TSTP Solution File: GRP654-11 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP654-11 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:19:27 EDT 2023
% Result : Unsatisfiable 4.49s 0.99s
% Output : Proof 5.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP654-11 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n026.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Mon Aug 28 20:35:50 EDT 2023
% 0.18/0.36 % CPUTime :
% 4.49/0.99 Command-line arguments: --ground-connectedness --complete-subsets
% 4.49/0.99
% 4.49/0.99 % SZS status Unsatisfiable
% 4.49/0.99
% 5.16/1.08 % SZS output start Proof
% 5.16/1.08 Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
% 5.16/1.08 Axiom 2 (f04): rd(mult(X, Y), Y) = X.
% 5.16/1.08 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 5.16/1.08 Axiom 4 (f03): mult(rd(X, Y), Y) = X.
% 5.16/1.08 Axiom 5 (f05): mult(X, mult(Y, mult(X, Z))) = mult(mult(mult(X, Y), X), Z).
% 5.16/1.08
% 5.16/1.08 Lemma 6: ld(rd(X, Y), X) = Y.
% 5.16/1.08 Proof:
% 5.16/1.08 ld(rd(X, Y), X)
% 5.16/1.08 = { by axiom 4 (f03) R->L }
% 5.16/1.08 ld(rd(X, Y), mult(rd(X, Y), Y))
% 5.16/1.08 = { by axiom 1 (f02) }
% 5.16/1.08 Y
% 5.16/1.08
% 5.16/1.08 Lemma 7: mult(X, mult(ld(X, Y), mult(X, Z))) = mult(mult(Y, X), Z).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(X, mult(ld(X, Y), mult(X, Z)))
% 5.16/1.08 = { by axiom 5 (f05) }
% 5.16/1.08 mult(mult(mult(X, ld(X, Y)), X), Z)
% 5.16/1.08 = { by axiom 3 (f01) }
% 5.16/1.08 mult(mult(Y, X), Z)
% 5.16/1.08
% 5.16/1.08 Lemma 8: mult(mult(X, Y), ld(Y, Z)) = mult(Y, mult(ld(Y, X), Z)).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(mult(X, Y), ld(Y, Z))
% 5.16/1.08 = { by lemma 7 R->L }
% 5.16/1.08 mult(Y, mult(ld(Y, X), mult(Y, ld(Y, Z))))
% 5.16/1.08 = { by axiom 3 (f01) }
% 5.16/1.08 mult(Y, mult(ld(Y, X), Z))
% 5.16/1.08
% 5.16/1.08 Lemma 9: mult(X, mult(ld(X, rd(X, X)), Y)) = Y.
% 5.16/1.08 Proof:
% 5.16/1.08 mult(X, mult(ld(X, rd(X, X)), Y))
% 5.16/1.08 = { by lemma 8 R->L }
% 5.16/1.08 mult(mult(rd(X, X), X), ld(X, Y))
% 5.16/1.08 = { by axiom 4 (f03) }
% 5.16/1.08 mult(X, ld(X, Y))
% 5.16/1.08 = { by axiom 3 (f01) }
% 5.16/1.08 Y
% 5.16/1.08
% 5.16/1.08 Lemma 10: rd(ld(X, Y), Y) = ld(X, rd(X, X)).
% 5.16/1.08 Proof:
% 5.16/1.08 rd(ld(X, Y), Y)
% 5.16/1.08 = { by lemma 9 R->L }
% 5.16/1.08 rd(ld(X, mult(X, mult(ld(X, rd(X, X)), Y))), Y)
% 5.16/1.08 = { by axiom 1 (f02) }
% 5.16/1.08 rd(mult(ld(X, rd(X, X)), Y), Y)
% 5.16/1.08 = { by axiom 2 (f04) }
% 5.16/1.08 ld(X, rd(X, X))
% 5.16/1.08
% 5.16/1.08 Lemma 11: rd(mult(X, mult(Y, mult(X, Z))), Z) = mult(mult(X, Y), X).
% 5.16/1.08 Proof:
% 5.16/1.08 rd(mult(X, mult(Y, mult(X, Z))), Z)
% 5.16/1.08 = { by axiom 5 (f05) }
% 5.16/1.08 rd(mult(mult(mult(X, Y), X), Z), Z)
% 5.16/1.08 = { by axiom 2 (f04) }
% 5.16/1.08 mult(mult(X, Y), X)
% 5.16/1.08
% 5.16/1.08 Lemma 12: rd(mult(X, mult(Y, Z)), ld(X, Z)) = mult(mult(X, Y), X).
% 5.16/1.08 Proof:
% 5.16/1.08 rd(mult(X, mult(Y, Z)), ld(X, Z))
% 5.16/1.08 = { by axiom 3 (f01) R->L }
% 5.16/1.08 rd(mult(X, mult(Y, mult(X, ld(X, Z)))), ld(X, Z))
% 5.16/1.08 = { by lemma 11 }
% 5.16/1.08 mult(mult(X, Y), X)
% 5.16/1.08
% 5.16/1.08 Lemma 13: mult(mult(X, rd(Y, Z)), X) = rd(mult(X, Y), ld(X, Z)).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(mult(X, rd(Y, Z)), X)
% 5.16/1.08 = { by lemma 12 R->L }
% 5.16/1.08 rd(mult(X, mult(rd(Y, Z), Z)), ld(X, Z))
% 5.16/1.08 = { by axiom 4 (f03) }
% 5.16/1.08 rd(mult(X, Y), ld(X, Z))
% 5.16/1.08
% 5.16/1.08 Lemma 14: rd(rd(mult(X, Y), ld(X, Z)), X) = mult(X, rd(Y, Z)).
