%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP655+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 16.52s 7.58s
% Output : Proof 17.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP655+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n014.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 27 10:32:07 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.52/7.58 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 16.52/7.58
% 16.52/7.58 % SZS status Theorem
% 16.52/7.58
% 17.33/7.64 % SZS output start Proof
% 17.33/7.64 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 17.33/7.64 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 17.33/7.64 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 17.33/7.64 Axiom 4 (f02): ld(X, mult(X, Y)) = Y.
% 17.33/7.64 Axiom 5 (f05): mult(X, mult(Y, mult(Z, Y))) = mult(mult(mult(X, Y), Z), Y).
% 17.33/7.64
% 17.33/7.64 Lemma 6: mult(rd(X, Y), mult(Y, mult(Z, Y))) = mult(mult(X, Z), Y).
% 17.33/7.64 Proof:
% 17.33/7.64 mult(rd(X, Y), mult(Y, mult(Z, Y)))
% 17.33/7.64 = { by axiom 5 (f05) }
% 17.33/7.64 mult(mult(mult(rd(X, Y), Y), Z), Y)
% 17.33/7.64 = { by axiom 2 (f03) }
% 17.33/7.64 mult(mult(X, Z), Y)
% 17.33/7.64
% 17.33/7.64 Lemma 7: rd(mult(X, mult(Y, mult(Z, Y))), Y) = mult(mult(X, Y), Z).
% 17.33/7.64 Proof:
% 17.33/7.64 rd(mult(X, mult(Y, mult(Z, Y))), Y)
% 17.33/7.64 = { by axiom 5 (f05) }
% 17.33/7.64 rd(mult(mult(mult(X, Y), Z), Y), Y)
% 17.33/7.64 = { by axiom 3 (f04) }
% 17.33/7.64 mult(mult(X, Y), Z)
% 17.33/7.64
% 17.33/7.64 Lemma 8: mult(ld(X, rd(X, Y)), Y) = ld(Y, Y).
% 17.33/7.64 Proof:
% 17.33/7.64 mult(ld(X, rd(X, Y)), Y)
% 17.33/7.64 = { by axiom 4 (f02) R->L }
% 17.33/7.64 ld(Y, mult(Y, mult(ld(X, rd(X, Y)), Y)))
% 17.33/7.64 = { by axiom 4 (f02) R->L }
% 17.33/7.64 ld(Y, ld(rd(X, Y), mult(rd(X, Y), mult(Y, mult(ld(X, rd(X, Y)), Y)))))
% 17.33/7.64 = { by lemma 6 }
% 17.33/7.64 ld(Y, ld(rd(X, Y), mult(mult(X, ld(X, rd(X, Y))), Y)))
% 17.33/7.64 = { by axiom 1 (f01) }
% 17.33/7.64 ld(Y, ld(rd(X, Y), mult(rd(X, Y), Y)))
% 17.33/7.64 = { by axiom 4 (f02) }
% 17.33/7.64 ld(Y, Y)
% 17.33/7.64
% 17.33/7.64 Lemma 9: rd(X, ld(Y, rd(Y, Z))) = mult(X, Z).
% 17.33/7.64 Proof:
% 17.33/7.64 rd(X, ld(Y, rd(Y, Z)))
% 17.33/7.64 = { by axiom 2 (f03) R->L }
% 17.33/7.64 mult(rd(rd(X, ld(Y, rd(Y, Z))), Z), Z)
% 17.33/7.64 = { by axiom 1 (f01) R->L }
% 17.33/7.64 mult(rd(rd(X, ld(Y, rd(Y, Z))), Z), mult(Z, ld(Z, Z)))
% 17.33/7.64 = { by lemma 8 R->L }
% 17.33/7.64 mult(rd(rd(X, ld(Y, rd(Y, Z))), Z), mult(Z, mult(ld(Y, rd(Y, Z)), Z)))
% 17.33/7.64 = { by lemma 6 }
% 17.33/7.64 mult(mult(rd(X, ld(Y, rd(Y, Z))), ld(Y, rd(Y, Z))), Z)
% 17.33/7.64 = { by axiom 2 (f03) }
% 17.33/7.64 mult(X, Z)
% 17.33/7.64
% 17.33/7.64 Lemma 10: mult(X, ld(Y, rd(Y, Z))) = rd(X, Z).
