(X, rd(X, X)), Y), Y)
% 2.18/0.71 = { by lemma 8 }
% 2.18/0.71 rd(mult(mult(X, ld(X, X)), Y), Y)
% 2.18/0.71 = { by axiom 3 (f03) }
% 2.18/0.71 rd(mult(ld(X, mult(X, X)), Y), Y)
% 2.18/0.71 = { by lemma 9 }
% 2.18/0.71 rd(ld(X, mult(X, mult(X, Y))), Y)
% 2.18/0.71 = { by lemma 10 }
% 2.18/0.71 rd(mult(X, Y), Y)
% 2.18/0.71
% 2.18/0.71 Lemma 13: mult(ld(X, X), X) = X.
% 2.18/0.71 Proof:
% 2.18/0.71 mult(ld(X, X), X)
% 2.18/0.71 = { by lemma 8 R->L }
% 2.18/0.71 mult(rd(X, X), X)
% 2.18/0.71 = { by axiom 4 (f04) }
% 2.18/0.71 rd(mult(X, X), X)
% 2.18/0.71 = { by axiom 2 (f02) }
% 2.18/0.71 X
% 2.18/0.71
% 2.18/0.71 Lemma 14: rd(mult(mult(X, Y), Y), Y) = mult(X, Y).
% 2.18/0.71 Proof:
% 2.18/0.71 rd(mult(mult(X, Y), Y), Y)
% 2.18/0.71 = { by lemma 11 R->L }
% 2.18/0.71 mult(X, rd(mult(Y, Y), Y))
% 2.18/0.71 = { by axiom 2 (f02) }
% 2.18/0.71 mult(X, Y)
% 2.18/0.72
% 2.18/0.72 Lemma 15: mult(ld(X, X), Y) = ld(X, mult(X, Y)).
% 2.18/0.72 Proof:
% 2.18/0.72 mult(ld(X, X), Y)
% 2.18/0.72 = { by lemma 14 R->L }
% 2.18/0.72 rd(mult(mult(ld(X, X), Y), Y), Y)
% 2.18/0.72 = { by axiom 4 (f04) R->L }
% 2.18/0.72 mult(rd(mult(ld(X, X), Y), Y), Y)
% 2.18/0.72 = { by lemma 8 R->L }
% 2.18/0.72 mult(rd(mult(rd(X, X), Y), Y), Y)
% 2.18/0.72 = { by axiom 5 (f07) R->L }
% 2.18/0.72 mult(ld(X, mult(X, ld(Y, Y))), Y)
% 2.18/0.72 = { by lemma 9 }
% 2.18/0.72 ld(X, mult(X, mult(ld(Y, Y), Y)))
% 2.18/0.72 = { by lemma 13 }
% 2.18/0.72 ld(X, mult(X, Y))
% 2.18/0.72
% 2.18/0.72 Lemma 16: ld(ld(X, Y), mult(ld(X, Y), Z)) = ld(X, mult(X, Z)).
% 2.18/0.72 Proof:
% 2.18/0.72 ld(ld(X, Y), mult(ld(X, Y), Z))
% 2.18/0.72 = { by lemma 13 R->L }
% 2.18/0.72 ld(ld(X, Y), mult(ld(X, Y), mult(ld(Z, Z), Z)))
% 2.18/0.72 = { by axiom 6 (f05) }
% 2.18/0.72 mult(ld(X, mult(X, ld(Z, Z))), Z)
% 2.18/0.72 = { by lemma 9 }
% 2.18/0.72 ld(X, mult(X, mult(ld(Z, Z), Z)))
% 2.18/0.72 = { by lemma 13 }
% 2.18/0.72 ld(X, mult(X, Z))
% 2.18/0.72
% 2.18/0.72 Lemma 17: ld(ld(X, X), ld(X, X)) = ld(X, X).