% 5.16/1.08 Proof:
% 5.16/1.08 rd(rd(mult(X, Y), ld(X, Z)), X)
% 5.16/1.08 = { by lemma 13 R->L }
% 5.16/1.08 rd(mult(mult(X, rd(Y, Z)), X), X)
% 5.16/1.08 = { by axiom 2 (f04) }
% 5.16/1.08 mult(X, rd(Y, Z))
% 5.16/1.08
% 5.16/1.08 Lemma 15: rd(X, ld(Y, X)) = Y.
% 5.16/1.08 Proof:
% 5.16/1.08 rd(X, ld(Y, X))
% 5.16/1.08 = { by axiom 3 (f01) R->L }
% 5.16/1.08 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 5.16/1.08 = { by axiom 2 (f04) }
% 5.16/1.08 Y
% 5.16/1.08
% 5.16/1.08 Lemma 16: mult(X, rd(Y, mult(X, Y))) = rd(X, X).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(X, rd(Y, mult(X, Y)))
% 5.16/1.08 = { by lemma 14 R->L }
% 5.16/1.08 rd(rd(mult(X, Y), ld(X, mult(X, Y))), X)
% 5.16/1.08 = { by lemma 15 }
% 5.16/1.08 rd(X, X)
% 5.16/1.08
% 5.16/1.08 Lemma 17: rd(ld(X, Y), Y) = rd(Z, mult(X, Z)).
% 5.16/1.08 Proof:
% 5.16/1.08 rd(ld(X, Y), Y)
% 5.16/1.08 = { by lemma 10 }
% 5.16/1.08 ld(X, rd(X, X))
% 5.16/1.08 = { by lemma 16 R->L }
% 5.16/1.08 ld(X, mult(X, rd(Z, mult(X, Z))))
% 5.16/1.08 = { by axiom 1 (f02) }
% 5.16/1.08 rd(Z, mult(X, Z))
% 5.16/1.08
% 5.16/1.08 Lemma 18: ld(rd(X, mult(Y, X)), Z) = mult(Y, Z).
% 5.16/1.08 Proof:
% 5.16/1.08 ld(rd(X, mult(Y, X)), Z)
% 5.16/1.08 = { by axiom 1 (f02) R->L }
% 5.16/1.08 ld(ld(Y, mult(Y, rd(X, mult(Y, X)))), Z)
% 5.16/1.08 = { by lemma 16 }
% 5.16/1.08 ld(ld(Y, rd(Y, Y)), Z)
% 5.16/1.08 = { by lemma 16 R->L }
% 5.16/1.08 ld(ld(Y, mult(Y, rd(Z, mult(Y, Z)))), Z)
% 5.16/1.08 = { by axiom 1 (f02) }
% 5.16/1.08 ld(rd(Z, mult(Y, Z)), Z)
% 5.16/1.08 = { by lemma 6 }
% 5.16/1.08 mult(Y, Z)
% 5.16/1.08
% 5.16/1.08 Lemma 19: mult(ld(X, Y), mult(X, Z)) = ld(X, mult(mult(Y, X), Z)).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(ld(X, Y), mult(X, Z))
% 5.16/1.08 = { by axiom 1 (f02) R->L }
% 5.16/1.08 ld(X, mult(X, mult(ld(X, Y), mult(X, Z))))
% 5.16/1.08 = { by lemma 7 }
% 5.16/1.08 ld(X, mult(mult(Y, X), Z))
% 5.16/1.08
% 5.16/1.08 Lemma 20: ld(rd(X, Y), mult(mult(Z, rd(X, Y)), Y)) = mult(ld(rd(X, Y), Z), X).
% 5.16/1.08 Proof:
% 5.16/1.08 ld(rd(X, Y), mult(mult(Z, rd(X, Y)), Y))
% 5.16/1.08 = { by lemma 19 R->L }
% 5.16/1.08 mult(ld(rd(X, Y), Z), mult(rd(X, Y), Y))
% 5.16/1.08 = { by axiom 4 (f03) }
% 5.16/1.08 mult(ld(rd(X, Y), Z), X)
% 5.16/1.08
% 5.16/1.08 Lemma 21: mult(X, rd(ld(X, Y), Y)) = rd(X, X).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(X, rd(ld(X, Y), Y))
% 5.16/1.08 = { by lemma 14 R->L }
% 5.16/1.08 rd(rd(mult(X, ld(X, Y)), ld(X, Y)), X)
% 5.16/1.08 = { by axiom 2 (f04) }
% 5.16/1.08 rd(X, X)
% 5.16/1.08
% 5.16/1.08 Lemma 22: mult(mult(rd(X, Y), Z), rd(X, Y)) = rd(mult(rd(X, Y), mult(Z, X)), Y).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(mult(rd(X, Y), Z), rd(X, Y))
% 5.16/1.08 = { by lemma 11 R->L }
% 5.16/1.08 rd(mult(rd(X, Y), mult(Z, mult(rd(X, Y), Y))), Y)
% 5.16/1.08 = { by axiom 4 (f03) }
% 5.16/1.08 rd(mult(rd(X, Y), mult(Z, X)), Y)
% 5.16/1.08
% 5.16/1.08 Lemma 23: mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)) = rd(X, Y).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y))
% 5.16/1.08 = { by lemma 22 }
% 5.16/1.08 rd(mult(rd(X, Y), mult(rd(Y, X), X)), Y)
% 5.16/1.08 = { by axiom 4 (f03) }
% 5.16/1.08 rd(mult(rd(X, Y), Y), Y)
% 5.16/1.08 = { by axiom 2 (f04) }
% 5.16/1.08 rd(X, Y)
% 5.16/1.08
% 5.16/1.08 Lemma 24: mult(rd(X, Y), mult(rd(Y, X), mult(rd(X, Y), Z))) = mult(rd(X, Y), Z).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(rd(X, Y), mult(rd(Y, X), mult(rd(X, Y), Z)))
% 5.16/1.08 = { by axiom 5 (f05) }
% 5.16/1.08 mult(mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)), Z)
% 5.16/1.08 = { by lemma 23 }
% 5.16/1.08 mult(rd(X, Y), Z)
% 5.16/1.08
% 5.16/1.08 Lemma 25: mult(rd(X, Y), mult(rd(Y, X), Z)) = Z.