% 17.33/7.64 Proof:
% 17.33/7.64 mult(X, ld(Y, rd(Y, Z)))
% 17.33/7.64 = { by axiom 3 (f04) R->L }
% 17.33/7.64 mult(X, rd(mult(ld(Y, rd(Y, Z)), Z), Z))
% 17.33/7.64 = { by lemma 8 }
% 17.33/7.64 mult(X, rd(ld(Z, Z), Z))
% 17.33/7.64 = { by lemma 8 R->L }
% 17.33/7.64 mult(X, rd(mult(ld(X, rd(X, Z)), Z), Z))
% 17.33/7.64 = { by axiom 3 (f04) }
% 17.33/7.64 mult(X, ld(X, rd(X, Z)))
% 17.33/7.64 = { by axiom 1 (f01) }
% 17.33/7.64 rd(X, Z)
% 17.33/7.64
% 17.33/7.64 Lemma 11: rd(mult(X, mult(Y, Z)), Y) = mult(mult(X, Y), rd(Z, Y)).
% 17.33/7.64 Proof:
% 17.33/7.64 rd(mult(X, mult(Y, Z)), Y)
% 17.33/7.64 = { by axiom 2 (f03) R->L }
% 17.33/7.64 rd(mult(X, mult(Y, mult(rd(Z, Y), Y))), Y)
% 17.33/7.64 = { by lemma 7 }
% 17.33/7.64 mult(mult(X, Y), rd(Z, Y))
% 17.33/7.64
% 17.33/7.64 Lemma 12: mult(X, rd(X, X)) = X.
% 17.33/7.64 Proof:
% 17.33/7.64 mult(X, rd(X, X))
% 17.33/7.64 = { by axiom 3 (f04) R->L }
% 17.33/7.64 rd(mult(mult(X, rd(X, X)), X), X)
% 17.33/7.64 = { by lemma 6 R->L }
% 17.33/7.64 rd(mult(rd(X, X), mult(X, mult(rd(X, X), X))), X)
% 17.33/7.64 = { by axiom 2 (f03) }
% 17.33/7.64 rd(mult(rd(X, X), mult(X, X)), X)
% 17.33/7.64 = { by lemma 9 R->L }
% 17.33/7.64 rd(mult(rd(X, X), rd(X, ld(Y, rd(Y, X)))), X)
% 17.33/7.64 = { by lemma 10 R->L }
% 17.33/7.64 rd(mult(mult(X, ld(Y, rd(Y, X))), rd(X, ld(Y, rd(Y, X)))), X)
% 17.33/7.64 = { by lemma 11 R->L }
% 17.33/7.64 rd(rd(mult(X, mult(ld(Y, rd(Y, X)), X)), ld(Y, rd(Y, X))), X)
% 17.33/7.64 = { by lemma 8 }
% 17.33/7.64 rd(rd(mult(X, ld(X, X)), ld(Y, rd(Y, X))), X)
% 17.33/7.64 = { by lemma 9 }
% 17.33/7.64 rd(mult(mult(X, ld(X, X)), X), X)
% 17.33/7.64 = { by axiom 3 (f04) }
% 17.33/7.64 mult(X, ld(X, X))
% 17.33/7.64 = { by axiom 1 (f01) }
% 17.33/7.65 X
% 17.33/7.65
% 17.33/7.65 Lemma 13: mult(rd(X, X), rd(X, X)) = rd(X, X).
% 17.33/7.65 Proof:
% 17.33/7.65 mult(rd(X, X), rd(X, X))
% 17.33/7.65 = { by axiom 3 (f04) R->L }
% 17.33/7.65 rd(mult(mult(rd(X, X), rd(X, X)), X), X)
% 17.33/7.65 = { by lemma 7 R->L }
% 17.33/7.65 rd(rd(mult(rd(X, X), mult(rd(X, X), mult(X, rd(X, X)))), rd(X, X)), X)
% 17.33/7.65 = { by lemma 12 }
% 17.33/7.65 rd(rd(mult(rd(X, X), mult(rd(X, X), X)), rd(X, X)), X)
% 17.33/7.65 = { by axiom 2 (f03) }
% 17.33/7.65 rd(rd(mult(rd(X, X), X), rd(X, X)), X)
% 17.33/7.65 = { by axiom 2 (f03) }
% 17.33/7.65 rd(rd(X, rd(X, X)), X)
% 17.33/7.65 = { by lemma 12 R->L }
% 17.33/7.65 rd(rd(mult(X, rd(X, X)), rd(X, X)), X)
% 17.33/7.65 = { by axiom 3 (f04) }
% 17.33/7.65 rd(X, X)
% 17.33/7.65
% 17.33/7.65 Lemma 14: mult(mult(X, rd(Y, Y)), rd(Y, Y)) = X.
