%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ALG401-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 : Wed Aug 30 16:09:31 EDT 2023

% Result   : Unsatisfiable 6.23s 6.41s
% Output   : Proof 6.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.22  % Problem    : ALG401-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.23  % Command    : do_cvc5 %s %d
% 0.23/0.44  % Computer : n002.cluster.edu
% 0.23/0.44  % Model    : x86_64 x86_64
% 0.23/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.44  % Memory   : 8042.1875MB
% 0.23/0.44  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.23/0.44  % CPULimit   : 300
% 0.23/0.44  % WCLimit    : 300
% 0.23/0.44  % DateTime   : Mon Aug 28 04:43:49 EDT 2023
% 0.23/0.45  % CPUTime    : 
% 0.30/0.68  %----Proving TF0_NAR, FOF, or CNF
% 0.30/0.69  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OIiJiMEIt4/cvc5---1.0.5_21466.p...
% 0.53/0.86  ------- get file name : TPTP file name is ALG401-1
% 0.69/0.86  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21466.smt2...
% 0.69/0.86  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.23/6.41  % SZS status Unsatisfiable for ALG401-1
% 6.23/6.41  % SZS output start Proof for ALG401-1
% 6.23/6.44  (
% 6.23/6.44  (let ((_let_1 (tptp.class_HOL_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex))) (let ((_let_3 (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex))) (let ((_let_4 (tptp.class_Ring__and__Field_Oring tptp.tc_Complex_Ocomplex))) (let ((_let_5 (tptp.class_Ring__and__Field_Ofield tptp.tc_Complex_Ocomplex))) (let ((_let_6 (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Complex_Ocomplex))) (let ((_let_7 (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex))) (let ((_let_8 (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Complex_Ocomplex))) (let ((_let_9 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))) (let ((_let_10 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex))) (let ((_let_11 (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex))) (let ((_let_12 (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))) (let ((_let_13 (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex))) (let ((_let_14 (tptp.c_Power_Opower__class_Opower tptp.v_w____ tptp.v_k____ tptp.tc_Complex_Ocomplex))) (let ((_let_15 (tptp.c_HOL_Otimes__class_Otimes tptp.v_a____ _let_14 tptp.tc_Complex_Ocomplex))) (let ((_let_16 (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_17 (tptp.c_HOL_Oplus__class_Oplus _let_16 _let_15 tptp.tc_Complex_Ocomplex))) (let ((_let_18 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_19 (tptp.c_Polynomial_Opoly tptp.v_q____ _let_18 tptp.tc_Complex_Ocomplex))) (let ((_let_20 (tptp.c_HOL_Oinverse__class_Oinverse _let_19 tptp.tc_Complex_Ocomplex))) (let ((_let_21 (tptp.c_Polynomial_Osmult _let_20 tptp.v_q____ tptp.tc_Complex_Ocomplex))) (let ((_let_22 (tptp.c_Polynomial_Opoly _let_21 tptp.v_w____ tptp.tc_Complex_Ocomplex))) (let ((_let_23 (= (tptp.c_RealVector_Onorm__class_Onorm _let_22 tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm _let_17 tptp.tc_Complex_Ocomplex)))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.c_Polynomial_OpCons tptp.v_a____ tptp.v_s____ tptp.tc_Complex_Ocomplex))) (let ((_let_26 (tptp.c_Polynomial_Opoly _let_25 tptp.v_w____ tptp.tc_Complex_Ocomplex))) (let ((_let_27 (tptp.c_HOL_Otimes__class_Otimes _let_14 _let_26 tptp.tc_Complex_Ocomplex))) (let ((_let_28 (tptp.c_Polynomial_Opoly _let_21 _let_18 tptp.tc_Complex_Ocomplex))) (let ((_let_29 (tptp.c_HOL_Oplus__class_Oplus _let_28 _let_27 tptp.tc_Complex_Ocomplex))) (let ((_let_30 (= _let_22 _let_29))) (let ((_let_31 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (let ((_let_32 (= tptp.v_s____ _let_31))) (let ((_let_33 (= _let_28 _let_16))) (let ((_let_34 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Osmult V_a V_p T_a) V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Polynomial_Opoly V_p V_x T_a) T_a)))))) (let ((_let_35 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))))) (let ((_let_36 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_37 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))))) (let ((_let_38 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) T_a)))))) (let ((_let_39 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_u T_a))) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) V_u))))) (let ((_let_40 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a)))))) (let ((_let_41 (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))))) (let ((_let_42 (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Polynomial_Opoly tptp.v_q____ _let_1 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.v_q____ tptp.tc_Complex_Ocomplex))) (= (tptp.c_Polynomial_Opoly _let_2 V_z tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Opoly _let_2 _let_1 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_z tptp.v_k____ tptp.tc_Complex_Ocomplex) (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_OpCons tptp.v_a____ tptp.v_s____ tptp.tc_Complex_Ocomplex) V_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))))))) (let ((_let_43 (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize _let_21 tptp.tc_Complex_Ocomplex))) (let ((_let_44 (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.v_q____ tptp.tc_Complex_Ocomplex))) (let ((_let_45 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_OpCons V_a V_p T_a) V_x T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_Polynomial_Opoly