% 5.16/1.08 Proof:
% 5.16/1.08 mult(rd(X, Y), mult(rd(Y, X), Z))
% 5.16/1.08 = { by axiom 1 (f02) R->L }
% 5.16/1.08 ld(rd(Y, X), mult(rd(Y, X), mult(rd(X, Y), mult(rd(Y, X), Z))))
% 5.16/1.08 = { by lemma 24 }
% 5.16/1.08 ld(rd(Y, X), mult(rd(Y, X), Z))
% 5.16/1.08 = { by axiom 1 (f02) }
% 5.16/1.08 Z
% 5.16/1.08
% 5.16/1.08 Lemma 26: mult(rd(X, Y), Z) = ld(rd(Y, X), Z).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(rd(X, Y), Z)
% 5.16/1.08 = { by axiom 1 (f02) R->L }
% 5.16/1.08 ld(rd(Y, X), mult(rd(Y, X), mult(rd(X, Y), Z)))
% 5.16/1.08 = { by lemma 25 }
% 5.16/1.08 ld(rd(Y, X), Z)
% 5.16/1.08
% 5.16/1.08 Lemma 27: mult(ld(X, X), Y) = ld(rd(X, X), Y).
% 5.16/1.08 Proof:
% 5.16/1.08 mult(ld(X, X), Y)
% 5.16/1.08 = { by axiom 1 (f02) R->L }
% 5.16/1.08 ld(X, mult(X, mult(ld(X, X), Y)))
% 5.16/1.08 = { by lemma 8 R->L }
% 5.16/1.08 ld(X, mult(mult(X, X), ld(X, Y)))
% 5.16/1.08 = { by lemma 18 R->L }
% 5.16/1.08 ld(X, mult(ld(rd(Z, mult(X, Z)), X), ld(X, Y)))
% 5.16/1.08 = { by lemma 17 R->L }
% 5.16/1.08 ld(X, mult(ld(rd(ld(X, Y), Y), X), ld(X, Y)))
% 5.16/1.08 = { by lemma 20 R->L }
% 5.16/1.08 ld(X, ld(rd(ld(X, Y), Y), mult(mult(X, rd(ld(X, Y), Y)), Y)))
% 5.16/1.08 = { by lemma 21 }
% 5.16/1.08 ld(X, ld(rd(ld(X, Y), Y), mult(rd(X, X), Y)))
% 5.16/1.08 = { by axiom 1 (f02) R->L }
% 5.16/1.08 ld(X, ld(ld(X, mult(X, rd(ld(X, Y), Y))), mult(rd(X, X), Y)))
% 5.16/1.08 = { by lemma 21 }
% 5.16/1.08 ld(X, ld(ld(X, rd(X, X)), mult(rd(X, X), Y)))
% 5.16/1.08 = { by lemma 21 R->L }
% 5.16/1.08 ld(X, ld(ld(X, mult(X, rd(ld(X, W), W))), mult(rd(X, X), Y)))
% 5.16/1.08 = { by axiom 1 (f02) }
% 5.16/1.08 ld(X, ld(rd(ld(X, W), W), mult(rd(X, X), Y)))
% 5.16/1.08 = { by lemma 17 }
% 5.16/1.08 ld(X, ld(rd(V, mult(X, V)), mult(rd(X, X), Y)))
% 5.16/1.08 = { by lemma 18 }
% 5.16/1.08 ld(X, mult(X, mult(rd(X, X), Y)))
% 5.16/1.08 = { by lemma 26 }
% 5.16/1.08 ld(X, mult(X, ld(rd(X, X), Y)))
% 5.16/1.08 = { by axiom 1 (f02) }
% 5.16/1.08 ld(rd(X, X), Y)
% 5.16/1.08
% 5.16/1.08 Lemma 28: rd(X, X) = ld(X, X).