% 2.18/0.72 Proof:
% 2.18/0.72 ld(ld(X, X), ld(X, X))
% 2.18/0.72 = { by axiom 1 (f01) R->L }
% 2.18/0.72 ld(ld(X, X), ld(X, ld(X, mult(X, X))))
% 2.18/0.72 = { by axiom 3 (f03) R->L }
% 2.18/0.72 ld(ld(X, X), ld(X, mult(X, ld(X, X))))
% 2.18/0.72 = { by lemma 15 R->L }
% 2.18/0.72 ld(ld(X, X), mult(ld(X, X), ld(X, X)))
% 2.18/0.72 = { by axiom 1 (f01) }
% 2.18/0.72 ld(X, X)
% 2.18/0.72
% 2.18/0.72 Lemma 18: ld(ld(X, X), ld(X, mult(X, Y))) = ld(X, mult(X, Y)).
% 2.18/0.72 Proof:
% 2.18/0.72 ld(ld(X, X), ld(X, mult(X, Y)))
% 2.18/0.72 = { by lemma 15 R->L }
% 2.18/0.72 ld(ld(X, X), mult(ld(X, X), Y))
% 2.18/0.72 = { by lemma 16 }
% 2.18/0.72 ld(X, mult(X, Y))
% 2.18/0.72
% 2.18/0.72 Lemma 19: ld(ld(X, X), Y) = ld(X, mult(X, Y)).
% 2.18/0.72 Proof:
% 2.18/0.72 ld(ld(X, X), Y)
% 2.18/0.72 = { by axiom 1 (f01) R->L }
% 2.18/0.72 ld(ld(ld(X, X), Y), mult(ld(ld(X, X), Y), ld(ld(X, X), Y)))
% 2.18/0.72 = { by lemma 16 }
% 2.18/0.72 ld(ld(X, X), mult(ld(X, X), ld(ld(X, X), Y)))
% 2.18/0.72 = { by axiom 3 (f03) }
% 2.18/0.72 ld(ld(X, X), ld(ld(X, X), mult(ld(X, X), Y)))
% 2.18/0.72 = { by lemma 17 R->L }
% 2.18/0.72 ld(ld(ld(X, X), ld(X, X)), ld(ld(X, X), mult(ld(X, X), Y)))
% 2.18/0.72 = { by lemma 18 }
% 2.18/0.72 ld(ld(X, X), mult(ld(X, X), Y))
% 2.18/0.72 = { by lemma 16 }
% 2.18/0.72 ld(X, mult(X, Y))
% 2.18/0.72
% 2.18/0.72 Lemma 20: rd(mult(X, ld(Y, Y)), ld(Y, Y)) = rd(mult(X, Y), Y).
% 2.18/0.72 Proof:
% 2.18/0.72 rd(mult(X, ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 13 R->L }
% 2.18/0.72 rd(mult(mult(ld(X, X), X), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 8 R->L }
% 2.18/0.72 rd(mult(mult(ld(X, X), X), ld(Y, Y)), rd(Y, Y))
% 2.18/0.72 = { by lemma 8 R->L }
% 2.18/0.72 rd(mult(mult(ld(X, X), X), rd(Y, Y)), rd(Y, Y))
% 2.18/0.72 = { by axiom 7 (f06) }
% 2.18/0.72 mult(ld(X, X), rd(mult(X, Y), Y))
% 2.18/0.72 = { by lemma 11 }
% 2.18/0.72 rd(mult(mult(ld(X, X), X), Y), Y)
% 2.18/0.72 = { by lemma 13 }
% 2.18/0.72 rd(mult(X, Y), Y)
% 2.18/0.72
% 2.18/0.72 Lemma 21: rd(mult(rd(X, ld(Y, Y)), Y), Y) = rd(X, ld(Y, Y)).
% 2.18/0.72 Proof:
% 2.18/0.72 rd(mult(rd(X, ld(Y, Y)), Y), Y)
% 2.18/0.72 = { by lemma 20 R->L }
% 2.18/0.72 rd(mult(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 13 R->L }
% 2.18/0.72 rd(mult(mult(ld(rd(X, ld(Y, Y)), rd(X, ld(Y, Y))), rd(X, ld(Y, Y))), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 11 R->L }
% 2.18/0.72 mult(ld(rd(X, ld(Y, Y)), rd(X, ld(Y, Y))), rd(mult(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y)))
% 2.18/0.72 = { by axiom 7 (f06) R->L }
% 2.18/0.72 rd(mult(mult(ld(rd(X, ld(Y, Y)), rd(X, ld(Y, Y))), rd(X, ld(Y, Y))), rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))
% 2.18/0.72 = { by lemma 14 }
% 2.18/0.72 mult(ld(rd(X, ld(Y, Y)), rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))
% 2.18/0.72 = { by lemma 13 }
% 2.18/0.72 rd(X, ld(Y, Y))
% 2.18/0.72
% 2.18/0.72 Lemma 22: rd(mult(X, Y), Y) = rd(X, ld(Y, Y)).
