%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP655+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 22.79s 3.30s
% Output : Proof 22.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP655+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 10:34:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.79/3.30 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 22.79/3.30
% 22.79/3.30 % SZS status Theorem
% 22.79/3.30
% 22.79/3.37 % SZS output start Proof
% 22.79/3.37 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 22.79/3.37 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 22.79/3.37 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 22.79/3.37 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 22.79/3.37 Axiom 5 (f05): mult(X, mult(Y, mult(Z, Y))) = mult(mult(mult(X, Y), Z), Y).
% 22.79/3.37
% 22.79/3.37 Lemma 6: mult(rd(X, Y), mult(Y, mult(Z, Y))) = mult(mult(X, Z), Y).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(rd(X, Y), mult(Y, mult(Z, Y)))
% 22.79/3.37 = { by axiom 5 (f05) }
% 22.79/3.37 mult(mult(mult(rd(X, Y), Y), Z), Y)
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.37 mult(mult(X, Z), Y)
% 22.79/3.37
% 22.79/3.37 Lemma 7: mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))) = mult(mult(Y, Z), ld(X, Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(X, mult(ld(X, Y), mult(Z, ld(X, Y))))
% 22.79/3.37 = { by axiom 5 (f05) }
% 22.79/3.37 mult(mult(mult(X, ld(X, Y)), Z), ld(X, Y))
% 22.79/3.37 = { by axiom 1 (f01) }
% 22.79/3.37 mult(mult(Y, Z), ld(X, Y))
% 22.79/3.37
% 22.79/3.37 Lemma 8: ld(X, mult(mult(Y, Z), ld(X, Y))) = mult(ld(X, Y), mult(Z, ld(X, Y))).
% 22.79/3.37 Proof:
% 22.79/3.37 ld(X, mult(mult(Y, Z), ld(X, Y)))
% 22.79/3.37 = { by lemma 7 R->L }
% 22.79/3.37 ld(X, mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))))
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 mult(ld(X, Y), mult(Z, ld(X, Y)))
% 22.79/3.37
% 22.79/3.37 Lemma 9: mult(ld(X, Y), mult(ld(Y, X), ld(X, Y))) = ld(X, Y).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(ld(X, Y), mult(ld(Y, X), ld(X, Y)))
% 22.79/3.37 = { by lemma 8 R->L }
% 22.79/3.37 ld(X, mult(mult(Y, ld(Y, X)), ld(X, Y)))
% 22.79/3.37 = { by axiom 1 (f01) }
% 22.79/3.37 ld(X, mult(X, ld(X, Y)))
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 ld(X, Y)
% 22.79/3.37
% 22.79/3.37 Lemma 10: mult(mult(X, ld(Y, Z)), ld(Z, Y)) = X.
% 22.79/3.37 Proof:
% 22.79/3.37 mult(mult(X, ld(Y, Z)), ld(Z, Y))
% 22.79/3.37 = { by lemma 6 R->L }
% 22.79/3.37 mult(rd(X, ld(Z, Y)), mult(ld(Z, Y), mult(ld(Y, Z), ld(Z, Y))))
% 22.79/3.37 = { by lemma 9 }
% 22.79/3.37 mult(rd(X, ld(Z, Y)), ld(Z, Y))
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.37 X
% 22.79/3.37
% 22.79/3.37 Lemma 11: mult(mult(X, rd(Y, ld(Z, X))), ld(Z, X)) = mult(Z, mult(ld(Z, X), Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(mult(X, rd(Y, ld(Z, X))), ld(Z, X))