V_p V_x T_a) T_a) T_a)))))) (let ((_let_46 (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oinverse__class_Oinverse V_y tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))))) (let ((_let_47 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_48 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))))) (let ((_let_49 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) V_a))))) (let ((_let_50 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a))) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d))))) (let ((_let_51 (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))))) (let ((_let_52 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))))) (let ((_let_53 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_54 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))))) (let ((_let_55 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))))) (let ((_let_56 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)))))) (let ((_let_57 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_58 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff _let_1 (tptp.c_Polynomial_Odegree _let_1 T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (let ((_let_59 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a) _let_1)))))) (let ((_let_60 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))))) (let ((_let_61 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))) (let ((_let_62 (= _let_16 _let_28))) (let ((_let_63 (tptp.c_Polynomial_OpCons _let_18 _let_31 tptp.tc_Complex_Ocomplex))) (let ((_let_64 (= _let_31 _let_63))) (let ((_let_65 (= _let_18 (tptp.c_Polynomial_Ocoeff _let_31 (tptp.c_Polynomial_Odegree _let_31 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_66 (tptp.c_HOL_Ouminus__class_Ouminus _let_27 tptp.tc_Complex_Ocomplex))) (let ((_let_67 (tptp.c_HOL_Ominus__class_Ominus _let_28 _let_66 tptp.tc_Complex_Ocomplex))) (let ((_let_68 (= _let_29 _let_67))) (let ((_let_69 (tptp.c_HOL_Ouminus__class_Ouminus _let_15 tptp.tc_Complex_Ocomplex))) (let ((_let_70 (tptp.c_HOL_Ominus__class_Ominus _let_16 _let_69 tptp.tc_Complex_Ocomplex))) (let ((_let_71 (= _let_17 _let_70))) (let ((_let_72 (tptp.c_HOL_Ouminus__class_Ouminus _let_18 tptp.tc_Complex_Ocomplex))) (let ((_let_73 (= _let_18 _let_72))) (let ((_let_74 (tptp.c_HOL_Oinverse__class_Odivide _let_18 _let_18 tptp.tc_Complex_Ocomplex))) (let ((_let_75 (= _let_18 _let_74))) (let ((_let_76 (tptp.c_HOL_Ominus__class_Ominus _let_17 _let_15 tptp.tc_Complex_Ocomplex))) (let ((_let_77 (= _let_16 _let_76))) (let ((_let_78 (tptp.c_Polynomial_Opoly tptp.v_s____ tptp.v_w____ tptp.tc_Complex_Ocomplex))) (let ((_let_79 (tptp.c_HOL_Otimes__class_Otimes tptp.v_w____ _let_78 tptp.tc_Complex_Ocomplex))) (let ((_let_80 (tptp.c_HOL_Oplus__class_Oplus tptp.v_a____ _let_79 tptp.tc_Complex_Ocomplex))) (let ((_let_81 (= _let_26 _let_80))) (let ((_let_82 (tptp.c_HOL_Oplus__class_Oplus _let_27 _let_28 tptp.tc_Complex_Ocomplex))) (let ((_let_83 (= _let_29 _let_82))) (let ((_let_84 (tptp.c_HOL_Oplus__class_Oplus _let_15 _let_16 tptp.tc_Complex_Ocomplex))) (let ((_let_85 (= _let_17 _let_84))) (let ((_let_86 (tptp.c_HOL_Oinverse__class_Oinverse _let_18 tptp.tc_Complex_Ocomplex))) (let ((_let_87 (= _let_18 _let_86))) (let ((_let_88 (tptp.c_HOL_Otimes__class_Otimes _let_14 tptp.v_a____ tptp.tc_Complex_Ocomplex))) (let ((_let_89 (= _let_15 _let_88))) (let ((_let_90 (= _let_22 (tptp.c_HOL_Otimes__class_Otimes _let_20 (tptp.c_Polynomial_Opoly tptp.v_q____ tptp.v_w____ tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_91 (= _let_74 (tptp.c_HOL_Otimes__class_Otimes _let_18 _let_86 tptp.tc_Complex_Ocomplex)))) (let ((_let_92 (tptp.c_HOL_Ominus__class_Ominus _let_18 _let_18 tptp.tc_Complex_Ocomplex))) (let ((_let_93 (= _let_72 _let_92))) (let ((_let_94 (= _let_92 (tptp.c_HOL_Oplus__class_Oplus _let_18 _let_72 tptp.tc_Complex_Ocomplex)))) (let ((_let_95 (tptp.c_HOL_Ouminus__class_Ouminus _let_28 tptp.tc_Complex_Ocomplex))) (let ((_let_96 (tptp.c_HOL_Ominus__class_Ominus _let_27 _let_95 tptp.tc_Complex_Ocomplex))) (let ((_let_97 (= _let_82 _let_96))) (let ((_let_98 (tptp.c_HOL_Ouminus__class_Ouminus _let_16 tptp.tc_Complex_Ocomplex))) (let ((_let_99 (tptp.c_HOL_Ominus__class_Ominus _let_15 _let_98 tptp.tc_Complex_Ocomplex))) (let ((_let_100 (= _let_84 _let_99))) (let ((_let_101 (tptp.c_HOL_Ominus__class_Ominus _let_66 _let_28 tptp.tc_Complex_Ocomplex))) (let ((_let_102 (= (tptp.c_HOL_Ouminus__class_Ouminus _let_67 tptp.tc_Complex_Ocomplex) _let_101))) (let ((_let_103 (tptp.c_HOL_Ominus__class_Ominus _let_69 _let_16 tptp.tc_Complex_Ocomplex))) (let ((_let_104 (= (tptp.c_HOL_Ouminus__class_Ouminus _let_70 tptp.tc_Complex_Ocomplex) _let_103))) (let ((_let_105 (tptp.c_HOL_Ominus__class_Ominus _let_15 _let_17 tptp.tc_Complex_Ocomplex))) (let ((_let_106 (= (tptp.c_HOL_Ouminus__class_Ouminus _let_76 tptp.tc_Complex_Ocomplex) _let_105))) (let ((_let_107 (= _let_15 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus _let_20 _let_20 tptp.tc_Complex_Ocomplex) _let_19 tptp.tc_Complex_Ocomplex) _let_15 tptp.tc_Complex_Ocomplex)))) (let ((_let_108 (= (tptp.c_RealVector_Onorm__class_Onorm _let_67 tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm _let_101 tptp.tc_Complex_Ocomplex)))) (let ((_let_109 (= (tptp.c_RealVector_Onorm__class_Onorm _let_70 tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm _let_103 tptp.tc_Complex_Ocomplex)))) (let ((_let_110 (tptp.c_Polynomial_Opoly _let_31 