% 5.16/1.08 Proof:
% 5.16/1.08 rd(X, X)
% 5.16/1.08 = { by lemma 6 R->L }
% 5.16/1.08 rd(ld(rd(X, X), X), X)
% 5.16/1.08 = { by lemma 17 }
% 5.16/1.08 rd(Y, mult(rd(X, X), Y))
% 5.16/1.08 = { by lemma 17 R->L }
% 5.16/1.08 rd(ld(rd(X, X), Z), Z)
% 5.16/1.08 = { by lemma 27 R->L }
% 5.16/1.08 rd(mult(ld(X, X), Z), Z)
% 5.16/1.08 = { by axiom 2 (f04) }
% 5.16/1.08 ld(X, X)
% 5.16/1.08
% 5.16/1.08 Lemma 29: ld(rd(X, Y), ld(rd(Y, X), Z)) = Z.
% 5.16/1.08 Proof:
% 5.16/1.08 ld(rd(X, Y), ld(rd(Y, X), Z))
% 5.16/1.08 = { by lemma 26 R->L }
% 5.16/1.08 mult(rd(Y, X), ld(rd(Y, X), Z))
% 5.16/1.08 = { by lemma 24 R->L }
% 5.16/1.08 mult(rd(Y, X), mult(rd(X, Y), mult(rd(Y, X), ld(rd(Y, X), Z))))
% 5.16/1.08 = { by axiom 3 (f01) }
% 5.16/1.08 mult(rd(Y, X), mult(rd(X, Y), Z))
% 5.16/1.08 = { by lemma 25 }
% 5.48/1.08 Z
% 5.48/1.08
% 5.48/1.08 Lemma 30: mult(X, mult(ld(X, rd(Y, X)), Z)) = mult(Y, ld(X, Z)).
% 5.48/1.08 Proof:
% 5.48/1.08 mult(X, mult(ld(X, rd(Y, X)), Z))
% 5.48/1.08 = { by lemma 8 R->L }
% 5.48/1.08 mult(mult(rd(Y, X), X), ld(X, Z))
% 5.48/1.08 = { by axiom 4 (f03) }
% 5.48/1.08 mult(Y, ld(X, Z))
% 5.48/1.08
% 5.48/1.08 Lemma 31: mult(ld(X, rd(Y, X)), Z) = ld(X, mult(Y, ld(X, Z))).
% 5.48/1.08 Proof:
% 5.48/1.08 mult(ld(X, rd(Y, X)), Z)
% 5.48/1.08 = { by axiom 1 (f02) R->L }
% 5.48/1.08 ld(X, mult(X, mult(ld(X, rd(Y, X)), Z)))
% 5.48/1.08 = { by lemma 30 }
% 5.48/1.08 ld(X, mult(Y, ld(X, Z)))
% 5.48/1.08
% 5.48/1.08 Lemma 32: rd(ld(rd(X, Y), Z), rd(Y, X)) = ld(rd(X, Y), mult(Z, rd(X, Y))).
% 5.48/1.08 Proof:
% 5.48/1.08 rd(ld(rd(X, Y), Z), rd(Y, X))
% 5.48/1.08 = { by axiom 2 (f04) R->L }
% 5.48/1.08 rd(rd(mult(ld(rd(X, Y), Z), X), X), rd(Y, X))
% 5.48/1.08 = { by lemma 20 R->L }
% 5.48/1.08 rd(rd(ld(rd(X, Y), mult(mult(Z, rd(X, Y)), Y)), X), rd(Y, X))
% 5.48/1.08 = { by lemma 26 R->L }
% 5.48/1.08 rd(rd(mult(rd(Y, X), mult(mult(Z, rd(X, Y)), Y)), X), rd(Y, X))
% 5.48/1.08 = { by axiom 4 (f03) R->L }
% 5.48/1.08 rd(rd(mult(rd(Y, X), mult(rd(mult(mult(Z, rd(X, Y)), Y), Y), Y)), X), rd(Y, X))
% 5.48/1.08 = { by lemma 22 R->L }
% 5.48/1.08 rd(mult(mult(rd(Y, X), rd(mult(mult(Z, rd(X, Y)), Y), Y)), rd(Y, X)), rd(Y, X))
% 5.48/1.08 = { by axiom 2 (f04) }
% 5.48/1.08 mult(rd(Y, X), rd(mult(mult(Z, rd(X, Y)), Y), Y))
% 5.48/1.08 = { by lemma 26 }
% 5.48/1.08 ld(rd(X, Y), rd(mult(mult(Z, rd(X, Y)), Y), Y))
% 5.48/1.08 = { by axiom 2 (f04) }
% 5.48/1.08 ld(rd(X, Y), mult(Z, rd(X, Y)))
% 5.48/1.08
% 5.48/1.08 Lemma 33: ld(rd(X, Y), mult(ld(rd(Y, X), Z), rd(X, Y))) = rd(Z, rd(Y, X)).
% 5.48/1.08 Proof:
% 5.48/1.08 ld(rd(X, Y), mult(ld(rd(Y, X), Z), rd(X, Y)))
% 5.48/1.08 = { by lemma 26 R->L }
% 5.48/1.08 ld(rd(X, Y), mult(mult(rd(X, Y), Z), rd(X, Y)))
% 5.48/1.08 = { by lemma 32 R->L }
% 5.48/1.08 rd(ld(rd(X, Y), mult(rd(X, Y), Z)), rd(Y, X))
% 5.48/1.08 = { by axiom 1 (f02) }
% 5.48/1.08 rd(Z, rd(Y, X))
% 5.48/1.08
% 5.48/1.08 Lemma 34: ld(rd(X, X), rd(X, X)) = rd(X, X).