% 17.33/7.65 Proof:
% 17.33/7.65 mult(mult(X, rd(Y, Y)), rd(Y, Y))
% 17.33/7.65 = { by lemma 6 R->L }
% 17.33/7.65 mult(rd(X, rd(Y, Y)), mult(rd(Y, Y), mult(rd(Y, Y), rd(Y, Y))))
% 17.33/7.65 = { by lemma 13 }
% 17.33/7.65 mult(rd(X, rd(Y, Y)), mult(rd(Y, Y), rd(Y, Y)))
% 17.33/7.65 = { by lemma 13 }
% 17.33/7.65 mult(rd(X, rd(Y, Y)), rd(Y, Y))
% 17.33/7.65 = { by axiom 2 (f03) }
% 17.33/7.65 X
% 17.33/7.65
% 17.33/7.65 Lemma 15: ld(mult(X, rd(Y, Y)), X) = rd(Y, Y).
% 17.33/7.65 Proof:
% 17.33/7.65 ld(mult(X, rd(Y, Y)), X)
% 17.33/7.65 = { by lemma 14 R->L }
% 17.33/7.65 ld(mult(X, rd(Y, Y)), mult(mult(X, rd(Y, Y)), rd(Y, Y)))
% 17.33/7.65 = { by axiom 4 (f02) }
% 17.33/7.65 rd(Y, Y)
% 17.33/7.65
% 17.33/7.65 Lemma 16: mult(ld(mult(X, Y), X), Y) = ld(Y, Y).
% 17.33/7.65 Proof:
% 17.33/7.65 mult(ld(mult(X, Y), X), Y)
% 17.33/7.65 = { by axiom 4 (f02) R->L }
% 17.33/7.65 ld(Y, mult(Y, mult(ld(mult(X, Y), X), Y)))
% 17.33/7.65 = { by axiom 4 (f02) R->L }
% 17.33/7.65 ld(Y, ld(X, mult(X, mult(Y, mult(ld(mult(X, Y), X), Y)))))
% 17.33/7.65 = { by axiom 5 (f05) }
% 17.33/7.65 ld(Y, ld(X, mult(mult(mult(X, Y), ld(mult(X, Y), X)), Y)))
% 17.33/7.65 = { by axiom 1 (f01) }
% 17.33/7.65 ld(Y, ld(X, mult(X, Y)))
% 17.33/7.65 = { by axiom 4 (f02) }
% 17.33/7.65 ld(Y, Y)
% 17.33/7.65
% 17.33/7.65 Lemma 17: mult(mult(X, ld(mult(Y, Z), Y)), Z) = X.
% 17.33/7.65 Proof:
% 17.33/7.65 mult(mult(X, ld(mult(Y, Z), Y)), Z)
% 17.33/7.65 = { by lemma 6 R->L }
% 17.33/7.65 mult(rd(X, Z), mult(Z, mult(ld(mult(Y, Z), Y), Z)))
% 17.33/7.65 = { by lemma 16 }
% 17.33/7.65 mult(rd(X, Z), mult(Z, ld(Z, Z)))
% 17.33/7.65 = { by axiom 1 (f01) }
% 17.33/7.65 mult(rd(X, Z), Z)
% 17.33/7.65 = { by axiom 2 (f03) }
% 17.33/7.65 X
% 17.33/7.65
% 17.33/7.65 Lemma 18: rd(X, ld(mult(Y, Z), Y)) = mult(X, Z).
% 17.33/7.65 Proof:
% 17.33/7.65 rd(X, ld(mult(Y, Z), Y))
% 17.33/7.65 = { by lemma 17 R->L }
% 17.33/7.65 mult(mult(rd(X, ld(mult(Y, Z), Y)), ld(mult(Y, Z), Y)), Z)
% 17.33/7.65 = { by axiom 2 (f03) }
% 17.33/7.65 mult(X, Z)
% 17.33/7.65
% 17.33/7.65 Lemma 19: rd(X, rd(Y, Y)) = mult(X, rd(Y, Y)).
% 17.33/7.65 Proof:
% 17.33/7.65 rd(X, rd(Y, Y))
% 17.33/7.65 = { by lemma 15 R->L }
% 17.33/7.65 rd(X, ld(mult(Z, rd(Y, Y)), Z))
% 17.33/7.65 = { by lemma 18 }
% 17.33/7.65 mult(X, rd(Y, Y))
% 17.33/7.65
% 17.33/7.65 Lemma 20: ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(Y, Y))) = mult(rd(Y, Y), mult(rd(X, X), rd(Y, Y))).