% 2.18/0.72 Proof:
% 2.18/0.72 rd(mult(X, Y), Y)
% 2.18/0.72 = { by lemma 20 R->L }
% 2.18/0.72 rd(mult(X, ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by axiom 4 (f04) R->L }
% 2.18/0.72 mult(rd(X, ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 17 R->L }
% 2.18/0.72 mult(rd(X, ld(ld(Y, Y), ld(Y, Y))), ld(Y, Y))
% 2.18/0.72 = { by lemma 21 R->L }
% 2.18/0.72 mult(rd(mult(rd(X, ld(ld(Y, Y), ld(Y, Y))), ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 12 }
% 2.18/0.72 mult(rd(rd(mult(rd(X, ld(ld(Y, Y), ld(Y, Y))), Y), Y), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 17 }
% 2.18/0.72 mult(rd(rd(mult(rd(X, ld(Y, Y)), Y), Y), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 21 }
% 2.18/0.72 mult(rd(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by axiom 4 (f04) }
% 2.18/0.72 rd(mult(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
% 2.18/0.72 = { by lemma 20 }
% 2.18/0.72 rd(mult(rd(X, ld(Y, Y)), Y), Y)
% 2.18/0.72 = { by lemma 21 }
% 2.18/0.72 rd(X, ld(Y, Y))
% 2.18/0.72
% 2.18/0.72 Lemma 23: ld(mult(X, Y), mult(mult(X, Y), Z)) = ld(X, mult(X, Z)).
% 2.18/0.72 Proof:
% 2.18/0.72 ld(mult(X, Y), mult(mult(X, Y), Z))
% 2.18/0.72 = { by lemma 10 R->L }
% 2.18/0.72 ld(mult(X, Y), mult(ld(X, mult(X, mult(X, Y))), Z))
% 2.18/0.72 = { by lemma 10 R->L }
% 2.18/0.72 ld(ld(X, mult(X, mult(X, Y))), mult(ld(X, mult(X, mult(X, Y))), Z))
% 2.18/0.72 = { by lemma 16 }
% 2.18/0.72 ld(X, mult(X, Z))
% 2.18/0.72
% 2.18/0.72 Lemma 24: rd(mult(X, mult(Y, Z)), mult(Y, Z)) = rd(mult(X, Z), Z).
% 2.18/0.73 Proof:
% 2.18/0.73 rd(mult(X, mult(Y, Z)), mult(Y, Z))
% 2.18/0.73 = { by lemma 14 R->L }
% 2.18/0.73 rd(mult(X, mult(Y, Z)), rd(mult(mult(Y, Z), Z), Z))
% 2.18/0.73 = { by lemma 14 R->L }
% 2.18/0.73 rd(mult(X, rd(mult(mult(Y, Z), Z), Z)), rd(mult(mult(Y, Z), Z), Z))
% 2.18/0.73 = { by lemma 13 R->L }
% 2.18/0.73 rd(mult(mult(ld(X, X), X), rd(mult(mult(Y, Z), Z), Z)), rd(mult(mult(Y, Z), Z), Z))
% 2.18/0.73 = { by axiom 7 (f06) }
% 2.18/0.73 mult(ld(X, X), rd(mult(X, Z), Z))
% 2.18/0.73 = { by axiom 7 (f06) R->L }
% 2.18/0.73 rd(mult(mult(ld(X, X), X), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 2.18/0.73 = { by lemma 13 }
% 2.18/0.73 rd(mult(X, rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 2.18/0.73 = { by axiom 2 (f02) }
% 2.18/0.73 rd(mult(X, Z), rd(mult(Z, Z), Z))
% 2.18/0.73 = { by axiom 2 (f02) }
% 2.18/0.73 rd(mult(X, Z), Z)
% 2.18/0.73
% 2.18/0.73 Lemma 25: rd(mult(X, Y), ld(Z, mult(Z, Y))) = rd(X, ld(ld(Z, Y), ld(Z, Y))).