% 5.48/1.08 Proof:
% 5.48/1.08 ld(rd(X, X), rd(X, X))
% 5.48/1.08 = { by lemma 9 R->L }
% 5.48/1.08 mult(X, mult(ld(X, rd(X, X)), ld(rd(X, X), rd(X, X))))
% 5.48/1.08 = { by lemma 29 R->L }
% 5.48/1.08 mult(X, ld(rd(X, X), ld(rd(X, X), mult(ld(X, rd(X, X)), ld(rd(X, X), rd(X, X))))))
% 5.48/1.08 = { by lemma 31 R->L }
% 5.48/1.08 mult(X, ld(rd(X, X), mult(ld(rd(X, X), rd(ld(X, rd(X, X)), rd(X, X))), rd(X, X))))
% 5.48/1.08 = { by lemma 33 }
% 5.48/1.08 mult(X, rd(rd(ld(X, rd(X, X)), rd(X, X)), rd(X, X)))
% 5.48/1.08 = { by lemma 10 }
% 5.48/1.08 mult(X, rd(ld(X, rd(X, X)), rd(X, X)))
% 5.48/1.08 = { by lemma 10 }
% 5.48/1.08 mult(X, ld(X, rd(X, X)))
% 5.48/1.08 = { by axiom 3 (f01) }
% 5.48/1.08 rd(X, X)
% 5.48/1.08
% 5.48/1.08 Lemma 35: mult(rd(X, Y), rd(Y, X)) = rd(rd(X, Y), rd(X, Y)).
% 5.48/1.08 Proof:
% 5.48/1.08 mult(rd(X, Y), rd(Y, X))
% 5.48/1.08 = { by axiom 2 (f04) R->L }
% 5.48/1.09 rd(mult(mult(rd(X, Y), rd(Y, X)), rd(X, Y)), rd(X, Y))
% 5.48/1.09 = { by lemma 23 }
% 5.48/1.09 rd(rd(X, Y), rd(X, Y))
% 5.48/1.09
% 5.48/1.09 Lemma 36: mult(rd(X, mult(Y, X)), Z) = ld(Y, Z).
% 5.48/1.09 Proof:
% 5.48/1.09 mult(rd(X, mult(Y, X)), Z)
% 5.48/1.09 = { by lemma 17 R->L }
% 5.48/1.09 mult(rd(ld(Y, W), W), Z)
% 5.48/1.09 = { by lemma 10 }
% 5.48/1.09 mult(ld(Y, rd(Y, Y)), Z)
% 5.48/1.09 = { by lemma 31 }
% 5.48/1.09 ld(Y, mult(Y, ld(Y, Z)))
% 5.48/1.09 = { by axiom 1 (f02) }
% 5.48/1.09 ld(Y, Z)
% 5.48/1.09
% 5.48/1.09 Lemma 37: rd(rd(X, Y), rd(X, Y)) = ld(rd(Y, X), rd(Y, X)).
% 5.48/1.09 Proof:
% 5.48/1.09 rd(rd(X, Y), rd(X, Y))
% 5.48/1.09 = { by lemma 35 R->L }
% 5.48/1.09 mult(rd(X, Y), rd(Y, X))
% 5.48/1.09 = { by lemma 26 }
% 5.48/1.09 ld(rd(Y, X), rd(Y, X))
% 5.48/1.09
% 5.48/1.09 Lemma 38: mult(mult(X, rd(Y, Y)), rd(Y, Y)) = rd(X, rd(Y, Y)).
% 5.48/1.09 Proof:
% 5.48/1.09 mult(mult(X, rd(Y, Y)), rd(Y, Y))
% 5.48/1.09 = { by lemma 34 R->L }
% 5.48/1.09 mult(mult(X, rd(Y, Y)), ld(rd(Y, Y), rd(Y, Y)))
% 5.48/1.09 = { by lemma 8 }
% 5.48/1.09 mult(rd(Y, Y), mult(ld(rd(Y, Y), X), rd(Y, Y)))
% 5.48/1.09 = { by lemma 26 }
% 5.48/1.09 ld(rd(Y, Y), mult(ld(rd(Y, Y), X), rd(Y, Y)))
% 5.48/1.09 = { by lemma 33 }
% 5.48/1.09 rd(X, rd(Y, Y))
% 5.48/1.09
% 5.48/1.09 Lemma 39: rd(mult(X, Y), ld(X, ld(Z, Y))) = mult(mult(X, Z), X).
% 5.48/1.09 Proof:
% 5.48/1.09 rd(mult(X, Y), ld(X, ld(Z, Y)))
% 5.48/1.09 = { by axiom 3 (f01) R->L }
% 5.48/1.09 rd(mult(X, mult(Z, ld(Z, Y))), ld(X, ld(Z, Y)))
% 5.48/1.09 = { by lemma 12 }
% 5.48/1.09 mult(mult(X, Z), X)
% 5.48/1.09
% 5.48/1.09 Lemma 40: rd(X, ld(Y, ld(Z, ld(Y, X)))) = mult(mult(Y, Z), Y).