% 22.79/3.37 = { by lemma 7 R->L }
% 22.79/3.37 mult(Z, mult(ld(Z, X), mult(rd(Y, ld(Z, X)), ld(Z, X))))
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.37 mult(Z, mult(ld(Z, X), Y))
% 22.79/3.37
% 22.79/3.37 Lemma 12: rd(X, ld(Y, Z)) = mult(X, ld(Z, Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 rd(X, ld(Y, Z))
% 22.79/3.37 = { by lemma 10 R->L }
% 22.79/3.37 mult(mult(rd(X, ld(Y, Z)), ld(Y, Z)), ld(Z, Y))
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.37 mult(X, ld(Z, Y))
% 22.79/3.37
% 22.79/3.37 Lemma 13: mult(mult(X, mult(ld(X, Y), Z)), ld(Y, X)) = mult(Y, mult(Z, ld(Y, X))).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(mult(X, mult(ld(X, Y), Z)), ld(Y, X))
% 22.79/3.37 = { by lemma 11 R->L }
% 22.79/3.37 mult(mult(mult(Y, rd(Z, ld(X, Y))), ld(X, Y)), ld(Y, X))
% 22.79/3.37 = { by lemma 10 }
% 22.79/3.37 mult(Y, rd(Z, ld(X, Y)))
% 22.79/3.37 = { by lemma 12 }
% 22.79/3.37 mult(Y, mult(Z, ld(Y, X)))
% 22.79/3.37
% 22.79/3.37 Lemma 14: mult(ld(X, Y), mult(mult(ld(Y, X), Z), ld(X, Y))) = mult(Z, ld(X, Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(ld(X, Y), mult(mult(ld(Y, X), Z), ld(X, Y)))
% 22.79/3.37 = { by lemma 8 R->L }
% 22.79/3.37 ld(X, mult(mult(Y, mult(ld(Y, X), Z)), ld(X, Y)))
% 22.79/3.37 = { by lemma 13 }
% 22.79/3.37 ld(X, mult(X, mult(Z, ld(X, Y))))
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 mult(Z, ld(X, Y))
% 22.79/3.37
% 22.79/3.37 Lemma 15: rd(mult(X, mult(Y, Z)), Y) = mult(mult(X, Y), rd(Z, Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 rd(mult(X, mult(Y, Z)), Y)
% 22.79/3.37 = { by axiom 2 (f03) R->L }
% 22.79/3.37 rd(mult(X, mult(Y, mult(rd(Z, Y), Y))), Y)
% 22.79/3.37 = { by axiom 5 (f05) }
% 22.79/3.37 rd(mult(mult(mult(X, Y), rd(Z, Y)), Y), Y)
% 22.79/3.37 = { by axiom 4 (f04) }
% 22.79/3.37 mult(mult(X, Y), rd(Z, Y))
% 22.79/3.37
% 22.79/3.37 Lemma 16: mult(mult(X, Y), rd(ld(Y, Y), Y)) = X.
% 22.79/3.37 Proof:
% 22.79/3.37 mult(mult(X, Y), rd(ld(Y, Y), Y))
% 22.79/3.37 = { by lemma 15 R->L }
% 22.79/3.37 rd(mult(X, mult(Y, ld(Y, Y))), Y)
% 22.79/3.37 = { by axiom 1 (f01) }
% 22.79/3.37 rd(mult(X, Y), Y)
% 22.79/3.37 = { by axiom 4 (f04) }
% 22.79/3.37 X
% 22.79/3.37
% 22.79/3.37 Lemma 17: mult(X, rd(ld(Y, Y), Y)) = rd(X, Y).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(X, rd(ld(Y, Y), Y))
% 22.79/3.37 = { by axiom 2 (f03) R->L }
% 22.79/3.37 mult(mult(rd(X, Y), Y), rd(ld(Y, Y), Y))
% 22.79/3.37 = { by lemma 16 }
% 22.79/3.37 rd(X, Y)
% 22.79/3.37
% 22.79/3.37 Lemma 18: mult(mult(X, rd(Y, Z)), Z) = mult(rd(X, Z), mult(Z, Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(mult(X, rd(Y, Z)), Z)
% 22.79/3.37 = { by lemma 6 R->L }
% 22.79/3.37 mult(rd(X, Z), mult(Z, mult(rd(Y, Z), Z)))
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.37 mult(rd(X, Z), mult(Z, Y))
% 22.79/3.37