% 2.18/0.73 Proof:
% 2.18/0.73 rd(mult(X, Y), ld(Z, mult(Z, Y)))
% 2.18/0.73 = { by axiom 3 (f03) R->L }
% 2.18/0.73 rd(mult(X, Y), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 10 R->L }
% 2.18/0.73 rd(ld(X, mult(X, mult(X, Y))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by axiom 3 (f03) R->L }
% 2.18/0.73 rd(mult(X, ld(X, mult(X, Y))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 23 R->L }
% 2.18/0.73 rd(mult(X, ld(mult(X, ld(Z, Z)), mult(mult(X, ld(Z, Z)), Y))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 15 R->L }
% 2.18/0.73 rd(mult(X, mult(ld(mult(X, ld(Z, Z)), mult(X, ld(Z, Z))), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 8 R->L }
% 2.18/0.73 rd(mult(X, mult(ld(mult(X, rd(Z, Z)), mult(X, ld(Z, Z))), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 13 R->L }
% 2.18/0.73 rd(mult(X, mult(ld(mult(X, rd(mult(ld(Z, Z), Z), Z)), mult(X, ld(Z, Z))), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 11 }
% 2.18/0.73 rd(mult(X, mult(ld(rd(mult(mult(X, ld(Z, Z)), Z), Z), mult(X, ld(Z, Z))), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 12 R->L }
% 2.18/0.73 rd(mult(X, mult(ld(mult(mult(X, ld(Z, Z)), ld(Z, Z)), mult(X, ld(Z, Z))), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 14 R->L }
% 2.18/0.73 rd(mult(X, mult(ld(mult(mult(X, ld(Z, Z)), ld(Z, Z)), rd(mult(mult(X, ld(Z, Z)), ld(Z, Z)), ld(Z, Z))), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 22 R->L }
% 2.18/0.73 rd(mult(X, mult(ld(mult(mult(X, ld(Z, Z)), ld(Z, Z)), rd(mult(mult(mult(X, ld(Z, Z)), ld(Z, Z)), Z), Z)), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 12 R->L }
% 2.18/0.73 rd(mult(X, mult(ld(mult(mult(X, ld(Z, Z)), ld(Z, Z)), mult(mult(mult(X, ld(Z, Z)), ld(Z, Z)), ld(Z, Z))), Y)), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 9 }
% 2.18/0.73 rd(mult(X, ld(mult(mult(X, ld(Z, Z)), ld(Z, Z)), mult(mult(mult(X, ld(Z, Z)), ld(Z, Z)), mult(ld(Z, Z), Y)))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 15 }
% 2.18/0.73 rd(mult(X, ld(mult(mult(X, ld(Z, Z)), ld(Z, Z)), mult(mult(mult(X, ld(Z, Z)), ld(Z, Z)), ld(Z, mult(Z, Y))))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 23 }
% 2.18/0.73 rd(mult(X, ld(mult(X, ld(Z, Z)), mult(mult(X, ld(Z, Z)), ld(Z, mult(Z, Y))))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 23 }
% 2.18/0.73 rd(mult(X, ld(X, mult(X, ld(Z, mult(Z, Y))))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by axiom 3 (f03) }
% 2.18/0.73 rd(ld(X, mult(X, mult(X, ld(Z, mult(Z, Y))))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 10 }
% 2.18/0.73 rd(mult(X, ld(Z, mult(Z, Y))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by axiom 3 (f03) R->L }
% 2.18/0.73 rd(mult(X, mult(Z, ld(Z, Y))), mult(Z, ld(Z, Y)))
% 2.18/0.73 = { by lemma 24 }
% 2.18/0.73 rd(mult(X, ld(Z, Y)), ld(Z, Y))
% 2.18/0.73 = { by lemma 22 }
% 2.18/0.73 rd(X, ld(ld(Z, Y), ld(Z, Y)))
% 2.18/0.73
% 2.18/0.73 Goal 1 (goals): tuple(rd(mult(x6_2, ld(x7_2, x8_2)), ld(x7_2, x8_2)), rd(mult(x6, rd(x7, x8)), rd(x7, x8))) = tuple(rd(mult(x6_2, x8_2), x8_2), rd(mult(x6, x8), x8)).