% 5.48/1.09 Proof:
% 5.48/1.09 rd(X, ld(Y, ld(Z, ld(Y, X))))
% 5.48/1.09 = { by axiom 3 (f01) R->L }
% 5.48/1.09 rd(mult(Y, ld(Y, X)), ld(Y, ld(Z, ld(Y, X))))
% 5.48/1.09 = { by lemma 39 }
% 5.48/1.09 mult(mult(Y, Z), Y)
% 5.48/1.09
% 5.48/1.09 Lemma 41: mult(mult(Z, rd(Y, X)), ld(rd(Y, X), W)) = ld(rd(X, Y), mult(ld(rd(Y, X), Z), W)).
% 5.48/1.09 Proof:
% 5.48/1.09 mult(mult(Z, rd(Y, X)), ld(rd(Y, X), W))
% 5.48/1.09 = { by lemma 8 }
% 5.48/1.09 mult(rd(Y, X), mult(ld(rd(Y, X), Z), W))
% 5.48/1.09 = { by lemma 26 }
% 5.48/1.09 ld(rd(X, Y), mult(ld(rd(Y, X), Z), W))
% 5.48/1.09
% 5.48/1.09 Lemma 42: mult(ld(rd(X, Y), Z), ld(rd(Y, X), W)) = ld(rd(X, Y), mult(mult(Z, rd(X, Y)), W)).
% 5.48/1.09 Proof:
% 5.48/1.09 mult(ld(rd(X, Y), Z), ld(rd(Y, X), W))
% 5.48/1.09 = { by axiom 3 (f01) R->L }
% 5.48/1.09 mult(rd(Y, X), ld(rd(Y, X), mult(ld(rd(X, Y), Z), ld(rd(Y, X), W))))
% 5.48/1.09 = { by lemma 41 R->L }
% 5.48/1.09 mult(rd(Y, X), mult(mult(Z, rd(X, Y)), ld(rd(X, Y), ld(rd(Y, X), W))))
% 5.48/1.09 = { by lemma 26 }
% 5.48/1.09 ld(rd(X, Y), mult(mult(Z, rd(X, Y)), ld(rd(X, Y), ld(rd(Y, X), W))))
% 5.48/1.09 = { by lemma 29 }
% 5.48/1.09 ld(rd(X, Y), mult(mult(Z, rd(X, Y)), W))
% 5.48/1.09
% 5.48/1.09 Lemma 43: rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y))) = mult(mult(X, rd(Y, Y)), X).
% 5.48/1.09 Proof:
% 5.48/1.09 rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y)))
% 5.48/1.09 = { by lemma 34 R->L }
% 5.48/1.09 rd(mult(X, ld(rd(Y, Y), rd(Y, Y))), ld(X, rd(Y, Y)))
% 5.48/1.09 = { by lemma 37 R->L }
% 5.48/1.09 rd(mult(X, rd(rd(Y, Y), rd(Y, Y))), ld(X, rd(Y, Y)))
% 5.48/1.09 = { by axiom 1 (f02) R->L }
% 5.48/1.09 rd(mult(X, rd(rd(Y, Y), rd(Y, Y))), ld(X, ld(rd(Y, Y), mult(rd(Y, Y), rd(Y, Y)))))
% 5.48/1.09 = { by lemma 35 }
% 5.48/1.09 rd(mult(X, rd(rd(Y, Y), rd(Y, Y))), ld(X, ld(rd(Y, Y), rd(rd(Y, Y), rd(Y, Y)))))
% 5.48/1.09 = { by lemma 39 }
% 5.48/1.09 mult(mult(X, rd(Y, Y)), X)
% 5.48/1.09
% 5.48/1.09 Lemma 44: ld(mult(mult(X, rd(Y, Y)), X), mult(mult(X, rd(Y, Y)), X)) = ld(mult(X, rd(Y, Y)), X).
% 5.48/1.09 Proof:
% 5.48/1.09 ld(mult(mult(X, rd(Y, Y)), X), mult(mult(X, rd(Y, Y)), X))
% 5.48/1.09 = { by lemma 28 R->L }
% 5.48/1.09 rd(mult(mult(X, rd(Y, Y)), X), mult(mult(X, rd(Y, Y)), X))
% 5.48/1.09 = { by axiom 1 (f02) R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), mult(mult(X, rd(Y, Y)), rd(mult(mult(X, rd(Y, Y)), X), mult(mult(X, rd(Y, Y)), X))))
% 5.48/1.09 = { by lemma 14 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(mult(mult(X, rd(Y, Y)), mult(mult(X, rd(Y, Y)), X)), ld(mult(X, rd(Y, Y)), mult(mult(X, rd(Y, Y)), X))), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by axiom 1 (f02) }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(mult(mult(X, rd(Y, Y)), mult(mult(X, rd(Y, Y)), X)), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 43 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(mult(mult(X, rd(Y, Y)), rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 6 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(mult(ld(rd(ld(X, rd(Y, Y)), mult(X, rd(Y, Y))), ld(X, rd(Y, Y))), rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 26 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(mult(mult(rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y))), ld(X, rd(Y, Y))), rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 39 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y))), ld(X, rd(Y, Y))), ld(rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y))), ld(ld(X, rd(Y, Y)), ld(X, rd(Y, Y))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by axiom 4 (f03) }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(rd(mult(X, rd(Y, Y)), ld(X, rd(Y, Y))), ld(ld(X, rd(Y, Y)), ld(X, rd(Y, Y))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 43 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(mult(mult(X, rd(Y, Y)), X), ld(ld(X, rd(Y, Y)), ld(X, rd(Y, Y))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 40 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(rd(ld(ld(X, rd(Y, Y)), ld(X, rd(Y, Y))), ld(X, ld(rd(Y, Y), ld(X, ld(ld(X, rd(Y, Y)), ld(X, rd(Y, Y))))))), ld(ld(X, rd(Y, Y)), ld(X, rd(Y, Y))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 6 