% 22.79/3.37 Lemma 19: ld(ld(X, Y), mult(Z, ld(X, Y))) = mult(mult(ld(Y, X), Z), ld(X, Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 ld(ld(X, Y), mult(Z, ld(X, Y)))
% 22.79/3.37 = { by axiom 3 (f02) R->L }
% 22.79/3.37 ld(ld(X, Y), ld(X, mult(X, mult(Z, ld(X, Y)))))
% 22.79/3.37 = { by lemma 13 R->L }
% 22.79/3.37 ld(ld(X, Y), ld(X, mult(mult(Y, mult(ld(Y, X), Z)), ld(X, Y))))
% 22.79/3.37 = { by axiom 1 (f01) R->L }
% 22.79/3.37 ld(ld(X, Y), ld(X, mult(mult(Y, ld(Y, mult(Y, mult(ld(Y, X), Z)))), ld(X, Y))))
% 22.79/3.37 = { by lemma 8 }
% 22.79/3.37 ld(ld(X, Y), mult(ld(X, Y), mult(ld(Y, mult(Y, mult(ld(Y, X), Z))), ld(X, Y))))
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 mult(ld(Y, mult(Y, mult(ld(Y, X), Z))), ld(X, Y))
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 mult(mult(ld(Y, X), Z), ld(X, Y))
% 22.79/3.37
% 22.79/3.37 Lemma 20: mult(ld(X, X), ld(X, X)) = ld(X, X).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(ld(X, X), ld(X, X))
% 22.79/3.37 = { by axiom 2 (f03) R->L }
% 22.79/3.37 mult(rd(mult(ld(X, X), ld(X, X)), X), X)
% 22.79/3.37 = { by lemma 17 R->L }
% 22.79/3.37 mult(mult(mult(ld(X, X), ld(X, X)), rd(ld(X, X), X)), X)
% 22.79/3.37 = { by lemma 17 R->L }
% 22.79/3.37 mult(mult(mult(ld(X, X), ld(X, X)), mult(ld(X, X), rd(ld(X, X), X))), X)
% 22.79/3.37 = { by lemma 12 R->L }
% 22.79/3.37 mult(mult(rd(ld(X, X), ld(X, X)), mult(ld(X, X), rd(ld(X, X), X))), X)
% 22.79/3.37 = { by lemma 18 R->L }
% 22.79/3.37 mult(mult(mult(ld(X, X), rd(rd(ld(X, X), X), ld(X, X))), ld(X, X)), X)
% 22.79/3.37 = { by lemma 19 R->L }
% 22.79/3.37 mult(ld(ld(X, X), mult(rd(rd(ld(X, X), X), ld(X, X)), ld(X, X))), X)
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.37 mult(ld(ld(X, X), rd(ld(X, X), X)), X)
% 22.79/3.37 = { by axiom 2 (f03) R->L }
% 22.79/3.37 mult(ld(mult(rd(ld(X, X), X), X), rd(ld(X, X), X)), X)
% 22.79/3.37 = { by lemma 16 R->L }
% 22.79/3.37 mult(ld(mult(rd(ld(X, X), X), X), mult(mult(rd(ld(X, X), X), X), rd(ld(X, X), X))), X)
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 mult(rd(ld(X, X), X), X)
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.37 ld(X, X)
% 22.79/3.37
% 22.79/3.37 Lemma 21: mult(mult(ld(X, Y), ld(X, Y)), mult(ld(Y, X), ld(Y, X))) = mult(ld(X, Y), ld(Y, X)).
% 22.79/3.37 Proof:
% 22.79/3.37 mult(mult(ld(X, Y), ld(X, Y)), mult(ld(Y, X), ld(Y, X)))
% 22.79/3.37 = { by lemma 12 R->L }
% 22.79/3.37 mult(rd(ld(X, Y), ld(Y, X)), mult(ld(Y, X), ld(Y, X)))
% 22.79/3.37 = { by lemma 10 R->L }
% 22.79/3.37 mult(rd(ld(X, Y), ld(Y, X)), mult(ld(Y, X), mult(mult(ld(Y, X), ld(X, Y)), ld(Y, X))))
% 22.79/3.37 = { by lemma 6 }
% 22.79/3.37 mult(mult(ld(X, Y), mult(ld(Y, X), ld(X, Y))), ld(Y, X))
% 22.79/3.37 = { by lemma 9 }
% 22.79/3.37 mult(ld(X, Y), ld(Y, X))
% 22.79/3.37
% 22.79/3.37 Lemma 22: ld(rd(X, Y), mult(Z, Y)) = mult(Y, mult(ld(X, Z), Y)).