% 2.18/0.73 Proof:
% 2.18/0.73 tuple(rd(mult(x6_2, ld(x7_2, x8_2)), ld(x7_2, x8_2)), rd(mult(x6, rd(x7, x8)), rd(x7, x8)))
% 2.18/0.73 = { by lemma 13 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, ld(x7_2, x8_2)), ld(x7_2, x8_2)), rd(mult(mult(ld(x6, x6), x6), rd(x7, x8)), rd(x7, x8)))
% 2.18/0.73 = { by axiom 7 (f06) }
% 2.18/0.73 tuple(rd(mult(x6_2, ld(x7_2, x8_2)), ld(x7_2, x8_2)), mult(ld(x6, x6), rd(mult(x6, x8), x8)))
% 2.18/0.73 = { by lemma 15 }
% 2.18/0.73 tuple(rd(mult(x6_2, ld(x7_2, x8_2)), ld(x7_2, x8_2)), ld(x6, mult(x6, rd(mult(x6, x8), x8))))
% 2.18/0.73 = { by lemma 11 }
% 2.18/0.73 tuple(rd(mult(x6_2, ld(x7_2, x8_2)), ld(x7_2, x8_2)), ld(x6, rd(mult(mult(x6, x6), x8), x8)))
% 2.18/0.73 = { by lemma 22 }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, x8_2), ld(x7_2, x8_2))), ld(x6, rd(mult(mult(x6, x6), x8), x8)))
% 2.18/0.73 = { by lemma 11 R->L }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, x8_2), ld(x7_2, x8_2))), ld(x6, mult(x6, rd(mult(x6, x8), x8))))
% 2.18/0.73 = { by lemma 12 R->L }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, x8_2), ld(x7_2, x8_2))), ld(x6, mult(x6, mult(x6, ld(x8, x8)))))
% 2.18/0.73 = { by lemma 10 }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, x8_2), ld(x7_2, x8_2))), mult(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 12 }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, x8_2), ld(x7_2, x8_2))), rd(mult(x6, x8), x8))
% 2.18/0.73 = { by lemma 22 }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, x8_2), ld(x7_2, x8_2))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 25 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, x8_2), ld(x7_2, mult(x7_2, x8_2))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 18 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, x8_2), ld(ld(x7_2, x7_2), ld(x7_2, mult(x7_2, x8_2)))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 15 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, x8_2), ld(ld(x7_2, x7_2), mult(ld(x7_2, x7_2), x8_2))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 25 }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(ld(x7_2, x7_2), x8_2), ld(ld(x7_2, x7_2), x8_2))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 19 }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, mult(x7_2, x8_2)), ld(ld(x7_2, x7_2), x8_2))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 19 }
% 2.18/0.73 tuple(rd(x6_2, ld(ld(x7_2, mult(x7_2, x8_2)), ld(x7_2, mult(x7_2, x8_2)))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 22 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, ld(x7_2, mult(x7_2, x8_2))), ld(x7_2, mult(x7_2, x8_2))), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 15 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, ld(x7_2, mult(x7_2, x8_2))), mult(ld(x7_2, x7_2), x8_2)), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 15 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, mult(ld(x7_2, x7_2), x8_2)), mult(ld(x7_2, x7_2), x8_2)), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 24 }
% 2.18/0.73 tuple(rd(mult(x6_2, x8_2), x8_2), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 22 }
% 2.18/0.73 tuple(rd(x6_2, ld(x8_2, x8_2)), rd(x6, ld(x8, x8)))
% 2.18/0.73 = { by lemma 22 R->L }
% 2.18/0.73 tuple(rd(x6_2, ld(x8_2, x8_2)), rd(mult(x6, x8), x8))
% 2.18/0.73 = { by lemma 22 R->L }
% 2.18/0.73 tuple(rd(mult(x6_2, x8_2), x8_2), rd(mult(x6, x8), x8))
% 2.18/0.73 % SZS output end Proof
% 2.18/0.73
% 2.18/0.73 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------