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(Y, Y), ld(X, ld(ld(X, rd(Y, Y)), ld(X, rd(Y, Y))))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by axiom 3 (f01) R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(Y, Y), ld(X, ld(ld(X, rd(Y, Y)), ld(X, mult(mult(rd(Y, Y), X), ld(mult(rd(Y, Y), X), rd(Y, Y))))))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 19 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(Y, Y), ld(X, ld(ld(X, rd(Y, Y)), mult(ld(X, rd(Y, Y)), mult(X, ld(mult(rd(Y, Y), X), rd(Y, Y))))))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by axiom 1 (f02) }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(Y, Y), ld(X, mult(X, ld(mult(rd(Y, Y), X), rd(Y, Y))))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by axiom 1 (f02) }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(Y, Y), ld(mult(rd(Y, Y), X), rd(Y, Y))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 26 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(Y, Y), ld(ld(rd(Y, Y), X), rd(Y, Y))))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 6 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(rd(Y, Y), ld(rd(Y, Y), ld(ld(rd(Y, Y), X), rd(Y, Y)))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 34 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(rd(Y, Y), ld(ld(rd(Y, Y), rd(Y, Y)), ld(ld(rd(Y, Y), X), rd(Y, Y)))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 37 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(rd(Y, Y), ld(rd(rd(Y, Y), rd(Y, Y)), ld(ld(rd(Y, Y), X), rd(Y, Y)))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 35 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(rd(Y, Y), ld(mult(rd(Y, Y), rd(Y, Y)), ld(ld(rd(Y, Y), X), rd(Y, Y)))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 23 R->L }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(mult(mult(rd(Y, Y), rd(Y, Y)), rd(Y, Y)), ld(mult(rd(Y, Y), rd(Y, Y)), ld(ld(rd(Y, Y), X), rd(Y, Y)))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 39 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(mult(mult(mult(rd(Y, Y), rd(Y, Y)), ld(rd(Y, Y), X)), mult(rd(Y, Y), rd(Y, Y))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 35 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(mult(mult(rd(rd(Y, Y), rd(Y, Y)), ld(rd(Y, Y), X)), mult(rd(Y, Y), rd(Y, Y))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 35 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(mult(mult(rd(rd(Y, Y), rd(Y, Y)), ld(rd(Y, Y), X)), rd(rd(Y, Y), rd(Y, Y))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 22 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(mult(rd(rd(Y, Y), rd(Y, Y)), mult(ld(rd(Y, Y), X), rd(Y, Y))), rd(Y, Y)), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 37 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(mult(ld(rd(Y, Y), rd(Y, Y)), mult(ld(rd(Y, Y), X), rd(Y, Y))), rd(Y, Y)), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 34 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(mult(rd(Y, Y), mult(ld(rd(Y, Y), X), rd(Y, Y))), rd(Y, Y)), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 26 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(rd(ld(rd(Y, Y), mult(ld(rd(Y, Y), X), rd(Y, Y))), rd(Y, Y)), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 32 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(ld(rd(Y, Y), mult(mult(ld(rd(Y, Y), X), rd(Y, Y)), rd(Y, Y))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 38 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(ld(rd(Y, Y), rd(ld(rd(Y, Y), X), rd(Y, Y))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 32 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(ld(rd(Y, Y), ld(rd(Y, Y), mult(X, rd(Y, Y)))), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 29 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(rd(mult(X, rd(Y, Y)), ld(X, ld(mult(X, rd(Y, Y)), rd(Y, Y)))), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by lemma 39 }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(rd(mult(mult(X, mult(X, rd(Y, Y))), X), X), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by axiom 2 (f04) }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), rd(mult(X, mult(X, rd(Y, Y))), mult(X, rd(Y, Y))))
% 5.48/1.09 = { by axiom 2 (f04) }
% 5.48/1.09 ld(mult(X, rd(Y, Y)), X)
% 5.48/1.09
% 5.48/1.09 Goal 1 (goal): mult(x0, rd(x1, x1)) = x0.