% 22.79/3.37 Proof:
% 22.79/3.37 ld(rd(X, Y), mult(Z, Y))
% 22.79/3.37 = { by axiom 1 (f01) R->L }
% 22.79/3.37 ld(rd(X, Y), mult(mult(X, ld(X, Z)), Y))
% 22.79/3.37 = { by lemma 6 R->L }
% 22.79/3.37 ld(rd(X, Y), mult(rd(X, Y), mult(Y, mult(ld(X, Z), Y))))
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 mult(Y, mult(ld(X, Z), Y))
% 22.79/3.37
% 22.79/3.37 Lemma 23: ld(rd(X, Y), X) = Y.
% 22.79/3.37 Proof:
% 22.79/3.37 ld(rd(X, Y), X)
% 22.79/3.37 = { by axiom 2 (f03) R->L }
% 22.79/3.37 ld(rd(X, Y), mult(rd(X, Y), Y))
% 22.79/3.37 = { by axiom 3 (f02) }
% 22.79/3.37 Y
% 22.79/3.37
% 22.79/3.37 Lemma 24: ld(mult(rd(ld(X, X), Y), ld(X, X)), ld(X, X)) = mult(ld(X, X), mult(Y, ld(X, X))).
% 22.79/3.37 Proof:
% 22.79/3.37 ld(mult(rd(ld(X, X), Y), ld(X, X)), ld(X, X))
% 22.79/3.37 = { by lemma 20 R->L }
% 22.79/3.37 ld(mult(rd(ld(X, X), Y), mult(ld(X, X), ld(X, X))), ld(X, X))
% 22.79/3.37 = { by axiom 2 (f03) R->L }
% 22.79/3.37 ld(mult(mult(rd(rd(ld(X, X), Y), mult(ld(X, X), ld(X, X))), mult(ld(X, X), ld(X, X))), mult(ld(X, X), ld(X, X))), ld(X, X))
% 22.79/3.37 = { by lemma 6 R->L }
% 22.79/3.37 ld(mult(rd(rd(rd(ld(X, X), Y), mult(ld(X, X), ld(X, X))), mult(ld(X, X), ld(X, X))), mult(mult(ld(X, X), ld(X, X)), mult(mult(ld(X, X), ld(X, X)), mult(ld(X, X), ld(X, X))))), ld(X, X))
% 22.79/3.37 = { by lemma 21 }
% 22.79/3.37 ld(mult(rd(rd(rd(ld(X, X), Y), mult(ld(X, X), ld(X, X))), mult(ld(X, X), ld(X, X))), mult(mult(ld(X, X), ld(X, X)), mult(ld(X, X), ld(X, X)))), ld(X, X))
% 22.79/3.37 = { by lemma 21 }
% 22.79/3.37 ld(mult(rd(rd(rd(ld(X, X), Y), mult(ld(X, X), ld(X, X))), mult(ld(X, X), ld(X, X))), mult(ld(X, X), ld(X, X))), ld(X, X))
% 22.79/3.37 = { by axiom 2 (f03) }
% 22.79/3.38 ld(rd(rd(ld(X, X), Y), mult(ld(X, X), ld(X, X))), ld(X, X))
% 22.79/3.38 = { by lemma 9 R->L }
% 22.79/3.38 ld(rd(rd(ld(X, X), Y), mult(ld(X, X), ld(X, X))), mult(ld(X, X), mult(ld(X, X), ld(X, X))))
% 22.79/3.38 = { by lemma 22 }
% 22.79/3.38 mult(mult(ld(X, X), ld(X, X)), mult(ld(rd(ld(X, X), Y), ld(X, X)), mult(ld(X, X), ld(X, X))))
% 22.79/3.38 = { by lemma 20 }
% 22.79/3.38 mult(mult(ld(X, X), ld(X, X)), mult(ld(rd(ld(X, X), Y), ld(X, X)), ld(X, X)))
% 22.79/3.38 = { by lemma 20 }
% 22.79/3.38 mult(ld(X, X), mult(ld(rd(ld(X, X), Y), ld(X, X)), ld(X, X)))
% 22.79/3.38 = { by lemma 23 }
% 22.79/3.38 mult(ld(X, X), mult(Y, ld(X, X)))
% 22.79/3.38
% 22.79/3.38 Lemma 25: rd(mult(rd(X, Y), Z), Y) = mult(X, rd(ld(Y, Z), Y)).