% 17.33/7.65 Proof:
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(Y, Y)))
% 17.33/7.65 = { by lemma 15 R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), ld(mult(rd(X, X), rd(Y, Y)), rd(X, X))))
% 17.33/7.65 = { by lemma 13 R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 19 R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 13 R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(rd(X, X), rd(X, X)), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by axiom 1 (f01) R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(mult(rd(X, X), ld(rd(X, X), rd(X, X))), rd(X, X)), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 18 R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(rd(mult(rd(X, X), ld(rd(X, X), rd(X, X))), ld(mult(Z, rd(X, X)), Z)), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 16 R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(rd(mult(rd(X, X), mult(ld(mult(Z, rd(X, X)), Z), rd(X, X))), ld(mult(Z, rd(X, X)), Z)), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 11 }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(mult(rd(X, X), ld(mult(Z, rd(X, X)), Z)), rd(rd(X, X), ld(mult(Z, rd(X, X)), Z))), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by axiom 3 (f04) R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(rd(mult(mult(rd(X, X), ld(mult(Z, rd(X, X)), Z)), rd(X, X)), rd(X, X)), rd(rd(X, X), ld(mult(Z, rd(X, X)), Z))), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 17 }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(rd(rd(X, X), rd(X, X)), rd(rd(X, X), ld(mult(Z, rd(X, X)), Z))), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 18 }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(rd(rd(X, X), rd(X, X)), mult(rd(X, X), rd(X, X))), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by axiom 1 (f01) R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(mult(mult(rd(X, X), rd(Y, Y)), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))), mult(rd(X, X), rd(X, X))), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by axiom 5 (f05) R->L }
% 17.33/7.65 ld(mult(rd(X, X), rd(Y, Y)), mult(mult(rd(X, X), rd(Y, Y)), mult(ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X))), mult(mult(rd(X, X), rd(X, X)), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))))
% 17.33/7.65 = { by axiom 4 (f02) }
% 17.33/7.65 mult(ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X))), mult(mult(rd(X, X), rd(X, X)), ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 19 }
% 17.33/7.65 mult(ld(mult(rd(X, X), rd(Y, Y)), rd(rd(X, X), rd(X, X))), mult(mult(rd(X, X), rd(X, X)), ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 19 }
% 17.33/7.65 mult(ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(X, X))), mult(mult(rd(X, X), rd(X, X)), ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(X, X)))))
% 17.33/7.65 = { by lemma 13 }
% 17.33/7.65 mult(ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(X, X))), mult(mult(rd(X, X), rd(X, X)), ld(mult(rd(X, X), rd(Y, Y)), rd(X, X))))
% 17.33/7.65 = { by lemma 13 }
% 17.33/7.65 mult(ld(mult(rd(X, X), rd(Y, Y)), mult(rd(X, X), rd(X, X))), mult(rd(X, X), ld(mult(rd(X, X), rd(Y, Y)), rd(X, X))))
% 17.33/7.65 = { by lemma 13 }
% 17.33/7.65 mult(ld(mult(rd(X, X), rd(Y, Y)), rd(X, X)), mult(rd(X, X), ld(mult(rd(X, X), rd(Y, Y)), rd(X, X))))
% 17.33/7.65 = { by lemma 15 }
% 17.33/7.65 mult(rd(Y, Y), mult(rd(X, X), ld(mult(rd(X, X), rd(Y, Y)), rd(X, X))))
% 17.33/7.65 = { by lemma 15 }
% 17.33/7.65 mult(rd(Y, Y), mult(rd(X, X), rd(Y, Y)))
% 17.33/7.65
% 17.33/7.65 Lemma 21: ld(X, rd(X, Y)) = rd(ld(Y, Y), Y).
% 17.33/7.65 Proof:
% 17.33/7.65 ld(X, rd(X, Y))
% 17.33/7.66 = { by axiom 3 (f04) R->L }
% 17.33/7.66 rd(mult(ld(X, rd(X, Y)), Y), Y)
% 17.33/7.66 = { by lemma 8 }
% 17.33/7.66 rd(ld(Y, Y), Y)
% 17.33/7.66
% 17.33/7.66 Lemma 22: mult(X, rd(ld(Y, Y), Y)) = rd(X, Y).