% 5.48/1.09 Proof:
% 5.48/1.09 mult(x0, rd(x1, x1))
% 5.48/1.09 = { by axiom 3 (f01) R->L }
% 5.48/1.09 mult(mult(mult(x0, rd(x1, x1)), ld(mult(x0, rd(x1, x1)), x0)), rd(x1, x1))
% 5.48/1.09 = { by lemma 44 R->L }
% 5.48/1.09 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), mult(mult(x0, rd(x1, x1)), x0))), rd(x1, x1))
% 5.48/1.09 = { by lemma 15 R->L }
% 5.48/1.09 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(mult(mult(x0, rd(x1, x1)), x0), mult(mult(x0, rd(x1, x1)), x0))))), rd(x1, x1))
% 5.48/1.09 = { by lemma 44 }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(mult(x0, rd(x1, x1)), x0)))), rd(x1, x1))
% 5.48/1.10 = { by lemma 29 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(rd(x1, x1), ld(mult(x0, rd(x1, x1)), x0)))))), rd(x1, x1))
% 5.48/1.10 = { by axiom 1 (f02) R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(rd(x1, x1), ld(mult(x0, rd(x1, x1)), ld(rd(x1, x1), mult(rd(x1, x1), x0)))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 26 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(x1, x1), ld(mult(x0, rd(x1, x1)), ld(rd(x1, x1), mult(rd(x1, x1), x0)))))))), rd(x1, x1))
% 5.48/1.10 = { by axiom 3 (f01) R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(x1, x1), ld(mult(x0, rd(x1, x1)), ld(rd(x1, x1), mult(ld(rd(x1, x1), x0), ld(ld(rd(x1, x1), x0), mult(rd(x1, x1), x0)))))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 41 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(x1, x1), ld(mult(x0, rd(x1, x1)), mult(mult(x0, rd(x1, x1)), ld(rd(x1, x1), ld(ld(rd(x1, x1), x0), mult(rd(x1, x1), x0)))))))))), rd(x1, x1))
% 5.48/1.10 = { by axiom 1 (f02) }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(x1, x1), ld(rd(x1, x1), ld(ld(rd(x1, x1), x0), mult(rd(x1, x1), x0)))))))), rd(x1, x1))
% 5.48/1.10 = { by axiom 3 (f01) }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(ld(rd(x1, x1), x0), mult(rd(x1, x1), x0)))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 26 }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)))))), rd(x1, x1))
% 5.48/1.10 = { by axiom 4 (f03) R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 15 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, ld(rd(ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))), X)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 26 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(rd(mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))), X)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 13 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(mult(mult(ld(rd(x1, x1), x0), rd(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))), ld(rd(x1, x1), x0)), X)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by axiom 5 (f05) R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), mult(rd(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), mult(ld(rd(x1, x1), x0), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 26 }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), ld(rd(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), mult(ld(rd(x1, x1), x0), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 28 }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), ld(ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), mult(ld(rd(x1, x1), x0), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 18 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), ld(ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 28 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), ld(rd(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 27 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), mult(ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 30 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), mult(rd(Y, mult(ld(rd(x1, x1), x0), Y)), mult(ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), rd(ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), rd(Y, mult(ld(rd(x1, x1), x0), Y)))), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 17 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), mult(rd(Y, mult(ld(rd(x1, x1), x0), Y)), mult(ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), rd(ld(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), rd(ld(ld(rd(x1, x1), x0), Z), Z))), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 28 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), mult(rd(Y, mult(ld(rd(x1, x1), x0), Y)), mult(ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), rd(rd(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), rd(ld(ld(rd(x1, x1), x0), Z), Z))), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 21 R->L }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), mult(rd(Y, mult(ld(rd(x1, x1), x0), Y)), mult(ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), rd(mult(ld(rd(x1, x1), x0), rd(ld(ld(rd(x1, x1), x0), Z), Z)), rd(ld(ld(rd(x1, x1), x0), Z), Z))), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by axiom 2 (f04) }
% 5.48/1.10 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), mult(rd(Y, mult(ld(rd(x1, x1), x0), Y)), mult(ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), ld(rd(x1, x1), x0)), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.10 = { by lemma 36 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), ld(ld(rd(x1, x1), x0), mult(ld(rd(Y, mult(ld(rd(x1, x1), x0), Y)), ld(rd(x1, x1), x0)), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 18 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(ld(rd(x1, x1), x0), ld(ld(rd(x1, x1), x0), mult(mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), X)))), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.11 = { by axiom 3 (f01) }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), mult(rd(X, mult(mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), X)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 36 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 42 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0)), mult(ld(rd(x1, x1), x0), ld(rd(x1, x1), x0))))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 42 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), rd(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0)), ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0))))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 40 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), mult(mult(rd(x1, x1), ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0))), rd(x1, x1)))), rd(x1, x1))
% 5.48/1.11 = { by lemma 26 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), mult(ld(rd(x1, x1), ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0))), rd(x1, x1)))), rd(x1, x1))
% 5.48/1.11 = { by axiom 3 (f01) R->L }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), mult(rd(x1, x1), ld(rd(x1, x1), mult(ld(rd(x1, x1), ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0))), rd(x1, x1)))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 33 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), mult(rd(x1, x1), rd(ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0)), rd(x1, x1))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 26 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), rd(ld(rd(x1, x1), mult(mult(x0, rd(x1, x1)), x0)), rd(x1, x1))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 32 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), ld(rd(x1, x1), ld(rd(x1, x1), mult(mult(mult(x0, rd(x1, x1)), x0), rd(x1, x1)))))), rd(x1, x1))
% 5.48/1.11 = { by lemma 29 }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), ld(mult(mult(x0, rd(x1, x1)), x0), mult(mult(mult(x0, rd(x1, x1)), x0), rd(x1, x1)))), rd(x1, x1))
% 5.48/1.11 = { by axiom 1 (f02) }
% 5.48/1.11 mult(mult(mult(x0, rd(x1, x1)), rd(x1, x1)), rd(x1, x1))
% 5.48/1.11 = { by lemma 38 }
% 5.48/1.11 rd(mult(x0, rd(x1, x1)), rd(x1, x1))
% 5.48/1.11 = { by axiom 2 (f04) }
% 5.48/1.11 x0
% 5.48/1.11 % SZS output end Proof
% 5.48/1.11
% 5.48/1.11 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------