% 22.79/3.38 Proof:
% 22.79/3.38 rd(mult(rd(X, Y), Z), Y)
% 22.79/3.38 = { by axiom 1 (f01) R->L }
% 22.79/3.38 rd(mult(rd(X, Y), mult(Y, ld(Y, Z))), Y)
% 22.79/3.38 = { by lemma 15 }
% 22.79/3.38 mult(mult(rd(X, Y), Y), rd(ld(Y, Z), Y))
% 22.79/3.38 = { by axiom 2 (f03) }
% 22.79/3.38 mult(X, rd(ld(Y, Z), Y))
% 22.79/3.38
% 22.79/3.38 Lemma 26: mult(mult(X, mult(ld(Y, Z), W)), ld(Z, Y)) = mult(mult(X, ld(Y, Z)), mult(W, ld(Z, Y))).
% 22.79/3.38 Proof:
% 22.79/3.38 mult(mult(X, mult(ld(Y, Z), W)), ld(Z, Y))
% 22.79/3.38 = { by lemma 12 R->L }
% 22.79/3.38 rd(mult(X, mult(ld(Y, Z), W)), ld(Y, Z))
% 22.79/3.38 = { by lemma 15 }
% 22.79/3.38 mult(mult(X, ld(Y, Z)), rd(W, ld(Y, Z)))
% 22.79/3.38 = { by lemma 12 }
% 22.79/3.38 mult(mult(X, ld(Y, Z)), mult(W, ld(Z, Y)))
% 22.79/3.38
% 22.79/3.38 Lemma 27: mult(ld(X, rd(X, Y)), Y) = ld(Y, Y).
% 22.79/3.38 Proof:
% 22.79/3.38 mult(ld(X, rd(X, Y)), Y)
% 22.79/3.38 = { by axiom 3 (f02) R->L }
% 22.79/3.38 ld(Y, mult(Y, mult(ld(X, rd(X, Y)), Y)))
% 22.79/3.38 = { by lemma 22 R->L }
% 22.79/3.38 ld(Y, ld(rd(X, Y), mult(rd(X, Y), Y)))
% 22.79/3.38 = { by axiom 3 (f02) }
% 22.79/3.38 ld(Y, Y)
% 22.79/3.38
% 22.79/3.38 Lemma 28: ld(mult(X, ld(Y, Z)), mult(W, ld(Z, Y))) = mult(ld(Z, Y), mult(ld(X, W), ld(Z, Y))).
% 22.79/3.38 Proof:
% 22.79/3.38 ld(mult(X, ld(Y, Z)), mult(W, ld(Z, Y)))
% 22.79/3.38 = { by lemma 12 R->L }
% 22.79/3.38 ld(rd(X, ld(Z, Y)), mult(W, ld(Z, Y)))
% 22.79/3.38 = { by lemma 22 }
% 22.79/3.38 mult(ld(Z, Y), mult(ld(X, W), ld(Z, Y)))
% 22.79/3.38
% 22.79/3.38 Lemma 29: ld(Y, Y) = ld(X, X).