% 17.33/7.66 Proof:
% 17.33/7.66 mult(X, rd(ld(Y, Y), Y))
% 17.33/7.66 = { by lemma 21 R->L }
% 17.33/7.66 mult(X, ld(Z, rd(Z, Y)))
% 17.33/7.66 = { by lemma 10 }
% 17.33/7.66 rd(X, Y)
% 17.33/7.66
% 17.33/7.66 Lemma 23: rd(Y, Y) = rd(X, X).
% 17.33/7.66 Proof:
% 17.33/7.66 rd(Y, Y)
% 17.33/7.66 = { by lemma 14 R->L }
% 17.33/7.66 mult(mult(rd(Y, Y), rd(X, X)), rd(X, X))
% 17.33/7.66 = { by axiom 3 (f04) R->L }
% 17.33/7.66 mult(mult(rd(Y, Y), rd(X, X)), rd(mult(rd(X, X), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by lemma 20 R->L }
% 17.33/7.66 mult(mult(rd(Y, Y), rd(X, X)), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by lemma 22 }
% 17.33/7.66 rd(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X)))
% 17.33/7.66 = { by axiom 4 (f02) R->L }
% 17.33/7.66 rd(ld(Z, mult(Z, mult(rd(Y, Y), rd(X, X)))), mult(rd(Y, Y), rd(X, X)))
% 17.33/7.66 = { by lemma 22 R->L }
% 17.33/7.66 mult(ld(Z, mult(Z, mult(rd(Y, Y), rd(X, X)))), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by axiom 3 (f04) R->L }
% 17.33/7.66 mult(ld(Z, rd(mult(mult(Z, mult(rd(Y, Y), rd(X, X))), ld(mult(Z, mult(rd(Y, Y), rd(X, X))), Z)), ld(mult(Z, mult(rd(Y, Y), rd(X, X))), Z))), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by axiom 1 (f01) }
% 17.33/7.66 mult(ld(Z, rd(Z, ld(mult(Z, mult(rd(Y, Y), rd(X, X))), Z))), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by axiom 3 (f04) R->L }
% 17.33/7.66 mult(ld(Z, rd(Z, ld(mult(Z, mult(rd(Y, Y), rd(X, X))), rd(mult(Z, mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X)))))), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by lemma 21 }
% 17.33/7.66 mult(ld(Z, rd(Z, rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by lemma 8 }
% 17.33/7.66 ld(rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by lemma 20 }
% 17.33/7.66 ld(rd(mult(rd(X, X), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by axiom 3 (f04) }
% 17.33/7.66 ld(rd(X, X), rd(ld(mult(rd(Y, Y), rd(X, X)), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by lemma 20 }
% 17.33/7.66 ld(rd(X, X), rd(mult(rd(X, X), mult(rd(Y, Y), rd(X, X))), mult(rd(Y, Y), rd(X, X))))
% 17.33/7.66 = { by axiom 3 (f04) }
% 17.33/7.66 ld(rd(X, X), rd(X, X))
% 17.33/7.66 = { by lemma 13 R->L }
% 17.33/7.66 ld(rd(X, X), mult(rd(X, X), rd(X, X)))
% 17.33/7.66 = { by axiom 4 (f02) }
% 17.33/7.66 rd(X, X)
% 17.33/7.66
% 17.33/7.66 Goal 1 (goals): tuple(mult(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2))) = tuple(x0, x0_2).
% 17.33/7.66 Proof:
% 17.33/7.66 tuple(mult(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2)))
% 17.33/7.66 = { by lemma 12 R->L }
% 17.33/7.66 tuple(mult(rd(x1, x1), x0), mult(mult(x0_2, rd(x1_2, x1_2)), rd(mult(x0_2, rd(x1_2, x1_2)), mult(x0_2, rd(x1_2, x1_2)))))
% 17.33/7.66 = { by lemma 23 R->L }
% 17.33/7.66 tuple(mult(rd(x1, x1), x0), mult(mult(x0_2, rd(x1_2, x1_2)), rd(x1_2, x1_2)))
% 17.33/7.66 = { by lemma 14 }
% 17.33/7.66 tuple(mult(rd(x1, x1), x0), x0_2)
% 17.33/7.66 = { by lemma 23 }
% 17.33/7.66 tuple(mult(rd(x0, x0), x0), x0_2)
% 17.33/7.66 = { by axiom 2 (f03) }
% 17.33/7.66 tuple(x0, x0_2)
% 17.33/7.66 % SZS output end Proof
% 17.33/7.66
% 17.33/7.66 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------