tptp.v_w____ tptp.tc_Complex_Ocomplex))) (let ((_let_111 (= _let_18 _let_110))) (let ((_let_112 (= (tptp.c_Polynomial_Opoly _let_63 tptp.v_w____ tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oplus__class_Oplus _let_18 (tptp.c_HOL_Otimes__class_Otimes tptp.v_w____ _let_110 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(tptp.c_HOL_Oplus__class_Oplus _let_15 _let_116 tptp.tc_Complex_Ocomplex)))) (let ((_let_121 (tptp.c_HOL_Ouminus__class_Ouminus _let_79 tptp.tc_Complex_Ocomplex))) (let ((_let_122 (= _let_121 (tptp.c_HOL_Ominus__class_Ominus _let_18 _let_79 tptp.tc_Complex_Ocomplex)))) (let ((_let_123 (= (tptp.c_HOL_Oplus__class_Oplus _let_18 _let_79 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ominus__class_Ominus _let_18 _let_121 tptp.tc_Complex_Ocomplex)))) (let ((_let_124 (= (tptp.c_HOL_Ouminus__class_Ouminus _let_96 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ominus__class_Ominus _let_95 _let_27 tptp.tc_Complex_Ocomplex)))) (let ((_let_125 (= (tptp.c_HOL_Ouminus__class_Ouminus _let_99 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ominus__class_Ominus _let_98 _let_15 tptp.tc_Complex_Ocomplex)))) (let ((_let_126 (= (tptp.c_HOL_Otimes__class_Otimes tptp.v_w____ _let_72 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes tptp.v_w____ _let_18 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_127 (SYMM (ASSUME :args (_let_33))))) (let ((_let_128 (ASSUME :args (_let_32)))) (let ((_let_129 (ASSUME :args (_let_30)))) (let ((_let_130 (not _let_1))) (let ((_let_131 (or _let_130 _let_64))) (let ((_let_132 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_HOL_Ozero T_a)) (= _let_1 (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a))))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (ASSUME :args (_let_1)))) (let ((_let_135 (or _let_130 _let_65))) (let ((_let_136 (_let_58))) (let ((_let_137 (ASSUME :args _let_136))) (let ((_let_138 (not _let_6))) (let ((_let_139 (or _let_138 _let_68))) (let ((_let_140 (_let_56))) (let ((_let_141 (ASSUME :args _let_140))) (let ((_let_142 ((tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)))) (let ((_let_143 (ASSUME :args (_let_6)))) 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:args (_let_73 false _let_6 false _let_145)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_138 _let_71 (not _let_144)))) _let_143 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_141 :args (tptp.tc_Complex_Ocomplex _let_16 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_142)) :args _let_140))) _let_141 :args (_let_144 false _let_56)) :args (_let_71 false _let_6 false _let_144)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_138 _let_68 (not _let_139)))) _let_143 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_141 :args (tptp.tc_Complex_Ocomplex _let_28 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_142)) :args _let_140))) _let_141 :args (_let_139 false _let_56)) :args (_let_68 false _let_6 false _let_139)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_135)) :args ((or _let_130 _let_65 (not _let_135)))) _let_134 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_137 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_HOL_Ozero T_a) false))))) :args _let_136))) _let_137 :args (_let_135 false _let_58)) :args (_let_65 false _let_1 false _let_135)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_130 _let_64 (not _let_131)))) _let_134 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_133 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_HOL_Ozero T_a) false))))) :args (_let_132))) _let_133 :args (_let_131 false _let_132)) :args (_let_64 false _let_1 false _let_131)) (ASSUME :args (_let_24)) _let_129 _let_128 _let_127 :args (false false _let_126 false _let_125 false _let_124 false _let_123 false _let_122 false _let_120 false _let_119 false _let_118 false _let_117 false _let_115 false _let_113 false _let_112 false _let_111 false _let_109 false _let_108 false _let_107 false _let_106 false _let_104 false _let_102 false _let_100 false _let_97 false _let_94 false _let_93 false _let_91 false _let_90 false _let_89 false _let_87 false _let_85 false _let_83 false _let_81 false _let_77 false _let_75 false _let_73 false _let_71 false _let_68 false _let_65 false _let_64 true _let_23 false _let_30 false _let_32 false _let_62)) :args ((forall ((T_a $$unsorted) (V_p $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_Polynomial_Opoly V_p V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ouminus__class_Ouminus V_c T_a) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) T_a) T_a) V_p _let_1)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_p $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (not (= (tptp.c_Polynomial_Osmult V_c V_p T_a) (tptp.c_Polynomial_OpCons V_a V_p T_a))) (= V_p (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (= _let_44 (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.v_pa____ tptp.tc_Complex_Ocomplex)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_p V_q _let_1) V_r _let_1) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_p V_r _let_1) (tptp.c_HOL_Otimes__class_Otimes V_q V_r _let_1) _let_1))))) (forall ((V_z1 $$unsorted) (V_z2 $$unsorted) (V_z3 $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_z1 V_z2 tptp.tc_RealDef_Oreal) V_z3 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z1 (tptp.c_HOL_Otimes__class_Otimes V_z2 V_z3 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) _let_2 _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p _let_2 _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal) (= V_x V_y) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((T_a $$unsorted) (V_q $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_q _let_1) (not (tptp.c_Polynomial_Opdivmod__rel V_x _let_1 V_q V_r T_a))))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_r _let_1) (not (tptp.c_Polynomial_Opdivmod__rel _let_1 V_y V_q V_r T_a))))) (forall ((T_a $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_q _let_1) (not (tptp.c_Polynomial_Opdivmod__rel _let_1 V_y V_q V_r T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.c_Polynomial_Opdivmod__rel V_x _let_1 V_q V_r T_a)) (= V_q _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Omonom V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_Polynomial_OpCons V_a (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_Omonom V_a V_n T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z _let_1) _let_1) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_y (tptp.c_Divides_Odiv__class_Omod (tptp.c_Divides_Odiv__class_Odiv V_x V_y _let_1) V_z _let_1) _let_1) (tptp.c_Divides_Odiv__class_Omod V_x V_y _let_1) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_b $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_Polynomial_OpCons V_b V_q T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_b $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_Polynomial_OpCons V_b V_q T_a))) (= V_p V_q))) (forall ((V_m $$unsorted)) (= (tptp.c_Power_Opower__class_Opower V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_r V_x) (not (tptp.c_Polynomial_Opdivmod__rel V_x (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_q V_r T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) (tptp.c_Divides_Odiv__class_Odiv V_w V_z T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_x V_w T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_w T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_Ocoeff V_p (tptp.c_Polynomial_Odegree V_p T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_p (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_a T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_r1 $$unsorted) (V_r2 $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q2 $$unsorted) (V_q1 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_r1 V_r2) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q2 V_r2 T_a)) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q1 V_r1 T_a)))) (forall ((T_a $$unsorted) (V_q1 $$unsorted) (V_q2 $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r2 $$unsorted) (V_r1 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_q1 V_q2) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q2 V_r2 T_a)) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q1 V_r1 T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (= V_z V_w) (not (tptp.c_lessequals V_w V_z tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_z V_w tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oone__class_Oone _let_1) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_p $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Osmult V_c V_p T_a) (tptp.c_Polynomial_OpCons V_a V_p T_a) _let_1) _let_2)) (= V_p _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Opoly V_p V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ouminus__class_Ouminus V_c T_a) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) T_a) T_a) V_p _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) _let_61 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_OpCons V_a (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly _let_1 V_h T_a) _let_1)))) _let_60 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Power_Opower__class_Opower (tptp.c_Polynomial_OpCons V_a (tptp.c_Polynomial_OpCons (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) T_a) T_a) V_n _let_1) T_a) V_n)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Omonom V_a V_n T_a) (tptp.c_Polynomial_Omonom V_b V_n T_a) (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat))) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (= V_m V_n))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_x V_z tptp.tc_nat))) (= V_y V_z))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel _let_1 V_y _let_1 _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_Omonom V_a V_m T_a) (tptp.c_Polynomial_Omonom V_b V_n T_a) (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_b V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a))) _let_59 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_HOL_Oplus__class_Oplus V_p V_q (tptp.tc_Polynomial_Opoly T_a)) V_n T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Ocoeff V_p V_n T_a) (tptp.c_Polynomial_Ocoeff V_q V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (not (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly V_p V_h T_a) _let_1)) (= V_p _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Polynomial_Omonom V_a V_x T_a) V_x T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_2 V_y _let_1) _let_2 _let_1) V_y _let_2 _let_2 T_a))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_2 _let_1) V_r _let_1) _let_2 _let_2 V_r T_a))))) _let_58 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Polynomial_OpCons V_a (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_HOL_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize V_p T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= V_p (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel V_x _let_1 _let_1 V_x T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_HOL_Otimes__class_Otimes V_p V_q _let_1) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Odegree V_p T_a) (tptp.c_Polynomial_Odegree V_q T_a) tptp.tc_nat)) (= V_q _let_2) (= V_p _let_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) _let_1)) (= V_p _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_b T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a_H T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_x V_y (tptp.tc_Polynomial_Opoly T_a)) V_q) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q V_r T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_b $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_Polynomial_OpCons V_b V_q T_a) _let_1) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_p V_q _let_1) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) V_n T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Polynomial_Omonom V_a V_n T_a) T_a) V_n) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_2 V_q _let_1) _let_2))))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_p _let_2 _let_1) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_OpCons V_a V_p T_a) V_q _let_1) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Osmult V_a V_q T_a) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_p V_q _let_1) T_a) _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_p (tptp.c_Polynomial_OpCons V_a V_q T_a) _let_1) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Osmult V_a V_p T_a) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_p V_q _let_1) T_a) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a tptp.tc_nat))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) V_m)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_q V_y _let_1) V_r _let_1)) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q V_r T_a))))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Power_Opower__class_Opower (tptp.c_Polynomial_OpCons V_a (tptp.c_Polynomial_OpCons _let_1 (tptp.c_HOL_Ozero__class_Ozero _let_2) T_a) T_a) V_n _let_2) V_n T_a) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_x V_z T_a) (tptp.c_Divides_Odiv__class_Odiv V_y V_z T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_HOL_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Omonom (tptp.c_HOL_Ozero__class_Ozero T_a) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_lessequals V_c _let_1 T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_h $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly V_p V_h T_a) T_a) (tptp.c_Polynomial_Odegree V_p T_a)))) (forall ((T_a $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly _let_1 V_h T_a) _let_1)))) (forall ((V_z $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal) V_z)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel V_x V_y (tptp.c_Divides_Odiv__class_Odiv V_x V_y _let_1) (tptp.c_Divides_Odiv__class_Omod V_x V_y _let_1) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly V_p V_h T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly (tptp.c_Polynomial_OpCons V_a V_p T_a) V_h T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Osmult V_h _let_1 T_a) (tptp.c_Polynomial_OpCons V_a _let_1 T_a) (tptp.tc_Polynomial_Opoly T_a)))))) (= (tptp.c_HOL_Oplus__class_Oplus _let_53 _let_53 tptp.tc_nat) _let_53) (forall ((V_z $$unsorted) (V_w $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_z V_w tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_w V_z tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Polynomial_Omonom V_a V_m T_a) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_m V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_x V_y (tptp.tc_Polynomial_Opoly T_a)) V_r) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q V_r T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) V_a T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_Polynomial_Opoly V_p (tptp.c_HOL_Ouminus__class_Ouminus V_c T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_OpCons V_c (tptp.c_Polynomial_OpCons (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) T_a) T_a) V_p _let_1)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Opoly V_p (tptp.c_HOL_Ouminus__class_Ouminus V_c T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_OpCons V_c (tptp.c_Polynomial_OpCons (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) T_a) T_a) V_p _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree V_q T_a))) (let ((_let_2 (tptp.c_Polynomial_Odegree V_p T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_HOL_Otimes__class_Otimes V_p V_q (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 tptp.tc_nat) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_Ocoeff V_p _let_2 T_a) (tptp.c_Polynomial_Ocoeff V_q _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_q_H $$unsorted) (V_r_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z _let_1) V_q_H (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_y V_r_H _let_1) V_r _let_1) T_a) (not (tptp.c_Polynomial_Opdivmod__rel V_q V_z V_q_H V_r_H T_a)) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q V_r T_a))))) (= (tptp.c_HOL_Otimes__class_Otimes _let_57 _let_57 tptp.tc_RealDef_Oreal) _let_57) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_a T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) _let_56 (forall ((V_a $$unsorted) (V_p $$unsorted)) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize (tptp.v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 V_a V_p) tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize V_p tptp.tc_Complex_Ocomplex))) (forall ((T_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero _let_1) V_q _let_1) V_q)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_p (tptp.c_HOL_Ozero__class_Ozero _let_1) _let_1) V_p)))) (forall ((V_x $$unsorted)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) V_n)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) _let_55 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) _let_54 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_b T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_Polynomial_Ocoeff V_p (tptp.c_Polynomial_Odegree V_p T_a) T_a) (tptp.c_Polynomial_Ocoeff V_q (tptp.c_Polynomial_Odegree V_q T_a) T_a))) (= V_p V_q) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_q V_p _let_1)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z _let_1) _let_1) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Odiv V_x V_y _let_1) V_z _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_j V_k tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_i V_j tptp.tc_RealDef_Oreal)))) (forall ((V_w $$unsorted)) (tptp.c_lessequals V_w V_w tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_y _let_2) (tptp.c_Polynomial_Opdivmod__rel (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_q V_y _let_1) _let_2 _let_1) V_y V_q _let_2 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_HOL_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_Omonom V_a V_n T_a) (tptp.c_Polynomial_Omonom V_b V_n T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_w V_z tptp.tc_RealDef_Oreal) (tptp.c_lessequals V_z V_w tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_lessequals V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (not (= tptp.v_k____ _let_53)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= V_a _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 V_a T_a))))) _let_52 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_d T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))))) _let_51 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_z V_w T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_w T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b (tptp.c_HOL_Otimes__class_Otimes V_b V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ominus__class_Ominus V_b V_b_H T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus V_y V_b T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) T_a)))) _let_50 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a))) (= V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_x V_n T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_x V_n T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_p T_a) (tptp.c_Power_Opower__class_Opower V_x V_q T_a) T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Oplus__class_Oplus V_p V_q tptp.tc_nat) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) V_n T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_m V_n))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_h $$unsorted)) (or (not (tptp.class_RealVector_Oreal__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) V_h T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) V_h T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) V_h T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_d $$unsorted) (V_x $$unsorted) (V_t $$unsorted) (V_k $$unsorted) (V_D $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus V_x V_t T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_x (tptp.c_HOL_Otimes__class_Otimes V_k V_D T_a) T_a) V_t T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_D T_a)))) (forall ((T_a $$unsorted) (V_d $$unsorted) (V_x $$unsorted) (V_k $$unsorted) (V_D $$unsorted) (V_t $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_x (tptp.c_HOL_Otimes__class_Otimes V_k V_D T_a) T_a) V_t T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus V_x V_t T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_D T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ominus__class_Ominus V_c V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y)) (= V_x (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) _let_49 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) V_h T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_h T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_r V_s tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) V_s tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_r tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_n tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) V_q _let_1)) (= V_q (tptp.c_HOL_Ozero__class_Ozero _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a)))) _let_48 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_c $$unsorted) (V_q $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_p (tptp.c_Polynomial_Osmult V_c V_q T_a) (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons V_r V_q T_a))) (= V_r (tptp.c_Polynomial_Opoly V_p V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Osmult V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Polynomial_Osmult V_a V_x T_a) V_y _let_1) (tptp.c_Polynomial_Osmult V_a (tptp.c_Divides_Odiv__class_Omod V_x V_y _let_1) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel (tptp.c_Polynomial_Osmult V_a V_x T_a) V_y (tptp.c_Polynomial_Osmult V_a V_q T_a) (tptp.c_Polynomial_Osmult V_a V_r T_a) T_a) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q V_r T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_HOL_Oplus__class_Oplus V_p V_q _let_1) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Osmult V_a V_p T_a) (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Polynomial_Osmult V_a V_x T_a) V_y _let_1) (tptp.c_Polynomial_Osmult V_a (tptp.c_Divides_Odiv__class_Odiv V_x V_y _let_1) T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1) (tptp.c_Polynomial_Osmult V_a (tptp.c_HOL_Otimes__class_Otimes V_p V_q _let_1) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1) (tptp.c_Polynomial_Osmult V_a (tptp.c_HOL_Otimes__class_Otimes V_p V_q _let_1) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oinverse__class_Oinverse V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_Omonom (tptp.c_HOL_Oone__class_Oone T_a) V_n T_a) V_p (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Polynomial_Opoly V_p V_x T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.v_s____ tptp.tc_Complex_Ocomplex) tptp.v_k____ tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) _let_43) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_n tptp.tc_RealDef_Oreal)))) (forall ((V_p $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.t_a))) (or (not (tptp.class_Ring__and__Field_Oidom tptp.t_a)) (not (= (tptp.v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2 V_p) _let_1)) (= (tptp.c_Polynomial_Opoly V_p V_z tptp.t_a) _let_1) (= V_z _let_1)))) _let_47 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Polynomial_Osmult V_a V_p T_a) T_a) (tptp.c_Polynomial_Odegree V_p T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_Polynomial_Osmult V_a V_p T_a) _let_1)) (= V_p _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_x (tptp.c_Polynomial_Osmult V_a V_y T_a) _let_1) (tptp.c_Divides_Odiv__class_Omod V_x V_y _let_1)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Otimes__class_Otimes V_p V_q (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_Opoly V_p V_x T_a) (tptp.c_Polynomial_Opoly V_q V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_h $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly V_p V_h T_a) V_x T_a) (tptp.c_Polynomial_Opoly V_p (tptp.c_HOL_Oplus__class_Oplus V_h V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Oplus__class_Oplus V_p V_q (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Opoly V_p V_x T_a) (tptp.c_Polynomial_Opoly V_q V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Polynomial_Osmult V_a V_p T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Polynomial_Ocoeff V_p V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_Polynomial_OpCons V_b V_p T_a) T_a) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_Polynomial_Osmult V_a V_p T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_Polynomial_Omonom V_b V_n T_a) T_a) (tptp.c_Polynomial_Omonom (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_p T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Polynomial_Osmult V_a V_p T_a) (tptp.c_Polynomial_Osmult V_b V_p T_a) (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Power_Opower__class_Opower V_p V_n (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_Polynomial_Opoly V_p V_x T_a) V_n T_a)))) (forall ((V_w $$unsorted)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_q____ (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_pa____ V_w tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Complex_Oexpi (tptp.c_HOL_Oplus__class_Oplus V_a V_b tptp.tc_Complex_Ocomplex)) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Complex_Oexpi V_a) (tptp.c_Complex_Oexpi V_b) tptp.tc_Complex_Ocomplex))) (forall ((V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (= (tptp.c_Polynomial_Opoly (tptp.v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 V_a V_p) V_q tptp.tc_Complex_Ocomplex) (tptp.c_Polynomial_Opoly V_p (tptp.c_HOL_Oplus__class_Oplus V_a V_q tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))) _let_46 (= (tptp.c_Complex_Oexpi _let_18) _let_16) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_x _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1 T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) _let_45 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) tptp.tc_RealDef_Oreal)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Omonom V_a V_n T_a) V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_q $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Polynomial_Opdivmod__rel V_x (tptp.c_Polynomial_Osmult V_a V_y T_a) (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_q T_a) V_r T_a) (not (tptp.c_Polynomial_Opdivmod__rel V_x V_y V_q V_r T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_x (tptp.c_Polynomial_Osmult V_a V_y T_a) _let_1) (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_x V_y _let_1) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.v_q____ (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oinverse__class_Oinverse _let_1 tptp.tc_Complex_Ocomplex) tptp.v_q____ tptp.tc_Complex_Ocomplex) V_w tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_q____ V_w tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm _let_1 tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.v_q____ (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_q____ V_w tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm _let_1 tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oinverse__class_Oinverse _let_1 tptp.tc_Complex_Ocomplex) tptp.v_q____ tptp.tc_Complex_Ocomplex) V_w tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (= _let_44 _let_43) _let_42 (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) _let_41 (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) V_m T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_m T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a))) (= V_y V_z) (= V_w V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_d T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))) (= V_c V_d) (= V_a V_b))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_m V_m T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) V_m T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))) _let_40 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.v_q____ (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))) (= (tptp.c_Polynomial_Opoly tptp.v_q____ V_z tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oinverse__class_Oinverse _let_1 tptp.tc_Complex_Ocomplex) tptp.v_q____ tptp.tc_Complex_Ocomplex) V_z tptp.tc_Complex_Ocomplex) _let_1 tptp.tc_Complex_Ocomplex)))) _let_39 (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1)))) (not (= tptp.v_a____ _let_18)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a))) (= V_y V_z))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_3 T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (not (= _let_19 _let_18)) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oone__class_Oone T_a) V_p T_a) V_p))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_m T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) _let_38 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_b_H T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_q T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_q T_a) (tptp.c_Power_Opower__class_Opower V_y V_q T_a) T_a)))) _let_37 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_d T_a) T_a))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1)) (= V_a _let_1)))) _let_36 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_2 T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_c T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_d T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_2 T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a))) _let_35 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oplus__class_Oplus V_a V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_e T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1)) (= V_x _let_1)))) _let_33 _let_34 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_Polynomial_Osmult V_b V_p T_a) T_a) (tptp.c_Polynomial_Osmult (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_p T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) _let_33 _let_32 _let_30 _let_24 (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Divides_Osemiring__div tptp.tc_nat) (tptp.class_Ring__and__Field_Odvd tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_HOL_Ozero tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__field tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Odivision__ring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__field tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Osemiring tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__field tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ofield tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Odvd tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal) (tptp.class_Power_Opower tptp.tc_RealDef_Oreal) (tptp.class_HOL_Ozero tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) _let_13 _let_12 _let_11 _let_10 (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) _let_9 (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__ring tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) _let_8 (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Complex_Ocomplex) _let_7 (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Complex_Ocomplex) _let_6 (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__field tptp.tc_Complex_Ocomplex) _let_5 _let_4 _let_3 (tptp.class_Ring__and__Field_Odvd tptp.tc_Complex_Ocomplex) _let_2 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) _let_1 (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semidom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__idom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Osemiring__0 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__zero (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Osemiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Divides_Osemiring__div (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ofield T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oidom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Odvd (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Divides_Oring__div (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ofield T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Int_Onumber__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Power_Opower (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_HOL_Ozero (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_HOL_Ozero T_1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 6.23/6.44  )
% 6.23/6.47  % SZS output end Proof for ALG401-1
% 6.23/6.48  % cvc5---1.0.5 exiting
% 6.23/6.48  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------