% 22.79/3.38 Proof:
% 22.79/3.38 ld(Y, Y)
% 22.79/3.38 = { by lemma 10 R->L }
% 22.79/3.38 mult(mult(ld(Y, Y), ld(X, X)), ld(X, X))
% 22.79/3.38 = { by lemma 14 R->L }
% 22.79/3.38 mult(ld(X, X), mult(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), ld(X, X)))
% 22.79/3.38 = { by lemma 10 R->L }
% 22.79/3.38 mult(ld(X, X), mult(mult(ld(X, X), mult(ld(Y, Y), mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y)))), ld(X, X)))
% 22.79/3.38 = { by lemma 24 R->L }
% 22.79/3.38 mult(ld(X, X), mult(mult(ld(X, X), ld(mult(rd(ld(Y, Y), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 12 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), ld(ld(Y, Y), mult(rd(ld(Y, Y), mult(ld(X, X), ld(Y, Y))), ld(Y, Y)))), ld(X, X)))
% 22.79/3.38 = { by lemma 19 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(mult(ld(Y, Y), rd(ld(Y, Y), mult(ld(X, X), ld(Y, Y)))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 3 (f02) R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(mult(ld(Y, Y), rd(ld(mult(ld(X, X), ld(Y, Y)), mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y))), mult(ld(X, X), ld(Y, Y)))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 10 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(mult(ld(Y, Y), rd(ld(mult(ld(X, X), ld(Y, Y)), ld(X, X)), mult(ld(X, X), ld(Y, Y)))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 25 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(rd(ld(Y, Y), mult(ld(X, X), ld(Y, Y))), ld(X, X)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 10 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(rd(ld(Y, Y), mult(ld(X, X), ld(Y, Y))), mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 18 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(Y, Y), rd(ld(Y, Y), mult(ld(X, X), ld(Y, Y)))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 14 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(Y, Y), rd(ld(Y, Y), mult(ld(Y, Y), mult(mult(ld(Y, Y), ld(X, X)), ld(Y, Y))))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 24 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(Y, Y), rd(ld(Y, Y), ld(mult(rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X))), ld(Y, Y)), ld(Y, Y)))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 1 (f01) R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(Y, Y), rd(mult(mult(rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X))), ld(Y, Y)), ld(mult(rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X))), ld(Y, Y)), ld(Y, Y))), ld(mult(rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X))), ld(Y, Y)), ld(Y, Y)))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 4 (f04) }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(Y, Y), mult(rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X))), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 8 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(ld(Y, mult(mult(Y, rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 12 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(ld(Y, rd(mult(Y, rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 1 (f01) R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(ld(Y, rd(mult(Y, mult(ld(Y, Y), ld(ld(Y, Y), rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))))), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 11 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(ld(Y, rd(mult(mult(Y, rd(ld(ld(Y, Y), rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))), ld(Y, Y))), ld(Y, Y)), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 4 (f04) }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(ld(Y, mult(Y, rd(ld(ld(Y, Y), rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))), ld(Y, Y)))), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 3 (f02) }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(rd(ld(ld(Y, Y), rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 12 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(ld(Y, Y), rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 26 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(ld(Y, Y), rd(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))), mult(ld(Y, Y), ld(X, X))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 27 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(ld(mult(ld(Y, Y), ld(X, X)), mult(ld(Y, Y), ld(X, X))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 28 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(X, X), mult(ld(ld(Y, Y), ld(Y, Y)), ld(X, X))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 9 R->L }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(X, X), mult(ld(ld(Y, Y), mult(ld(Y, Y), mult(ld(Y, Y), ld(Y, Y)))), ld(X, X))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 3 (f02) }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(X, X), mult(mult(ld(Y, Y), ld(Y, Y)), ld(X, X))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 20 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(X, X), mult(ld(Y, Y), ld(X, X))), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 26 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(rd(mult(mult(ld(X, X), ld(Y, Y)), mult(ld(X, X), ld(Y, Y))), mult(ld(X, X), ld(Y, Y))), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by axiom 4 (f04) }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), mult(mult(ld(X, X), ld(Y, Y)), ld(Y, Y))), ld(X, X)))
% 22.79/3.38 = { by lemma 10 }
% 22.79/3.38 mult(ld(X, X), mult(rd(ld(X, X), ld(X, X)), ld(X, X)))
% 22.79/3.38 = { by lemma 12 }
% 22.79/3.38 mult(ld(X, X), mult(mult(ld(X, X), ld(X, X)), ld(X, X)))
% 22.79/3.38 = { by lemma 14 }
% 22.79/3.38 mult(ld(X, X), ld(X, X))
% 22.79/3.38 = { by lemma 20 }
% 22.79/3.38 ld(X, X)
% 22.79/3.38
% 22.79/3.38 Goal 1 (goals): tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2))) = tuple(x0, x0_2).
% 22.79/3.38 Proof:
% 22.79/3.38 tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(x1_2, x1_2)))
% 22.79/3.38 = { by lemma 10 R->L }
% 22.79/3.38 tuple(mult(ld(x1, x1), x0), mult(mult(mult(x0_2, ld(x1_2, x1_2)), ld(x1_2, x1_2)), ld(x1_2, x1_2)))
% 22.79/3.38 = { by axiom 5 (f05) R->L }
% 22.79/3.38 tuple(mult(ld(x1, x1), x0), mult(x0_2, mult(ld(x1_2, x1_2), mult(ld(x1_2, x1_2), ld(x1_2, x1_2)))))
% 22.79/3.38 = { by lemma 28 R->L }
% 22.79/3.38 tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(mult(x1_2, ld(x1_2, x1_2)), mult(x1_2, ld(x1_2, x1_2)))))
% 22.79/3.38 = { by lemma 29 R->L }
% 22.79/3.38 tuple(mult(ld(x1, x1), x0), mult(x0_2, ld(x0_2, x0_2)))
% 22.79/3.38 = { by axiom 1 (f01) }
% 22.79/3.38 tuple(mult(ld(x1, x1), x0), x0_2)
% 22.79/3.38 = { by lemma 29 }
% 22.79/3.38 tuple(mult(ld(x0, x0), x0), x0_2)
% 22.79/3.38 = { by axiom 3 (f02) R->L }
% 22.79/3.38 tuple(mult(ld(X, mult(X, ld(x0, x0))), x0), x0_2)
% 22.79/3.38 = { by axiom 4 (f04) R->L }
% 22.79/3.38 tuple(mult(ld(X, rd(mult(mult(X, ld(x0, x0)), x0), x0)), x0), x0_2)
% 22.79/3.38 = { by lemma 23 R->L }
% 22.79/3.38 tuple(mult(ld(X, rd(mult(mult(X, ld(x0, x0)), ld(rd(X, x0), X)), x0)), x0), x0_2)
% 22.79/3.38 = { by lemma 12 R->L }
% 22.79/3.38 tuple(mult(ld(X, rd(rd(mult(X, ld(x0, x0)), ld(X, rd(X, x0))), x0)), x0), x0_2)
% 22.79/3.38 = { by lemma 27 R->L }
% 22.79/3.38 tuple(mult(ld(X, rd(rd(mult(X, mult(ld(X, rd(X, x0)), x0)), ld(X, rd(X, x0))), x0)), x0), x0_2)
% 22.79/3.38 = { by lemma 15 }
% 22.79/3.38 tuple(mult(ld(X, rd(mult(mult(X, ld(X, rd(X, x0))), rd(x0, ld(X, rd(X, x0)))), x0)), x0), x0_2)
% 22.79/3.38 = { by axiom 1 (f01) }
% 22.79/3.38 tuple(mult(ld(X, rd(mult(rd(X, x0), rd(x0, ld(X, rd(X, x0)))), x0)), x0), x0_2)
% 22.79/3.38 = { by lemma 12 }
% 22.79/3.38 tuple(mult(ld(X, rd(mult(rd(X, x0), mult(x0, ld(rd(X, x0), X))), x0)), x0), x0_2)
% 22.79/3.38 = { by lemma 23 }
% 22.79/3.38 tuple(mult(ld(X, rd(mult(rd(X, x0), mult(x0, x0)), x0)), x0), x0_2)
% 22.79/3.38 = { by lemma 25 }
% 22.79/3.38 tuple(mult(ld(X, mult(X, rd(ld(x0, mult(x0, x0)), x0))), x0), x0_2)
% 22.79/3.38 = { by axiom 3 (f02) }
% 22.79/3.38 tuple(mult(ld(X, mult(X, rd(x0, x0))), x0), x0_2)
% 22.79/3.38 = { by axiom 3 (f02) }
% 22.79/3.38 tuple(mult(rd(x0, x0), x0), x0_2)
% 22.79/3.38 = { by axiom 2 (f03) }
% 22.79/3.38 tuple(x0, x0_2)
% 22.79/3.38 % SZS output end Proof
% 22.79/3.38
% 22.79/3.38 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------